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DL MESO USER MANUAL - Scientific Computing Department

1. 4 al 3 PISAS Ko O NIN IN I ol jo SHI IN elOl mim al M TFT a ha re Speed vector Ci z Ci y Cia 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 36 CHAPTER 4 DL MESO _LBE BASIC DEFINITION Table 4 1 Boundary condition category value meaning 0 liquid 10 domain boundary 11 inside solid 12 on grid bounce back boundary 13 mid link bounce back boundary 100 199 constant speed composition and temperature boundary 200 299 constant speed Neumann composition and temperature boundary 300 399 constant speed and composition Neumann temperature boundary 400 499 constant speed and temperature Neumann composition boundary 500 599 constant pressure composition and temperature boundary 600 699 constant pressure Neumann composition and temperature boundary 700 799 constant pressure and composition Neumann temperature boundary 800 899 constant pressure and temperature Neumann composition boundary 4 2 Data structure 4 2 1 Storage of particle distribution functions For a system with a square lattice the total number of grid points lbsy nx x lbsy ny x lbsy nz where lbsy nx lbsy ny and lbsy nz are the numbers of grid points along the x y and z axes respectively The grid points are arranged in a serial order of 9000 9001 900 1bsy nz gt
2. lur 1 1 Car ii lt rotr U rig id SR de 11 64 00 Tij 2 To T Tmax 11 6 BOND INTERACTIONS BETWEEN PARTICLES 153 3 Marko Siggia Worm Like Chain WLC 37 2 kgT 1 1 y ag Tij Tij T ij lt Tmaz U riz lt We MA AE haa HST 11 65 oo Tij Tmax 4 Morse potential bond 44 U riz De 1 exp 8 rij ro 11 66 where Tij Ti T ro is an equilibrium bond length rmaz the maximum specified bond length or extension k is a spring force constant A the persistence length of a wormlike chain De the potential well depth and p the potential width The force on particle due to a bond potential is obtained from the general formula 3 1 o g a Ca Orij U tr rig 11 67 Tij with the force acting on particle j equal to the negative of this and the virial contribution from the stretching bond given by with only one contribution per bond 11 6 2 Bond angles DL_MESO_DPD includes three methods for modelling potentials and forces between three bonded particles due to the angle formed between them 0 x The potentials are given as follows 1 Harmonic K U ijk 5 Oije 00 11 69 2 Harmonic cosine U ijk 5 cos 65 COS bo 11 70 3 Cosine U Oijk A L cos m0j x 11 71 where A and are angle force constants m is the multiplicity the angle at minimum potential and 0y an equilibrium bond angle The angle across par
3. 0 r2 1 exp 28rij 1 28ra 1 Bra 11 0 2 4nr 2 Wi ij 2 ij ij rij x 152 CHAPTER 11 DL MESO DPD FEATURES Even though the forces on frozen particles are ignored during integration these do contribute to the system potential energy virial and stress tensor terms and should therefore be evaluated The self energy correction term is constant for a given system for all time steps and is equal to Ta Us 3 oe 11 61 An i while the system charge correction is 2 cc T Ui aay 20 l 11 62 No additional forces are required for these terms In DL_MESO_DPD the module ewald_module contains the most important routines for calculating electrostatic interactions using the algorithm described above The real space short range component is calculated in routine ewald_real_slater using a link cell algorithm with a cutoff radius of re a larger boundary halo than for standard pairwise interactions is therefore required The reciprocal space long range component is calculated using the scheme described by 58 parallelized by distribution over atomic sites which requires global summations but is more efficient in terms of memory usage than distribution of k vectors The routine ewald reciprocal also adds the self interaction and charged system corrections which are calculated using the routine elecgen in config module The routine ewald_frozen_slater calculates the corrections to forces potential energy virial
4. The number of additional particles created during import of particle forces is greater than the current processor can accommodate Action This error message suggests non constant particle densities across the system and poor load balancing The user may wish to use the densvar directive in the CONTROL file to increase the value of maxdim and thus accommodate larger numbers of particles Message 72 import coordinate buffers exceeded for lees edwards shear The number of additional particles created during import of particle forces with Lees Edwards shearing is greater than the current processor can accommodate Action This error message suggests non constant particle densities across the system and poor load balancing The user may wish to use the densvar directive in the CONTROL file to increase the value of maxdim and thus accommodate larger numbers of particles Message 81 export coordinate buffers exceeded The number of additional particles created during export of particles into boundary halos is greater than the current processor can accommodate Action This error message suggests non constant particle densities across the system and poor load balancing The user may wish to use the densvar directive in the CONTROL file to increase the value of maxdim and thus accommodate larger numbers of particles 236 APPENDIX C DL MESO _DPD ERROR MESSAGES Message 82 export coordinate buffers exceeded for lees edwards shear The numb
5. e Comments The serial version of this function returns 1 timchk e Header records SUBROUTINE timchk ktim time e Function Determines the time elapsed since the start of the calculation run and if ktim gt 0 prints the time to the OUTPUT file e Dependencies None e Arguments ktim input integer time output real KIND dp e Comments The serial version of DL_MESO_DPD uses the generic SYSTEM_CLOCK call while the parallel version uses MPI_wtime 13 2 4 error_module This module is used to print error messages and shut down DL_MESO_DPD in a controlled manner It requires the modules constants and comms_module to be loaded beforehand 178 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE error e Header records SUBROUTINE error idnode iode value e Function Prints user friendly error message in OUTPUT file and closes down DL_MESO_DPD e Dependencies abortcomms e Arguments idnode input integer iode input integer value input integer e Comments The error code iode closes down DL _MESO_DPD when positive negative values can be used to print warning messages for non fatal problems 13 2 5 parse_utils getword e Header records CHARACTER LEN mxword FUNCTION getword txt n e Function Obtains the nth word from a line of text txt separated by spaces or commas e Dependencies None e Arguments txt input character LEN n input integer getword output character LEN mxword parseint e
6. i eia a fi T7 s Tf M s l fSiteFluidIncomCollisionMRTSegregation e Header records int fSiteFluidIncomCollisionMRTSegregation double startpos double sitespeed double bodyforce double phaseindex e Function Calculates collisions and phase segregation for the Lishchuk algorithm at a grid point using Multiple Relaxation Time MRT models for incompressible fluids e Dependencies fGetAllMassSite fGetTotMassSite fReciprocal fGetMomentEquilibriumFIncom fGetMRTCollide e Arguments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer phaseindex input double pointer e Comments Collisions are carried out on a single achromatic fluid using multiple relaxation time MRT schemes 33 8 fluid segregation takes place using the D Ortona algorithm 9 p pop A fi a gt BP z i Nab P bla P fSiteFluidCollisionMRT Guo e Header records int fSiteFluidCollisionMRTGuo double startpos double sitespeed double bodyforce e Function Calculates collisions at a grid point using Multiple Relaxation Time MRT models coupled with Guo like forcing terms for compressible fluids e Dependencies fGetOneMassSite fGetMomentEquilibriumF fGetMomentForce fGetMRTCollide 108 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Arguments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer e Comments Collisions for eac
7. 11 12 13 14 15 Hans C Andersen Molecular dynamics simulations at constant pressure and or temperature Journal of Chemical Physics 72 4 2384 2393 1980 H J C Berendsen J P M Postma W F van Gunsteren A DiNola and J R Haak Molecular dynamics with coupling to an external bath Journal of Chemical Physics 81 8 3684 3690 1984 Gerhard Besold Ilpo Vattulainen Mikko Karttunen and James M Polson Towards better integrators for dissipative particle dynamics simulations Physical Review E 62 6 R7611 R7614 December 2000 P L Bhatnagar E R Gross and M Krook A model for collision processes in gases I Small amplitude processes in charged and neutral one component systems Physical Review 94 3 511 525 May 1954 A Chatterjee Modification to Lees Edwards periodic boundary condition for dissipative particle dynamics simulation with high dissipation rates Molecular Simulation 33 15 1233 1236 2007 Shiyi Chen and Gary D Doolen Lattice Boltzmann method for fluid flows Annual Review of Fluid Mechanics 30 1 329 364 1998 Paul J Dellar Bulk and shear viscosities in lattice Boltzmann equations Physical Review E 64 3 031203 August 2001 Dominique d Humieres Irina Ginzburg Manfred Krafczyk Pierre Lallemand and Li Shi Luo Multiple relaxation time lattice Boltzmann models in three dimensions Philosophical Transactions of the Royal Society of London Series A Mathematical Physic
8. 22 23 24 25 26 27 28 29 30 31 32 33 34 BIBLIOGRAPHY Robert D Groot and Patrick B Warren Dissipative particle dynamics Bridging the gap between atomistic and mesoscopic simulation Journal of Chemical Physics 107 11 4423 4435 1997 Andrew J Gunstensen Daniel H Rothman St phane Zaleski and Gianluigi Zanetti Lattice Boltzmann model of immiscible fluids Physical Review A 43 8 4320 4327 April 1991 Zhaoli Guo Baochang Shi and Chuguang Zheng A coupled lattice BGK model for the Boussinesq equations International Journal for Numerical Methods in Fluids 39 4 325 342 2002 Zhaoli Guo Chuguang Zheng and Baochang Shi Discrete lattice effects on the forcing term in the lattice Boltzmann method Physical Review E Statistical Nonlinear and Soft Matter Physics 65 4 046308 April 2002 I Halliday A P Hollis and C M Care Lattice Boltzmann algorithm for continuum multicomponent flow Physical Review E Statistical Nonlinear and Soft Matter Physics 76 2 026708 2007 I Halliday R Law C M Care and A Hollis Improved simulation of drop dynamics in a shear flow at low Reynolds and capillary number Physical Review E Statistical Nonlinear and Soft Matter Physics 73 5 056708 2006 Cecil Hastings Approximations for digital computers Princeton University Press Princeton NJ 1955 Xiaoyi He Shiyi Chen and Gary D Doolen A novel thermal model for
9. 734 PCBCETR 743 PCBCETL 744 PCBCEDL 745 PCBCEDR 746 PCBCETF 747 PCBCELF 748 PCBCEDF 749 PCBCERF 750 PCBCETB 751 PCBCELB 752 PCBCEDB 753 PCBCERB 754 PBBPST 821 PBBPSD 822 PBBPSL 823 PBBPSR 824 PBBPSF 825 PBBPSB 826 PBBCCTRB 827 PBBCCTLB 828 PBBCCDLB 829 PBBCCDRB 830 PBBCCTRF 831 PBBCCTLF 832 PBBCCDLF 833 PBBCCDRF 834 PBBCETR 843 PBBCETL 844 PBBCEDL 845 PBBCEDR 846 PBBCETF 847 PBBCELF 848 PBBCEDF 849 PBBCERF 850 PBBCETB 851 PBBCELB 852 PBBCEDB 853 PPBCERB 854 4 2 3 Storage of running information The Lattice Boltzmann component of DL MESO defines three structures to store the system information The parameters in these structures are listed in Tables 4 4 4 5 4 6 and 4 7 Table 4 4 System information parameter meaning lbsy nd space dimension lbsy nq number of discrete speeds lbsy nf number of fluids lbsy nc number of solutes lbsy nt number of temperature scalars 0 or 1 lbsy pf phase field order parameter lbsy nx number of grid points in x direction lbsy ny number of grid points in y direction lbsy nz number of grid points in z direction lbsy nz 1 when 1bsy nd 2 4 3 The Parameters and Their Functions Table 4 8 lists all the parameters defined in DL_MESO_LBE The whole range parameters are named with the prefix 1b Because DL_MESO is an ongoing project and new parameters might be added to the package in the future
10. a ete os Ore Fig x Fal ar F nF jr 005 Sei Fig Fyre 005 Sen 215 mirada Se 945 Calla de 50 11 88 a ee Edd are Pin X Peal Wh IFjnTjml Oa Sex Fa etl 025 den 215 FerTet a Sek ej Fin Fra Sek Fer 11 89 It can be shown both algebraically and thermodynamically that the dihedral makes no contribution to the virial 59 Improper dihedrals which limit the geometry of molecules can be applied using the same procedure as standard dihedrals and no distinction is made between them in DL_MESO_DPD 11 7 Surface interactions The default boundaries for a simulation box are periodic i e particles leaving the system are replaced at the opposite face with the same velocity Certain systems may require alternative boundary conditions and DL_MESO_DPD can include these at the system boundaries The directive surface in the CONTROL file can be used to specify the type of surface interaction hard frozen or shear and which surface s are to be included srfx srfy srfz each set to 0 for periodic boundaries and 1 or greater for other types Parameters required for wall particle interactions can be specified using the same directive in the FIELD file The module surface module includes routines to set up and apply boundary conditions at those surfaces Care should be taken to ensure that the initial configuration does not include bonds crossing any boundary
11. bic particles 14 7 VesicleFormation This simulation example consists of 37 440 unbonded water particles and 1008 molecules each consisting of one hydrophilic head particle and three hydrophobic tail particles bonded together with stiff harmonic bonds of equilibrium length 1 0 between them 71 The molecules represent amphiphiles and during the course of the simulation self assemble into a vesicle and encapsulate a number of water particles Figure 14 7 shows the self assembled vesicle both in three dimensions and in a cross section to show the encapsulated water An AVI video file of the simulation can be found in the Example Simulations page of the DL MESO website a Vesicle water omitted for clarity b Cross section orthogonal to z axis Figure 14 7 Visualizations of DPD VesicleFormation test case at t 50 000 red for hydrophile green for hydrophobe blue for water 14 8 POISEUILLEFLOW 219 14 8 PoiseuilleFlow This simulation example consists of 3000 unbonded particles in a box of 10 x 10 x 10 DPD length units with walls of frozen particles added to the surfaces orthogonal to the x axis of thickness 1 DPD length unit and particle density of 3 A constant body force in the direction of the y axis is added to each non frozen particle which in combination with the frozen particle walls approximating no slip boundaries gives Poiseuille flow of the DPD fluid Figure 14 8 gives a snapshot of the system at the final time step as
12. e Header records SUBROUTINE importdensity_shear nlimit mdir begin final shove shovel shove2 sidel side2 e Function Imports local densities from boundary halos for Lees Edwards shearing e Dependencies error msg_receive_unblocked msg_receive_sca_blocked msg_send_blocked msg_send_sca_blocked msg_wait 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 195 e Arguments nlimit input output integer mdir input integer begin input real KIND dp final input real KIND dp shove input real KIND dp shovel input real KIND dp shove2 input real KIND dp sidel input real KIND dp side2 input real KIND dp e Comments Only exists in parallel version of DL_MESO_DPD This routine requires information for the two dimensions along the surface of the shearing boundary the variables shove1 and shove2 represent the displacement due to shear while side1 and side2 are the domain dimensions export e Header records SUBROUTINE export nlimit mdir mp begin final shove skip Parallel version SUBROUTINE export nlimit mdir begin final shove Serial version e Function Exports particle data positions velocity to neighbouring domain as boundary halo e Dependencies error global_sca_and_all Parallel version only msg_receive_unblocked Parallel version only msg_receive_sca_blocked Parallel version only msg_send_blocked Parallel version only msg_send_sca_blocked Parallel version only msg_wait Parallel v
13. integer integer output double precision 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS 69 e Comments Mass density is calculated according to the definition p gt fi In the first case startpos is the start point for the summation of particle distribution functions and must be assigned correctly The second case carries out the same calculation for the fpos th fluid and tpos th grid point while the third carries it out for the fpos th fluid at the grid point indicated by the Cartesian coordinate xpos ypos zpos The latter two are more readable to the user but a bit slower to carry out fGet AllMassSite e Header records three cases int fGetAllMassSite double rho double startpos int fGetAllMassSite int fpos long tpos int fGetAllMassSite int fpos int xpos int ypos int zpos e Function Calculates the individual mass densities of all fluids at a grid point e Dependencies None e Arguments startpos input double pointer tpos input long integer xpos input integer ypos input integer zpos input integer rho output double precision array e Comments Mass density is calculated according to the definition p gt fi In the first case startpos is the start point for the summation of particle distribution functions and must be assigned correctly The second case carries out the same calculation for the tpos th grid point while the third carries it out at the grid point indicated by the Cartesian coordinate xp
14. 2 for z component sets velocity at top boundary for all fluids sets velocity at bottom boundary for all fluids sets velocity at left boundary for all fluids sets velocity at right boundary for all fluids sets velocity at front boundary for all fluids sets velocity at back boundary for all fluids sets initial density for fluid f throughout system f between 0 and 1bsy nf 1 sets constant density for incompressible fluid f sets density for fluid f at top boundary sets density for fluid f at bottom boundary sets density for fluid f at left boundary sets density for fluid f at right boundary sets density for fluid f at front boundary sets density for fluid f at back boundary sets relaxation time vy for fluid f sets relaxation frequency Ga for fluid f 2Either the keyword or the number can be used to specify the types 3If set to an unrecognised word or to 0 interactions will be switched off 6 1 INPUT FILES bulk_relaxation_fluid_f bulk_relax_freq_fluid_f solute_ini_s solute_top_s solute_bot_s solute_lef_s solute_rig_s solute_fro_s solute_bac_s relax_solute_s relax_freq_solute_s temperature_ini temperature_top temperature_bottom temperature_left temperature_right temperature_front temperature_back heating_rate_sys heating_rate_top heating_rate_bottom heating_rate_left heating_rate_right heating_rate_front heating rate back relax thermal relax_freq_thermal body_force_n body _force_x_f body
15. BGK model with the Guo forcing term for compressible fluids e Dependencies fGetAllMassSite fGetAllMassSite fReciprocal fGetEquilibriumF e Arguments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer phaseindex input double pointer e Comments Collisions are carried out on a single achromatic fluid using the BGK single relaxation time 4 with the Guo forcing term 19 also acting on the achromatic fluid fluid segregation takes place using the D Ortona algorithm 9 pa ae ae ab PEL fi z t fi Zt 58 Wi z i Nab P ba P fSiteFluidIncomCollisionmBGKGuo e Header records int fSiteFluidIncomCollisionBGKGuo double startpos double sitespeed double bodyforce e Function Calculates collisions at a grid point using the Bhatnagar Grook Krook BGK model with the Guo forcing term for incompressible fluids e Dependencies fGetOneMassSite fReciprocal fGetEquilibriumFIncom 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS 105 e Arguments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer e Comments Collisions for each fluid species are carried out using the BGK single relaxation time 4 with the following Guo forcing term 19 acting on each fluid 1 eia a fi gt f 1 wi 3 eia Va 9 0 Fa fSiteFluidIncomCollisionBGKGuoSegregation e Header records int fSiteFluidIncomCollisionBGKGuoSegreg
16. Premnath and John Abraham Three dimensional multi relaxation time MRT lattice Boltzmann models for multiphase flow Journal of Computational Physics 224 2 539 559 2007 P Prinsen P B Warren and M A J Michels Mesoscale simulations of surfactant dissolution and mesophase formation Physical Review Letters 89 14 148302 September 2002 M Revenga I Zuniga and P Espanol Boundary conditions in dissipative particle dynamics Com puter Physics Communications 121 122 309 311 1999 Proceedings of the Europhysics Conference on Computational Physics CCP 1998 A G Schlijper P J Hoogerbrugge and C W Manke Computer simulation of dilute polymer solutions with the dissipative particle dynamics method Journal of Rheology 39 3 567 579 1995 Xiaowen Shan Analysis and reduction of the spurious current in a class of multiphase lattice Boltzmann models Physical Review E 73 4 047701 2006 250 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 BIBLIOGRAPHY Xiaowen Shan Pressure tensor calculation in a class of nonideal gas lattice Boltzmann models Physical Review E 77 6 066702 June 2008 Xiaowen Shan and Hudong Chen Lattice Boltzmann model for simulating flows with multiple phases and components Physical Review E Statistical Physics Plasmas Fluids and related interdisciplinary topics 47 3 1815 1819 March 1993 Xiao
17. Zpos input long integer fGetFracSite output double precision fGetOneSpeedSite e Header records three cases int fGetOneSpeedSite double speed double startpos int fGetOneSpeedSite double speed int fpos long tpos int fGetOneSpeedSite double speed int fpos int xpos int ypos int zpos e Function Calculates the macroscopic speed of compressible fluid fpos at the grid point e Dependencies fReciprocal 72 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Arguments startpos input double pointer fpos input integer tpos input long integer xpos input integer ypos input integer Zpos input integer speed output double precision array e Comments The calculation is based on vg an is The second and third cases are slightly slower than the first but more readable fGetOneSpeedIncomSite e Header records three cases int fGetOneSpeedIncomSite double speed double startpos double rho0 int fGetOneSpeedIncomSite double speed int fpos long tpos int fGetOneSpeedIncomSite double speed int fpos int xpos int ypos int zpos e Function Calculates the macroscopic speed of incompressible fluid fpos at the grid point e Dependencies fReciprocal e Arguments startpos input double pointer rho0 input double precision fpos input integer tpos input long integer xpos input integer ypos input integer Zpos input integer speed output double precision array e Comments The calculation is based on
18. and its ability to model complex system geometries and or fluid interactions with comparatively little additional computational cost 3 2 Basic Definitions Triangular and rectangular lattices are two of the most popular grid forms used in Lattice Boltzmann simulations Triangular lattices have sixth order rotation isotropy and have been widely applied in two dimensional systems 23 24 CHAPTER 3 THE LATTICE BOLTZMANN EQUATION BASIC THEORY e g the D2Q7 and D2Q13 models Rectangular lattices have only fourth order rotation isotropy but can more easily handle the simulation of three dimensional systems with complex boundary conditions The local equilibria for D2Q9 and D3Q27 lattice models can be derived a priori from the Maxwell equilibrium distribution D3Q15 and D3Q19 models appear to be more popular than D3Q27 because the latter is much more expensive in terms of computing cost It is required that the equilibrium state should be able to reproduce elementary macroscopic fluid variables p ih 3 1 q Pa y Si ia 3 2 i 0 where p is the density fi the th particle distribution function the ith lattice link vector and ua the macroscopic velocity along the a axis In the Lattice Boltzmann method the lattice link vectors do not represent the thermal velocities of a particle and therefore EASY nea 3 3 Equation 3 3 implies that the temperature cannot ordinarily be derived from the lattice particle distrib
19. nlimit input output integer mdir input integer begin input real KIND dp final input real KIND dp shove input real KIND dp shovel input real KIND dp shove2 input real KIND dp sidel input real KIND dp side2 input real KIND dp e Comments Only exists in parallel version of DL_MESO_DPD Setting first to true imports both sets of forces constant and variable while setting to false imports just the variable forces This routine is suitable for thermostats where two types of forces need to be kept separate and or recalculated i e the DPD thermostat with DPD Velocity Verlet integration DPD VV and Stoyanov Groot thermostat This rou tine requires information for the two dimensions along the surface of the shearing boundary the variables 194 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE shovel and shove2 represent the displacement due to shear while side1 and side2 are the domain dimensions importdensity e Header records SUBROUTINE importdensity nlimit mdir mp begin final e Function Imports local densities from boundary halo e Dependencies error global_sca_and_all msg_receive_unblocked msg_receive_sca_blocked msg_send_blocked msg_send_sca_blocked msg_wait e Arguments nlimit input output integer mdir input integer mp input integer begin input real KIND dp final input real KIND dp shove input real KIND dp e Comments Only exists in parallel version of DL_MESO_DPD importdensity_shear
20. that will be non periodic DL_MESO_DPD will ensure this is the case for simulations starting from scratch but cannot check for bonds crossing non periodic boundaries in CONFIG files 156 CHAPTER 11 DL MESO DPD FEATURES 11 7 1 Hard reflecting boundaries hard This boundary condition is applied by using a combination of specular free slip reflection at the system boundaries and a soft short range wall repulsion to reduce density oscillations 50 The reflection is achieved by moving any particle leaving the system at a particular boundary back into it and inverting the velocity component normal to the wall but maintaining the tangential momentum which is achieved with the routine surfacebounce The soft short range wall repulsion is given by 2 z Uwatt Z 5 Awall a e 1 A z lt Zc 11 90 c where Awall a is the repulsive force magnitude with species a z is the distance between the particle and the wall and z the surface repulsion range The repulsion is applied at the same time as all pairwise forces using the routine hardreflect Since the walls are assumed to be non porous no interactions across them are included and thus boundary halos adjacent to walls are not used The repulsive force magnitudes between the boundary and each species are specified in the FIELD file using the directive surface while the same directive in the CONTROL file is used to determine the surface repulsion cutoff and which boundary surfaces sho
21. twister generator mtrnd i e Ci x V12 u 0 5 which produces statistically similar results 10 and is computationally more efficient than using the Gaus sian random number subroutine gaussmp although this or the duni random number generator may be substituted if required For systems involving Lees Edwards boundary conditions thermostats are not applied between particle pairs that cross shearing boundaries 5 dragforces_dpdvv Header records SUBROUTINE dragforces_dpdvv nlimit Function Recalculates dissipative forces between particles within cut off radius Dependencies None Arguments nlimit input integer idnode input integer Comments Only required for DPD Velocity Verlet DPD VV integration shearing boundaries are omitted 5 plcfor_ e Header records SUBROUTINE plcfor_ Function Particle pairs that cross Lees Edwards Sets up parallel link cells structure and calculates forces including those involving particles in boundary halo Dependencies exportdata parlnk local_density 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 211 importdensitydata exportdensitydata forces_ importdata importdata_dpdvv1 importdata_dpdvv2 importdata_stoyanov freeze_beads freeze_beads e Header records SUBROUTINE freeze_beads e Function Quenches forces and velocities of frozen particles by resetting them to zero e Dependencies None 13 2 14 integrate module This m
22. 11 IbpSUB fWeakMemory e Header records inline void fWeakMemory e Function Terminates calculation if system has insufficient memory 96 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Dependencies None e Comments If called will print error message error cannot allocate more memory fMemory Allocation e Header records int fMemoryAllocation e Function Allocates memory for lattice Boltzmann calculations e Dependencies fWeakMemory e Comments If memory allocation is unsuccessful will print error message and stop calculation fFreeMemory e Header records int fFreeMemory e Function Frees allocated memory e Dependencies None fSetSerialDomain e Header records int fSetSerialDomain e Function Sets domain parameters for serial running e Dependencies None e Comments Default routine sets domain boundary width 1bdm bwid to zero fSetSerialDomainBuffer e Header records int SetSerialDomainBuffer e Function Sets domain parameters for serial running including additional boundary points e Dependencies None 7 2 DL MESO _LBE SUBROUTINES AND FUNCTIONS 97 e Comments Similar to fSetSerialDomain but does not modify the domain boundary width from its user specified value fStartDLMESO e Header records int fStartDLMESO O e Function Announces start of DL_MESO_LBE run e Dependencies None e Comments If preferred the call to this
23. 19 146 CHAPTER 11 DL MESO DPD FEATURES where Ny is the number of degrees of freedom for a three dimensional box containing N moving i e non frozen particles Ny 3 N 1 yp and op 4 3mWykgT are respectively the drag and random coefficients for the piston and Cp a is a Gaussian random number for dimension a this is set to the same value for all three dimensions if operating isotropically When both yp and a are set to zero the Langevin barostat reduces to the extended system method The subsequent simulation cell size La can be determined by La Psala ug aLa 11 20 g with the barostat mass W chosen to be equal to N bel where Tp is the characteristic barostat time and should be set equal to between r and oa The velocities and positions of the particles are calculated by integration of slightly modified differential equa tions dvi a Esa 1 a aVia Ky Vio QU 11 21 dE Ein E man d 1 0 A Via Ug ali a 11 22 where the force on particle 7 E includes any thermostatting forces the time integral of these forces can be determined for all thermostat types The implementation of this barostat is carried out using the Velocity Verlet scheme to integrate the equations of motion for both the particles and the barostat The first Velocity Verlet stage integrates the forces on the particles At Fj t Vi a t At Vio t a E Atug aUi a 11 23 Mii which is followed by a similar integration for the ba
24. 239 Bibliography 247 Acknowledgements DL_MESO was developed under the auspices of the Engineering and Physical Sciences Research Council EP SRC for the EPSRC s Collaborative Computational Project for the Computer Simulation of Condensed Phases CCP5 The members of the CCP5 DL_MESO consortium were David M Heyes University of Surrey Chris M Care Sheffield Hallam University Peter V Coveney University College London David Emerson STFC Daresbury Laboratory Rob English North East Wales Institute Andrea Ferrante Unilever Port Sunlight lan Halliday Sheffield Hallam University John Harding University of Sheffield Sebastian Reich Imperial College Bill Smith STFC Daresbury Laboratory Patrick B Warren Unilever Port Sunlight Julia Yeomans Oxford University Many other people have given advice and encouragement in the development of DL_MESO We gratefully acknowledge the support of the following people Maurice Leslie Richard Wain Alexandre Dupuis Jonathan Chin Michael Dupin Weiming Liu and John Purton Particular thanks go to Rongshan Qin at Imperial College as the original author of the Lattice Boltzmann Equation source code DL_MESO_LBE and the DL_MESO graphical user interface and Richard Anderson at STFC Daresbury Laboratory and Ard van Bergen at Novidec for their contributions to the Dissipative Particle Dynamics source code DL_MESO_DPD Chapter 1 DL MESO General Information 1 1 Description DL_MESO is
25. Closes Message Passing Interface MPI e Dependencies None 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS fGlobalValue e Header records six cases int fGlobalValue double vqua int nnum int fGlobalValue int vqua int nnum int vtot int fGlobalValue int vqua int nnum int fGlobalValue long int vqua int nnum int fGlobalValue long int vqua int nnum long int vtot e Function Sums values from all processes and distributes the sum fGlobalProduct e Header records two cases int fGlobalProduct double vqua int nnum int fGlobalProduct int vqua int nnum e Function Multiplies together values from all processors and distributes the product fArrangeProcessors e Header records int fArrangeProcessors e Function Arrange processors according to system dimensions e Comments Calculations are based on lbdm xdim 1bdm ydim J1bdm zdim lbsy nx lbsy ny lbsy nz lbdm xdim x 1bdm ydim x 1bdm zdim 1bdm size fDefineDomain e Header records int fDefineDomain e Function Determines domain parameters for system calculation fDefineMessage e Header records int fDefineMessage e Function 115 Defines vector messages for system distribution functions boundary properties and interaction forces 116 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE fDefineNeighbours e Header records int fDefineNeighbours e Function Calculates the names of neighbouring processes and the
26. DPD simulations that are bonded together i e molecules A random flight generation system is used to generate the coordinates of bonded beads which can form branched molecule chains a constant distance apart within a cube of a size specified by the user which will be used by DL_MESO_DPD to insert the molecule into the system This utility can be compiled to produce the executable molecule exe with the command e c o molecule exe molecule generate cpp if c is the command for the available C compiler This utility can be run from the command line or via the GUI in Set DPD Molecules which runs the utility in a new command line shell window When running the utility if a FIELD file exists in the same directory as the executable the number of species and their names will be read from it otherwise the user will be asked to enter this information and this will be 228 APPENDIX B DL_MESO UTILITIES written to a new FIELD file The user will then be asked for the number of molecules required the numbers of bond angles and dihedrals and their types and parameters For each molecule the user is asked for its name the number to be included in the system and whether or not isomers of the molecule can be included The side length for the cube inside which the molecule will fit is then required followed by the bond length the number of molecule chains and the number of particles for each chain If the chain in question is not the fir
27. Figure 14 5 Visualizations of DPD Polyelectrolyte test case red for polyelectrolyte polymer green for salt cations cyan for anions orange for counterions water omitted for clarity 14 6 AmphiphileMesophases This example consists of four separate simulations each with 12 000 particles consisting of dimers molecules consisting of two particles one hydrophilic and the other hydrophobic with harmonic bonds of equilibrium length 0 5 between them and unbonded monomers 31 Defining the composition as the ratio of DPD particles within dimers to the total number of particles in the system the interaction data for simulations with 218 CHAPTER 14 DL MESO DPD EXAMPLES dimer compositions of 30 55 75 and 90 are provided with filenames FIELD 30 FIELD 55 FIELD 75 and FIELD 90 respectively Each of these files should be renamed to FIELD to run the simulation while the CONTROL defining the simulation properties can be used for all four simulations These systems provide four points on a phase diagram corresponding to isotropic dimer hexagonal lamellar and isotropic monomer phases respectively The final configurations obtained for each phase can be seen in Figure 14 6 shown as isosurfaces of the hydrophobic particles to highlight the distinctions between the phases A a 0 30 b 0 55 c 4 0 75 d 0 90 Figure 14 6 Visualizations of DPD AmphiphileMesophases test case at final time step isosurfaces of hydropho
28. KIND dp z component of piston velocity upz real KIND dp x component of piston velocity at previous timestep upx1 real KIND dp y component of piston velocity at previous timestep upy1 real KIND dp z component of piston velocity at previous timestep upzi real KIND dp piston mass Wg psmass real KIND dp x component of piston force fpx real KIND dp y component of piston force fpy real KIND dp z component of piston force fpz real KIND dp 2ykpT 1This incorporates the time step for Velocity Verlet integration and is thus equal to 4 HB 2The pair list arrays are not allocated for the DPD thermostat MD VV or DPD VV A 10 2 THE PARAMETERS AND THEIR FUNCTIONS Table 10 4 DL_ MESO_DPD Parameters continued 137 function parameter data type notation instantaneous virial ivrl real KIND dp A 3 Langevin random force parameter op sigmalang real KIND dp electrostatic algorithm type etype integer electrostatic coupling parameter T gammaelec real KIND dp total system charge gt gt qi qchg real KIND dp Ewald real space convergence parameter a alphaew real KIND dp reciprocal of real space convergence parameter ralphaew real KIND dp maximum reciprocal vector size in x dimension k7 9 kmax1 integer gt 1 maximum reciprocal vector size in y dimension k3 kmax2 integer gt 1 maximum reciprocal vector size in z dimension k3 o kmax3 integer 21 Ewald self interaction correcti
29. PCTCCTLF PCTCETR PCTCEDR PCTCEDF PCTCELB PBTPST PBTPSR PBTCCTRB PBTCCDRB PBTCCDLF 122 125 128 131 134 145 148 151 154 223 226 229 232 243 246 249 252 321 324 327 330 333 344 347 350 353 422 425 428 431 434 445 448 451 454 523 526 529 532 543 546 549 552 621 624 627 630 633 VCTPSL VCTPSB VCTCCDLB VCTCCTLF VCTCETR VCTCEDR VCTCEDF VCTCELB VBBPST VBBPSR VBBCCTRB VBBCCDRB VBBCCDLF VBBCETL VBBCETF VBBCERF VBBCEDB VCBPSD VCBPSF VCBCCTLB VCBCCTRE VCBCCDRF VCBCEDL VCBCELF VCBCETB VCBCERB VBTPSL VBTPSB VBTCCDLB VBTCCTLF VBTCETR VBTCEDR VBTCEDF VBTCELB PCTPST PCTPSR PCTCCTRB PCTCCDRB PCTCCDLF PCTCETL PCTCETF PCTCERF PCTCEDB PBTPSD PBTPSF PBTCCTLB PBTCCTRF PBTCCDRF 123 126 129 132 143 146 149 152 221 224 227 230 233 244 247 250 253 322 325 328 331 334 345 348 351 304 423 426 429 432 443 446 449 452 521 524 527 530 533 544 547 550 553 622 625 628 631 634 4 3 THE PARAMETERS AND THEIR FUNCTIONS 39 Table 4 3 Notation of boundary condition continued PBTCETR 643 PBTCETL 644 PBTCEDL 645 PBTCEDR 646 PBTCETF 647 PBTCELF 648 PBTCEDF 649 PBTCERF 650 PBTCETB 651 PBTCELB 652 PBTCEDB 653 PBTCERB 654 PCBPST 721 PCBPSD 722 PCBPSL 723 PCBPSR 724 PCBPSF 725 PCBPSB 726 PCBCCTRB 727 PCBCCTLB 728 PCBCCDLB 729 PCBCCDRB 730 PCBCCTRF 731 PCBCCTLF 732 PCBCCDLF 733 PCBCCDRF
30. T 1 1 1 1 1 1 bulk 52 1 54 1 84 1 84 T Tp TF Tf Tf 514 V 1 2 Ar At 2 Tf bulk 9 33 1 I 2 2 1 2 2 1 11 4 4 1 1 11 4 4 1 2 11 4 4 4 8 1 36 Ci z hiena Wi 1 1 2 2 1 1 1 Weight factor Ciy 1 1 1 1 2 2 1 Cia 1 1 1 1 1 1 3 10 12 4 9 13 18 Speed vector 12 13 14 15 16 17 18 4 1 LATTICE MODELS D3Q19 11 11 4 1 1 1 11 4 1 1 2 ooo oo ooo Oo 1 30 12 0 0 0 0 0 0 0 34 r LTs jne TF 9 bulk 5 CHAPTER 4 DL_MESO_LBE BASIC DEFINITION p p 19 e amp 4 llp po is tiy J eea wept dy Pda z de qa 3Jx dy jy a 3ty iz de qsa ie 3Jz A La 2j j2 32 TT PO ca 2 2 p am po 252 jy Ja Psw tte med Wax 2 2 apap po is 92 Pry daly 7 Po Pye Jylz ed Po pe dada mo n ma 0 m 0 0 38 07 Fo Vy Fy v2F 11 vs Fs vyFy 004 E Fx 2F Fy 3Fy Fz S 2 2u Fy Uy Fy v F 207Fy 0yFy vzF 2u Ey UzFs vyFy v F Uy Fy vy Fo Uy EF uzFy v2 Fy UL Fs 0 0 0 T 1 1 1 1 1 1 bulk 52 1 54 1 54 1 54 77 4 Tf 1S4 Tp Tp Tp 16 516 516 a aay 35 4 1 LATTICE MODELS D3Q27 Weight factor
31. The HISTORY files can be used with the utilities traject and trajectselected in the DPD utility directory to produce plottable VMD files with sets of bonded particles represented as residues The utility local in the same directory can calculate localized properties e g temperature composition from the same files and produces VTK files with these properties as cell data Appendix B gives instructions for their use Statistical data file CORREL If the parameter 1corr is set to true DL_MESO_DPD will generate an ANSI text file containing statistical data every iscorr time steps which can later be imported into a spreadsheet or used by graph plotting software The formatting of the data varies depending on which kinds of interactions bonds angles dihedrals electrostatics were used and whether a barostat was applied based on the overall format in a single line t Etot Ebpot tot Epot elec Enot bond Epot angle Ebpot dihed P xx Cay Ozz Oye Coy Cyr Sze Ozy Ozz V T bond Toond max Tbond min angle ddihed where t is the time E energy tot denoting total pot potential P pressure o stress tensor V volume T temperature Tpona the mean bond length rpond max aNd Trond min the maximum and minimum bond lengths angle the mean bond angle in degrees and Odinea the mean bond dihedral in degrees Any property which does not vary or is not measured during the simulation e g volume for NVT ensembles is omitted from each line of
32. The Stoyanov Groot thermostat is used for this system to control both the fluid viscosity and system temperature Figure 14 9 gives the time averaged emergent velocity profile yielding a shear rate of 0 1941 in DPD units close to the applied shear rate of 0 2 against a measured stress component oyy 0 2063 220 CHAPTER 14 DL MESO DPD EXAMPLES Time averaged horizontal velocity lt v gt IE 1 l l 1 L 1 l 1 J 0 2 4 6 8 10 Vertical position y Figure 14 9 Plot of x component velocity from DPD ShearFlow test case red line denotes best fit for deter mining shear rate 14 10 VapourLiquid This simulation example consists of 1000 unbonded water particles initially distributed uniformly in a box of 5 x 5 x 22 DPD length units using the default many body DPD interactions with Aj 50 and By 25 to apply vapour liquid interactions and surface tension 68 12 Figure 14 10 shows the system at the final timestep after the water particles have coalesced into a single body surrounded by empty space Figure 14 10 Visualization of system at final time step from DPD VapourLiquid test case Appendix A Manual compiliation and running of DL_MESO A 1 DL MESO LBE DL_MESO_LBE has been written in C in a modular form and the main program codes slbe cpp for serial running plbe cpp for parallel running are designed to allow the user to change algorithms for collision mesophases etc by specifying them
33. _force_y_f body_force_z_f boussinesq_force_n boussinesq force_x_f boussinesq_force_y_f boussinesq_force_z_f boussinesq_boussinesq_high boussinesq_boussinesq_low interaction_n interaction_f _ fo segregation segregation_n segregation_f_fo Define space lbin spa 57 sets bulk relaxation time Tf buik for fluid f sets bulk relaxation frequncy TF but for fluid f sets initial concentration for solute s throughout system s between 0 and lbsy nc 1 sets concentration for solute s at top boundary sets concentration for solute s at bottom boundary sets concentration for solute s at left boundary sets concentration for solute s at right boundary sets concentration for solute s at front boundary sets concentration for solute s at back boundary sets relaxation time Ts for solute s sets relaxation frequency T7 for solute s sets initial temperature throughout system sets temperature at top boundary sets temperature at bottom boundary sets temperature at left boundary sets temperature at right boundary sets temperature at front boundary sets temperature at back boundary sets rate of change in temperature with time based on real life units through out system sets rate of change in temperature at top boundary sets rate of change in temperature at bottom boundary sets rate of change in temperature at left boundary sets rate of change in temperature at right boundary sets rate of change in temper
34. a general purpose mesoscopic simulation package developed at Daresbury Laboratory by Dr Michael Seaton under the auspices of the Engineering and Physical Sciences Research Council EPSRC for the EPSRC s Collaborative Computational Project for the Computer Simulation of Condensed Phases CCP5 The package is the property of the Science and Technology Facilities Council STFC DL_MESO is issued free under licence to academic institutions pursuing scientific research of a non commercial nature All recipients of the code must first agree to the terms and conditions of the licence and register with us to be kept aware of new developments and discovered bugs Commercial organisations interested in acquiring the package should approach the Scientific Computing Department STFC Daresbury Laboratory in the first instance Daresbury Laboratory is the sole centre for distribution of the package Under no account is it to be redistributed to third parties without consent of the owners DL_MESO contains two mesoscale simulation methods e Lattice Boltzmann Equation included with version 1 0 and later e Dissipative Particle Dynamics included with version 2 0 and later 1 2 Functionality The following is a list of the features that DL_MESO currently supports Users are reminded that we are interested in hearing what other features could be usefully incorporated We obviously have ideas of our own and CCP5 strongly influences developments but other in
35. ah eA a Pee a bee oa ea ed 120 8 5 2D Lid avity rasas sia a sori 54 Foe ee Sk we A ee ee a 120 8 6 2D RayleighBenardis aa tgs Sn ag eels oe ea AEB ee ee eo aed a aS 121 80 2D Dropolear tddi aes ee Bw Beak Savy Selah ee ete ae eA Rae Ee a 121 8 8 3D PhaseSeparation 4 2 2 face eee ele Ree Se ee ered a ee eee 122 8 9 SD Shear oid tet ds de A he Ae do ah oe A dl ab tot bot Lal SA ee ae 122 8 10 3DRayleighBenard sce in apta ea ke A A eee PE ee ORE eae ee 123 II Dissipative Particle Dynamics DPD 125 9 Dissipative Particle Dynamics Basic Theory 127 91 JTiitroductiony 2s 4 dus ie SOAS a bate Geek SA eee RE RE AB ee Se 4 127 9 2 Outline of Method s 13 4 a a ae Se eee bo eG we Bh dd A 127 9 3 Equation of state and dynamic properties ee 129 9 4 Derivation of Equilibrium 129 9 5 Summary of Dissipative Particle Dynamics o 0 0000000000000 130 10 DL_MESO_DPD Basic Definition 131 10 2 Data Structure ss wart sow a vay ee AAA A EE AA We whl Beat nee at 131 10 2 The Parameters and Their Functions 134 11 DL_MESO_DPD Features 141 11 1 Domain decomposition and linked list cell calculations 0 0 000200 141 11 2 Thermostats and integration algorithms 0000000000004 142 Td Barostatss 22 ELA A ee Pe BE E nee eh ht BS dk oc Ba 145 11 4 Particle particle interactions 147 11 5 Long ranged Electrostatic Coulombic Potentials 2 2 0 20 0 000000 0008 150 11 6 Bond inte
36. all the specified time steps after equilibration containing the following data for each cuboidal cell e the mean velocity for all unfrozen beads e the number of unfrozen beads e overall temperature e partial temperatures for each dimension i e for dimension a Ta gt M40 a e densities for each bead species e volume fractions for bead species starting from type 01 e volume fractions for molecule types starting from type 00 for all unbonded beads An additional file averages vtk is also produced with time averaged values for the velocities species densities overall and partial temperatures in each cuboidal cell The scalar properties including compositions may be considered to act across the entire volumes of the cells while the velocities are representative for the cell centres Appendix C DL MESO DPD Error Messages This appendix documents the error and warning messages currently available in the DPD code in DL_MESO DL_MESO_DPD and recommendations for users to try and overcome the errors Users may contact the authors of DL_MESO after attempting the recommended actions Message 1 cutoff radius value not set A valid cutoff radius r for all interactions cannot be found in the CONTROL file this is a compulsory parameter for DPD simulations Action Look in the CONTROL file and make sure the cutoff directive is included with a non zero value Message 2 temperature not set A valid system temperature kg
37. an ensemble of particles by a single distribution function This difference allows LBE to simulate both dilute fluids i e those in which the mean free path of component particles is much larger than the lattice spacing and condensed matter such as liquids The Lattice Boltzmann method uses fully discretized space time and velocity to describe the evolution of fluid Space is represented by a regularly distributed grid time flow is obtained by integrating over discrete time steps and discrete velocity vectors lattice links are defined to ensure that a particle moves from one grid point to another without falling between them The Lattice Boltzmann algorithm can be summarized by the following e Fluid properties are mapped onto a discrete lattice e The physical state of the fluid at each lattice point is described by a set of particle distribution functions e The system evolves towards an equilibrium or steady state by means of a two step process 1 Collision relaxation of the distribution function towards its local equilibrium form 2 Propagation of collided distribution functions along lattice links to neighbouring points e Macroscopic fluid variables e g density momenta can be calculated from moments of the distribution functions Major benefits of the Lattice Boltzmann Equation method include the local nature of its most computationally intensive process collision making the method inherently and massively parallelizable
38. and Lees Edwards shearing periodic boundaries The boundaries with the specified condition can be selected by clicking on set surfaces Switches to use global storage of bonds global bonds to ignore CONFIG files and to override index numbers in a CONFIG file can be set using these tickboxes Note that the DPD code uses reduced units in which the unit of length is the particle size the unit of mass is the particle mass and the unit of energy is the primary energy parameter of the potential energy function From these the time unit may be derived The temperature is defined to be 2 of the system kinetic energy If a valid CONTROL file already exists in the current working directory the OPEN button can be clicked to load its information into the GUI which can then be viewed and edited The CONTROL file for input into DL_MESO_DPD is created by clicking the SAVE button 14 CHAPTER 2 THE DL_MESO GUI A LBE DPD SPH Manual Help Exit EAE r x job header CONTROL file generated by DL MESO GUI 1l Dissipative Particle Dynamics e EN 1250 0 T F 2 temperature ko f pressure 3 interaction cutoff 1 0 many body cutoff 1 0 4 electrostatic cutoff 1 surface cutoff LO 5 boundary halo 0 0 time step oo 6 total steps 000 equilibration steps 1000 Tj stack interval o temp scale interval 10 8 save start ooo save interval 10 9 print interval o plot file interval o 10 dum
39. and functions into a module file called user_module 90 so future upgrades of DL_MESO will not interfere with their contributions 13 2 DL_MESO_DPD Subroutines and Functions 13 2 1 Main program dlmesodpd Both the serial and parallel versions of the program operate in a similar way Before DPD calculations start the following tasks are carried out For parallel running only MPI is started up initcomms and the node properties are determined e An I O channel for the general OUTPUT file is opened e The system clock is consulted for a start time timchk e The starting banner for DL_MESO_DPD is printed e System and bond data are read in and initialized sysdef e Initial values are set zero e The starting configuration is set up start either from scratch or specified by the user using a CONFIG file e The system clock is consulted again for the start of the DPD calculation cycle timchk 13 2 DL_MESO_DPD SUBROUTINES AND FUNCTIONS 169 A loop for DPD calculations is then called from run_module depending on the integrator and barostat selected by the user Each step of DPD calculations involves the following The step counter nstep is increased The system clock is checked timchk The first stage of the required integrator is used to update the motion of the particles and their positions Masses and particle molecule names are reassigned to the particles The parallel link cell structure is set up and the p
40. and or across periodic boundary conditions for calculation of many body DPD interaction forces e Dependencies exportdensity e Arguments nlimit input output integer e Comments Non periodic boundaries do not require boundary halos these are excluded from the export of particle local densities exportdensitydata_shear e Header records SUBROUTINE exportdensitydata_shear nlimit e Function Applies export of local densities for particles to boundary halos of neighbouring domains and or across periodic boundary conditions with Lees Edwards shearing for calculation of many body DPD interaction forces e Dependencies exportdensity exportdensity_shear Parallel version only e Arguments nlimit input output integer 13 2 11 start module This module requires the modules constants variables error_module comms_module numeric_container parse_utils ewald_module and surface_module to be loaded beforehand 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 205 start e Header records SUBROUTINE start e Function Sets up starting configuration for DPD calculations depending on availablity of CONFIG or restart files e Dependencies initialize revive read_config initialvelocity ewald_frozen_slater initialize e Header records SUBROUTINE initialize e Function Sets up starting configuration for DPD calculations without given initial or restart configuration e Dependencies global_sca_and error duni m
41. be commented out to increase calculational efficiency A 2 DL MESO DPD The Fortran90 modules for DL MESO_DPD must be compiled in a particular order to satisfy dependencies of shared variables and arrays e constants e variables e numeric_container e comms_module e error_module e parse_utils e bond module e surface_module e ewald_ module e manybody_module e domain module e start_module e config_module e field module e integrate_module e statistics module e run module e dimesodpd If running DL_MESO_DPD in serial the modules comms_module and domain_module should be replaced by comms_module_ser and domain_module_ser respectively To simplify the process a makefile may be created either in the DPD directory or in the working directory to automatically compile the modules and build the executable Examples of these for running in the DPD directory may be found in the DPD makefiles directory and modified by the user The compiler after FC and flags after FFLAGS may need changing depending on the Fortran90 compiler available if MPI is available the A 2 DL MESO DPD 223 Fortran90 compiler wrapped with MPI most commonly mpif90 is required If invoking from the working directory the modules for DL_MESO_DPD should either be preceded by the path i e DPD in the list of compile sources or the directive VPATH DPD can be used before the source list the latter strategy is used by the DL_MESO GUI when
42. be loaded beforehand surfacenodes e Header records SUBROUTINE surfacenodes e Function Identifies nodes containing surfaces or other boundary conditions e Dependencies None e Comments If using Lees Edwards boundary conditions these are only applied after equilibration hardreflect e Header records SUBROUTINE hardreflect k e Function Applies boundary condition for hard reflecting walls calculates short range forces on particles when k 1 applies bounce back condition when k 2 for particles about to pass through boundary e Dependencies surfacebounce e Arguments k input integer e Comments The boundary condition is given by 50 the applied wall potential on each particle is given as 1 Le Uwatt i Z Aval Z for z lt Ze surfacebounce e Header records SUBROUTINE surfacebounce ddd vdd sided e Function Applies boundary condition on a leaving particle by means of specular reflection move particle back into system and invert velocity component normal to wall 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 181 Dependencies None e Arguments ddd input output real KIND dp vdd input output real KIND dp sided input real KIND dp e Comments Momentum tangential to the boundary is preserved i e this applies a free slip boundary condition frozenbead e Header records SUBROUTINE frozenbead e Function Determines number of frozen particles required for boundary walls
43. by module and routine names Action Increase the amount of memory available for running DL _MESO_DPD by closing any other running applications running the simulation on a larger number of processors to reduce the memory required per processor underpopulating multicore processors i e using fewer cores per processor than the maximum available or upgrading your machine Alternatively try running a smaller simulation Appendix D DL MESO Licence Agreement Academic Purposes 1 DEFINITIONS AND INTERPRETATION 1 1 In this Licence Agreement the following expressions have the meanings set opposite Academic Purposes a Derived Work the DL_MESO Software the DL_MESO Website a Harmful Element fundamental or basic research or academic teaching including any fundamental research that is funded by any public or charitable body but not any purpose that generates revenue as opposed to grant income for the Licensee or any third party Any research that is wholly or partially sponsored by any profit making organisation or that is carried out for the benefit of any profit making organisation is not an Academic Purpose any modification of or enhancement or improvement to any of the DL_MESO Software and any software or other work developed or derived from any of the DL_MESO Software the release and version of the DL_MESO Software downloaded by the Licensee from the DL_MESO Website immediately after the Licensee agr
44. creating makefiles DL_MESO_DPD can be compiled using the command make if the makefile is called Makefile or if it has a custom name e g Makefile custom by the command e make f Makefile custom The example makefiles will produce an executable with the name dpd exe which can be copied to the working directory if necessary The required input files CONTROL and FIELD will also need to be created in or copied into the same directory as well as an optional CONFIG file to specify an initial configuration for a new simulation export files from a previous run can be used for restarting a previous simulation providing the number of processing units remains the same if the number of processing units changes the utility exportconfig can be used to convert the restart files into a CONFIG file If running in serial the executable can just be run using the command e dpd exe if running in Windows or e dpd exe if running in Unix like operating systems while the parallel version requires a command to run N identical copies of the program on N processors e g e mpirun np N dpd exe and may need to be launched via a batch job script please consult your machine administrator or documentation for further details The maximum numbers of particles per process maxdim pairs of unbonded interactions maxpair and the maximum sizes of transfer buffers maxbuf are automatically set according to the total number of particles in the system and
45. data Chapter 13 DL MESO DPD Package Reference 13 1 Overview DL_MESO_DPD consists of seventeen Fortran90 modules which should be compiled in the following order prior to the main program itself e constants Contains the constants and parameters required by DL_MESO_DPD e variables Contains the globally available variables and arrays required by DL_MESO_DPD e numeric_container Contains random number generators and other general purpose functions e g scale sum complementary error function e comms_module Contains all subroutines necessary for parallel computation e error module Contains subroutines to print error messages and close down DL_MESO_DPD in a controlled manner e parse_utils Contains functions to read in text data from input files e surface_module Contains subroutines for applying boundary conditions at system planes e g solid walls e ewald_ module Contains subroutines for calculating forces due to electrostatic interactions using Ewald summation based methods e manybody_module Contains subroutines for calculating density dependent forces between particles including the calculation of localized densities e bond module Contains book keeping and force calculation routines for bonds angles and dihedrals e domain_module Contains subroutines to construct parallel link cells import and deport particles in and export particle data to domain boundary halos 167 168 CHAPTER
46. dt K s Ei solute concentration initial o 1 top 0 o 8 relaxation time 1 FEMME E ts 7 a 5 o bulk relaxation time 1 1 16 bottom 0 3 interaction parameters fluid O fluid 1 left o 4 an 2 A fluid 0 o 11 right o 5 o 4 fluid 1 trani 6 front 10 back 7 segregation parameter lo 18 solute relaxation time 1 8 sic 11 SAVE F CANCEL F SAVE C CANCEL C SAVE T CANCEL T a Fluid parameters b Solute parameters c Thermal parameters Figure 2 3 Fluid solute and thermal parameter pop up windows The fluid densities at the right boundary The fluid densities at the front boundary Greyed out for two dimensional systems The fluid densities at the back boundary Greyed out for two dimensional systems The relaxation time rp for each fluid these values should be greater than 0 5 to give non zero kinetic viscosities The bulk relaxation time Tf buik for each fluid these values are only used in multiple relaxation time schemes to define the bulk viscosity and again should be greater than 0 5 If more than one phase is being modelled non zero interaction parameters between the fluid species are required gab The Shan Chen algorithm can accept values of gap for both a b and a b while the Lishchuk algorithm only requires gap for a b If the Shan Chen pseudopotential algorithm with wetting is to be used wall interaction parameters between the fluid species and solid surfaces are required ga wau If the Lishchuk continu
47. file e Dependencies revive e Arguments idnode input integer nodes input integer statis e Header records SUBROUTINE statis e Function Calculates statistical properties of system including rolling averages and fluctuations e Dependencies sclsum global_sum_dble global_sca_max_dble global_sca_min_dble Chapter 14 DL MESO DPD Examples Test cases for Dissipative Particle Dynamics simulations using DL_MESO including the required input and sample output files can be found in the DEMO DPD subdirectory All of the following examples can be run using either the serial or parallel versions of DL_MESO_DPD 96 processing units were used to test them in parallel although smaller and larger numbers should also work The smaller problems i e with up to 20 000 particles are best suited to running in serial or on a small number of processor cores e g 16 or less to limit the times required for interprocess communication while larger problems are better suited to running in parallel to reduce the memory requirements per processor core Images of all test cases and videos for some can be found in the Example Simulations page of the DL_MESO website a link to it can be found at www ccp5 ac uk DL_MESO 14 1 Mixture_Small This simulation consists of 1000 particles with 3 species with populations of 333 333 and 334 respectively All particle types have identical sizes and masses but different energy parameters using the defa
48. if adding a new bond angle type to DL_MESO DPD the scan_field and read_field routines in config_module need to be modified Message 34 unrecognised bond dihedral type defined in FIELD file A bond dihedral type not included in Table 12 5 has been found in the FIELD file Action Check the FIELD file to ensure all bond dihedral types are valid if adding a new bond dihedral type to DL_MESO_DPD the scan_field and read_field routines in config_module need to be modified 233 Message 35 non existent species given in FIELD file for molecule i An undefined species has been found in the definition for the th molecule type in the FIELD file Action Check the FIELD file particularly the i th molecule type and the species definitions to ensure the species in the molecule are defined Message 36 unrecognised bond definition in FIELD file for molecule i A bond definition has been found in the FIELD file for the th molecule that was not detected during the initial scan of the input file Action This error should never occur If it does please contact the authors of DL_MESO Message 37 unrecognised bond angle definition in FIELD file for molecule i A bond angle definition has been found in the FIELD file for the i th molecule that was not detected during the initial scan of the input file Action This error should never occur If it does please contact the authors of DL_MESO Message 38 unrecognised dihedral angle defin
49. in both the expression above and as the velocity for calculating equilibrium distribution functions The former is used by default in CollisionBGK while the latter method by Guo et al can be invoked using Co1lisionBGKGuo 5 1 1 2 Multiple Relaxation Time MRT The MRT collision operator operates on a similar principle to the quasilinear Lattice Boltzmann Equation 25 which expresses collisions in terms of a square matrix with dimensions equal to the number of lattice links per grid point m 1bsy nq Unlike quasilinear LBE however MRT collision schemes are applied to the moments for each lattice point rather than the distribution functions 33 8 which are related to each other by M Tf 5 3 where f is a vector of all m distribution functions for the point ie fo fi seat M the vector of moments also of size m and dependent on the lattice system and T the transformation matrix that renders the moments in terms of the distribution functions Equilibrium values for the moments M 4 can be determined by transforming the standard local equilibrium distribution function into moment space by Met T fe 5 4 where fea is the vector of local equilibrium distribution functions the resulting equilibrium moments can alternatively be expressed directly as functions of fluid density and velocity Certain moments such as density and momentum must be conserved and their equilibrium values are set so that no changes are made The post
50. in input files Customised codes slbecustom cpp and plbecustom cpp are also available to allow users to hardwire the algorithms for collisions mesophases etc into the code which might improve computational efficiency Using incompressible fluids would require setting the parameter incompress equal to 1 this can either be hard wired into the customised codes or specified in the lbin sys file To compile the code and produce an executable in the working directory at a command line type e c LBE slbe cpp o lbe exe assuming that c is the name of the available C compiler s1be cpp is the version of the code being compiled and lbe exe is the name of the executable required If compiling the parallel version of the code the command for the C compiler wrapped with MPI is required which is commonly mpiCC Additional compiler flags may be used between the compiler name and the reference to the code to improve computation speed or assist in debugging Before running the executable the required input files 1bin sys lbin spa and optionally lbin init need to be copied or moved into the working directory If running in serial the executable can just be run using the command e lbe exe if running in Windows or e lbe exe if running in Unix like operating systems while the parallel version requires a command to run N identical copies of the program on N processors e g e mpirun np N lbe exe and may need to b
51. integer A nmoldef mxbonds dihedral table storage for molecule insertion dhdinp2 integer A nmoldef mxbonds dihedral table storage for molecule insertion dhdinp3 integer A nmoldef mxbonds dihedral table storage for molecule insertion dhdinp4 integer A nmoldef mxbonds dihedral table storage for molecule insertion dhdinp5 integer A nmoldef mxbonds localized densities rhomb real KIND dp A maxdim nspe surface type sr type integer surface switch for boundary normal to x axis sr x integer surface switch for boundary normal to y axis srfy integer surface switch for boundary normal to z axis sr z integer switches for surfaces in current node srflge logical A6 surface repulsion parameters Awall aasr real KIND dp A nspe species of frozen beads for surface frzwspe integer number of frozen beads in x dimension for wall normal to x axis npxfwx integer number of frozen beads in y dimension for wall normal to x axis npxfwy integer number of frozen beads in z dimension for wall normal to x axis npxfwz integer number of frozen beads in x dimension for wall normal to y axis npyfwx integer number of frozen beads in y dimension for wall normal to y axis npyfwy integer number of frozen beads in z dimension for wall normal to y axis npyfwz integer number of frozen beads in x dimension for wall normal to z axis npzfwx integer number of frozen beads in y dimension for wall normal to z axis npzfwy integer number of frozen beads in z dimension f
52. is Mea Tf the exact form of which is dependent on the lattice scheme given for D2Q9 by 33 and for D3Q15 and D3Q19 by 8 Parameters for calculating the square of energy e and fourth order moments Taa can be modified by the user in the 1bpMODEL module fGetMomentForce e Header records int fGetMomentForce double source double v double force e Function Calculates Guo like forcing terms in moment space e Dependencies None e Arguments meq output double pointer v input double pointer force input double pointer 7 2 DL MESO _LBE SUBROUTINES AND FUNCTIONS 101 e Comments The forcing terms in moment space 49 calculated here are gt TT 3 6 T 9 0 i F the exact form of which is dependent on the lattice scheme given for D2Q9 D3Q15 and D3Q19 fGetMRTCollide e Header records int fGetMRTCollide double collide double omegashear double omegabulk e Function Calculates collision vector for Multiple Relaxation Time MRT scheme with specified fluid relaxation frequencies e Dependencies None e Arguments collide output double pointer omegashear input double precision omegabulk input double precision e Comments The exact form of the collision vector is dependent on the lattice scheme given for D2Q9 by 33 and for D3Q15 and D3Q19 by 8 Tuneable parameters for calculation stability can be modified by the user in the LbpMODEL module fInitializeSys
53. is fundamental to Lattice Boltzmann calculations and should not be modified fCollisionMRT e Header records int fCollisionMRTO e Function Collision steps for all compressible and incompressible fluids using MRT model e Dependencies fSiteFluidCollisionMRT fSiteFluidIncomCollisionMRT fSiteSoluteCollisionBGK fSiteThermalCollisionBGK fGetSpeedSite fGetSpeedIncomSite e Comments This routine is fundamental to Lattice Boltzmann calculations and should not be modified fCollisionMRTSegregation e Header records int fCollisionMRTSegregation e Function Collision and segregation steps for all compressible and incompressible fluids using MRT model with Lishchuk mesophase interactions e Dependencies fSiteFluidCollisionMRTSegregation fSiteFluidIncomCollisionMRTSegregation fSiteSoluteCollisionBGK fSiteThermalCollisionBGK fGetOneMassSite fGetTotMassSite fGetSpeedSite fGetSpeedIncomSite e Comments This routine is fundamental to Lattice Boltzmann calculations and should not be modified fCollisionMRT Guo e Header records int CollisionMRTGuo e Function Collision steps for all compressible and incompressible fluids using MRT model with Guo like forcing terms 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS 113 e Dependencies fSiteFluidCollisionMRTGuo fSiteFluidIncomCollisionMRTGuo fSiteSoluteCollisionBGK fSiteThermalCollisionBGK fGetSpeedSite fGetSpeedIncomSite e Comments This routine is fundamental to
54. it is strongly suggested that users of DL_MESO would not name their own parameters with prefixes 1b dp or sp 1Referring to the physical system being simulated rather than the computer system 40 CHAPTER 4 DL MESO _LBE BASIC DEFINITION Table 4 5 Domain information parameter meaning lbdm rank name of the processor lbdm size number of processors lbdm bwid domain boundary width set to zero for serial running lbdm xcor x coordinate of the processor lbdm ycor y coordinate of the processor lbdm zcor z coordinate of the processor 1bdm zcor 0 when 1bsy nd 2 lbdm xdim number of processors along x axis lbdm ydim number of processors along y axis lbdm zdim number of processors along z axis lbdm zdim 1 when lbsy nd 2 lbdm xs x coordinate of domain start position lbdm xe xa coordinate of domain end position lbdm xinner number of grid points along z axis in the domain lbdm xouter number of grid points along x axis in the domain including the boundary lbdm ys y coordinate of domain start position lbdm ye y coordinate of domain end position lbdm yinner number of grid points along y axis in the domain lbdm youter number of grid points along y axis in the domain including the boundary lbdm zs z coordinate of domain start position lbdm ze z coordinate of domain end position lbdm zinner number of grid points along z axis in the domain lbdm zouter number of grid points along z axis in the domain incl
55. mesophase interactions are calculated not required if only using constant body forces such as gravity fCalcPotential_ShanChen e Header records int CalcPotential_ShanChen e Function Calculates the interaction potential pg 1 exp 5 as suggested by the Shan Chen model for 0 each species and lattice point 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS 93 e Dependencies fGetOneMassSite e Comments The Shan Chen model is detailed in 55 56 Alternative mesoscale interaction potentials based on this model can be introduced here fCalcInteraction_ShanChen e Header records int fCalcInteraction ShanChen int xpos int ypos int zpos e Function Calculates particle interaction forces according to Shan Chen model e Arguments xpos input integer ypos input integer zpos input integer e Comments Further details can be found in 55 56 Similarly named routines to calculate interaction forces for alternative mesoscale algorithms can be added by the user fCalcInteraction_ShanChen Wetting e Header records int fCalcInteraction_ShanChenWetting int xpos int ypos int zpos e Function Calculates particle interaction forces according to Shan Chen model with additional fluid solid wetting forces e Arguments xpos input integer ypos input integer zpos input integer e Comments Further details can be found in 55 56 and 41 Similarly named routines to calculate interaction forces for altern
56. pairwise interaction potentials These potentials use an effective mass for each component 4 which is a function of density and most frequently defined as wa 05 i e 5 14 Po where p is the local density of component a and pg is the reference density for the same component The function in this form can be used to apply phase separation for a single component and can be changed by the user by modifying the subroutine fCalcPotential_ShanChen Defining gap as the interaction coefficient between components a and b the overall force on component a due to interactions with other components is defined as F ap 2 Y gab D wiy E i ory b i and any suitable forcing algorithm can be used to apply this force on a Lattice Boltzmann Equation simulation For a particular interaction the resulting equation of state 53 is defined as 1 P pes Z Cs gab p 5 16 and the interfacial tension between the components 54 is given as 4 Ag 2 t gt 2 x O Ae 5 17 2 Z dz where ex is a lattice dependent constant and z distance along the normal from the phase interface Optional fluid solid interaction forces can be added 41 for each fluid to control its wetting Foo Y E gawau X wis Z s s 5 18 i where s 2 0 for a pore fluid site at position 7 and s 1 for a solid site The interaction coefficient between component a and the wall Ya wan can be given a positive negative valu
57. purpose Define initial state CONFIG An optional CONFIG file can be included to define the initial state of the system which can include the positions velocities and forces for each particle This file is read by the subroutine read_config in start_module and scanned by the subroutine scan_config in config_module At the beginning of the file five lines of information of which the first two are mandatory have to be included e The simulation name 80 characters e The CONFIG file key levcfg integer the periodic boundary key imcon integer the number of particles in the file integer optional and the configuration energy real optional e The x y and z components for the x axis vector real optional e The x y and z components for the y axis vector real optional e The z y and z components for the z axis vector real optional The file key levcfg is set depending on the information available for each particle 0 for positions only 1 for positions and velocities or 2 for positions velocities and forces If particle velocities are not specified these are generated at random to produce a distribution corresponding to the required system temperature while unknown forces are set to zero The simulation name number of particles in the file and configuration energy are not read by DL_ MESO_DPD and can thus be ignored although the line for the simulation name must remain If axes vectors are included in the CONFI
58. rate of temperature change at the left boundary The temperature and rate of temperature change at the right boundary The temperature and rate of temperature change at the front boundary This is greyed out for two dimensional systems The temperature and rate of temperature change at the back boundary This is greyed out for two dimensional systems After filling in all the required values clicking the relevant save button SAVE F SAVE C or SAVE T will store the data in preparation for writing to the lbin sys input file The cancel buttons CANCEL F CANCEL C and CANCEL T will close the pop ups without saving any values 2 2 2 Defining the Space Properties If this option is selected before saving the LBE system data a warning message advising that the system should be re defined will appear Figure 2 4 shows the Set LBE Space panel with the rows for data entry labelled in red numbering The following data are required 1 The top boundary condition can be selected using the pull down list from e periodic e on grid bounce back e mid grid bounce back 2 2 LATTICE BOLTZMANN AND THE DL_MESO GUI 11 g LBE DPD SPH Manual Help 4 atticainaltemanin top periodic boundary condition bottom periodic boundary condition eft periodic boundary condition right periodic boundary condition front periodic boundary condition o uh WN back periodic boundary condition ADD OBSTACLES boun
59. reappears on the opposite face with the same velocity density etc DL_MESO_LBE applies periodic boundary conditions in two different ways depending on the size of the bound ary domain 1bdm bwid If there is no boundary domain the default for serial running periodic boundary 5 2 BOUNDARY CONDITIONS 49 conditions are automatically applied during the propagation step by using the function fCppMod to adjust the destination of distribution functions leaving the system so they are placed at the opposite side No periodic boundary using this implementation needs to be defined by the space property which can be left equal to zero as for the bulk fluid For systems that include a non zero boundary domain size the distribution functions at the edges of the actual system are copied into the buffer at the opposing sides before collisions and propagation take place This requires the use of the space property 1bphi i 10 to determine the location of the domain buffer which can be set up using the routine fMarkBoundArea and either fsPeriodic and similar routines for serial running or fNonBlockCommunication and similar routines for running in parallel to copy the distribution functions into the buffers 5 2 2 On grid bounce back The on grid bounce back condition applies a no slip condition i e zero fluid velocity at a boundary that lies halfway between grid points This is applied after the propagation stage by reversing the distribution fu
60. routine can be commented out fFinishDLMESO e Header records int fFinishDLMESO e Function Announces end of DL_MESO_LBE run prints simulation time efficiency measure Millions of Lattice Updates Per Second and a message encouraging citations of DL_ MESO e Dependencies None e Comments If preferred the call to this routine can be commented out fGet Model e Header records int GetModel e Function Initializes vectors 1bv lbw and lbopv for lattice model e Dependencies D2Q9 D3Q15 D3Q19 D3Q27 e Comments Parameters are specified according to requested space dimension and number of discrete velocities fMarkBoundArea e Header records int fMarkBoundArea 98 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Function Denotes where boundary areas for message passing and or periodic boundary conditions are located e Dependencies int fMarkBoundArea3D int fMarkBoundArea2D e Comments Only used when boundary areas are used primarily for parallel computing fGetEquilibriumF e Header records int fGetEquilibriumF double feq double v double rho e Function Calculates equilibrium distribution function for compressible fluid e Dependencies None e Arguments feq output double pointer v input double pointer rho input double precision e Comments The equilibrium distribution function calculated here is 3 8 9 G 8 3u c2 2c 2c f wip 14 which is only sui
61. s Tf M s fSiteFluidCollisionMRTSegregation e Header records int fSiteFluidCollisionMRTSegregation double startpos double sitespeed double bodyforce double phaseindex e Function Calculates collisions and phase segregation for the Lishchuk algorithm at a grid point using Multiple Relaxation Time MRT models for compressible fluids e Dependencies fGetAllMassSite fGetTotMassSite fReciprocal fGetMomentEquilibriumF fGetMRTCollide e Arguments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer phaseindex input double pointer e Comments Collisions are carried out on a single achromatic fluid using multiple relaxation time MRT schemes 33 8 fluid segregation takes place using the D Ortona algorithm 9 p pep E 7 ut Bw 7 fab ba fSiteFluidIncomCollisionMRT e Header records int fSiteFluidIncomCollisionMRT doublex startpos double sitespeed double bodyforce e Function Calculates collisions at a grid point using Multiple Relaxation Time MRT models for incompressible fluids e Dependencies fGetOneMassSite fGetMomentEquilibriumFIncom fGetMRTCollide 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS 107 e Arguments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer e Comments Collisions for each fluid species are carried out using multiple relaxation time MRT schemes 33 8
62. schemes are available The tickbox can be selected to specify that the fluids in the system should be treated as incompressible 2 The collision forcing type for the system can be selected out of BGK BGK with Guo forcing MRT and MRT with Guo like forcing 2 2 10 11 12 13 LATTICE BOLTZMANN AND THE DL_MESO GUI 7 using temperature scalar gt gt set thermal parametersl8 O lt 5 L_MESO LBE DPD SPH Manual Help Exit kamanaman LBE model O incompressible i collision forcing type 2 interactions 3 number of grid points x 40 y 30 z 4 total steps 10 equilibration steps lo 5 Set LBE Space save span 5 boundary width a 6 output format vik vw T Change LBE Code sound speed 540 kinetic viscosity 0 001 gi top boundary speed Vx 0 Vy 0 Vz 9 bottom boundary speed Vx 0 Vy 0 Vz 10 Compile LBE Code left boundary speed Vx 0 Vy 0 Vz 11 right boundary speed Vx 0 Vy 0 Vz 12 front boundary speed Vx Vy V2 13 back boundary speed Vx Vy Vz 14 noise 0 1 0 phase field Y no phase field5 Gather LBE Data number of fluids phases E gt gt set fluid parameters 16 Piot LBE Results number of solutes o gt gt set solute parameters 17 Figure 2 2 Define LBE System The required mesophase interactions can be selected from the pull down
63. sidel input real KIND dp side2 input real KIND dp e Comments Only exists in parallel version of DL_MESO_DPD This routine requires information for the two dimensions along the surface of the shearing boundary the variables shovel and shove2 represent the displacement due to shear sidel and side2 are the domain dimensions and vshovel and vshove2 are the velocity corrections to particles passing through the shearing boundary import e Header records SUBROUTINE import nlimit mdir mp begin final shove skip e Function Imports particle forces from boundary halo for integration schemes and thermostats that only require one set of forces to be calculated e Dependencies error global_sca and all msg receive unblocked msg receive_sca blocked msg send_ blocked msg_send_sca_blocked msg_wait e Arguments nlimit input output integer mdir input integer mp input integer begin input real KIND dp final input real KIND dp shove input real KIND dp skip input logical e Comments Only exists in parallel version of DL_ MESO_DPD This routine is suitable for thermostats using the standard Velocity Verlet algorithm for force integration and one set of forces this includes the DPD thermostat with MD integration MD VV the Lowe Andersen and Peters thermostats The switch skip prevents the importing of forces from the boundary halo of the current domain this is useful for applying non periodic boundary conditions e g hard surfa
64. start points for sending and receiving messages e Comments This subroutine must not be changed fNonBlockCommunication e Header records int fNonBlockCommunication e Function Passes distribution function information for either 2D or 3D system fOutputInfo e Header records int fOutputInfo e Function Outputs number of processes and lengths of integers and floats e Comments This subroutine is necessary for gathering and rearranging the 1bout data and produces the files lbout info and lbout ext fBoundNonBlockCommunication e Header records int fBoundNonBlockCommunication e Function Passes boundary information for either 2D or 3D systems fForceNonBlockCommunication e Header records int fForceNonBlockCommunication e Function Passes interaction force information for either 2D or 3D systems fIndexNonBlockCommunication e Header records int fIndexNonBlockCommunication e Function Passes phase index information for either 2D or 3D systems 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS fCheckTimeMPI e Header records int fCheckTimeMPI O e Function Outputs time in seconds since initial call e Arguments fCheckTimeMPI output double e Comments Obtains calculation time based on MPI wall clock fPrintSystemMass e Header records int fPrintSystemMass e Function Calculates and prints total and individual fluid masses in entire system e Dependencies fGetTo
65. system since the parallel VTK format links to these rather than creates autonomous files for the entire system Legacy VTK format lbout vtk Legacy VTK files written by DL_MESO_LBE include the lattice dimensions numbers of grid points in each direction the Cartesian coordinates of the grid points in real life units and the following data e A scalar property fluid density mass fraction solute concentration or scalar temperature e g P0 0 0 Pnz 1 ny 1 nz 1 e Fluid velocity Uo 0 0 Vo o 0 Wo o o Una 1 ny 1 nz 1 Vne 1l ny 1 nz 1 Wha 1 ny 1 nz 1 e The space boundary condition property 0 0 0 na 1 ny 1 nz 1 If all properties are to be output they are all included in the same file for each time step under unique names Plot3D format Output grid position lbout xyz NT NY nz L0 0 0 Tnx 1 ny 1 nz 1 Y0 0 0 gt Ynx 1 ny 1 nz 1 20 0 0 Zng 1 ny 1 nz 1 where nx is the total number of grid points in x direction ny is the total number of grid points in y direction nz is the total number of grid points in z direction and i j k Yi j k Zi j k is the Cartesian coordinate of grid point 2 7 k 60 CHAPTER 6 DL MESO _LBE INPUT AND OUTPUT FILES Output macroscopic quantities 1bout q NL NY NZ c 1 0 Re t P0 0 0 Pna 1 ny 1 nz 1 Uo 0 0 Chest ai ne Vo 0 05 Var tny Laris Wo 0 0 Wrz 1 ny 1 nz 1 D0 0 0 gt ves Ore Tyne
66. system thermostat the dissipative and random forces as defined for DPD with the standard molec ular dynamics form of the Velocity Verlet integrator DPD MD VV is the default but recalculation of dissipative forces at the end of each step DPD DPD VV 13 the Lowe Andersen 36 Peters 47 and Stoyanov Groot 62 thermostats can also be selected Values of y for the DPD and Peters thermostats and I for the Lowe Andersen and Stoyanov Groot thermostats can be specified elsewhere for each pair of species but an additional parameter for the Stoyanov Groot thermostat should be set by clicking on set thermostat see below for more details The system barostat no barostat is used by default but Langevin 29 and Berendsen 2 barostats are available in combination with all five thermostats If either barostat is selected its parameters can be set by clicking on set barostat and the target system pressure can be specified The electrostatics scheme for the simulation an Ewald sum method with Slater type exponential charge smearing 14 is available in DL_MESO_DPD If selected the short range electrostatic cutoff can be edited and the parameters for the Ewald sum and charge smearing can be specified by clicking on set electrostatics The surfaces to be applied to the system by default periodic boundary conditions are used but alterna tive boundary conditions include hard walls with soft repulsions and specular reflection 50 walls of frozen beads
67. the terms and conditions of this Licence Agreement provided that 2 1 1 the Licensee may not distribute any of the DL_MESO Software or any Derived Work to any third party or share their use with any third party whether free of charge or otherwise and the Licensee may not sub license the use of any of the DL_MESO Software to any third party unless in each case that third party has complied with clause 2 3 below 2 1 2 the Licensee may not use the DL_MESO Software on behalf of or for the benefit of any third party including without limitation using it to provide bureau outsourcing or application services or facilities management services party unless that third party has complied with clause 2 3 below and 2 1 3 the DL_MESO Software and any Derived Work may be used by the Licensee and its employees and registered students for Academic Purposes only 2 2 If the Licensee wishes to use the DL_MESO Software or any Derived Work in any way except for Academic Purposes or wishes to distribute or make the DL_MESO Software or any Derived Work 2 3 2 4 241 available to any third party for non Academic Purposes it must obtain a commercial licence from STFC STFC may refuse to grant the Licensee a commercial licence If STFC agrees to grant a commercial licence that licence will be on such terms and conditions as STFC sees fit If the Licensee wishes to carry out any collaboration for Academic Purposes with any third
68. the lattice Boltzmann method in incompressible limit Journal of Computational Physics 146 1 282 300 1998 Xiaoyi He and Li Shi Luo Lattice Boltzmann model for the incompressible Navier Stokes equation Journal of Statistical Physics 88 3 4 927 944 1997 F J Higuera and J Jim nez Boltzmann approach to lattice gas simulations EPL Europhysics Letters 9 7 663 668 1989 R W Hockney and J W Eastwood Computer simulation using particles McGraw Hill International 1981 Takaji Inamuro Masato Yoshino Hiroshi Inoue Riki Mizuno and Fumimaru Ogino A lattice Boltzmann method for a binary miscible fluid mixture and its application to a heat transfer problem Journal of Computational Physics 179 1 201 215 2002 Takaji Inamuro Masato Yoshino and Fumimaru Ogino A non slip boundary condition for lattice Boltz mann simulations Physics of Fluids 7 12 2928 2930 1995 Ask F Jakobsen Constant pressure and constant surface tension simulations in dissipative particle dy namics Journal of Chemical Physics 122 12 124901 2005 J E Jones On the determination of molecular fields II From the equation of state of a gas Proceedings of the Royal Society of London Series A 106 738 463 477 October 1924 Simon Jury Peter Bladon Mike Cates Sujata Krishna Maarten Hagen Noel Ruddock and Patrick Warren Simulation of amphiphilic mesophases using dissipative particle dynamics Physical Chemistry Chemical Physics 1 9 2
69. up input files modifying and compiling the program code running the simulation and gathering the results files 5 6 CHAPTER 2 THE DL_MESO GUI a x 2 DMIMESO DL_MESO LBE DPD SPH Manual Help Exit Welcome to DL MESO R S Qin W Smith amp M A Seaton Copyright STFC 2012 Click one of the above buttons to start Figure 2 1 DL MESO GUI on startup for plotting and visualization The SPH button is for Smoothed Particle Hydrodynamic simulations which will be included in future versions of DL_MESO clicking on this button will currently produce a warning message This user manual can be read in Adobe Acrobat Reader if installed by clicking the Manual button while Help will advise you to visit the DL MESO website at www ccp5 ac uk DL_MESO 2 2 Lattice Boltzmann and the DL_MESO GUI To access the LBE facilities in the DL_MESO GUI proceed as follows e Click the LBE button to get the LBE panel e Click the Define LBE System button and supply the required information The file 1bin sys will be created by the step e Click the Set LBE Space button to define the simulation space The file 1bin spa will be created by this step 2 2 1 Defining the System Figure 2 2 shows the Define LBE System panel with the rows for data entry labelled in red numbering The required data are as follows 1 The required LBE model can be selected from the pull down list the D2Q9 D3Q15 D3Q19 and D3Q27 square lattice
70. will be produced if either of the files lbout info and 1bout ext are missing No other error messages are produced so care should be taken to ensure no solution files for the pieces are missing before running the utility Since the data is copied into the combined structure and solution files the original output files can be deleted after this utility is run lbevtkgather lbevtkgather is a utility written in C to gather Structured Grid XML formatted VTK output files produced by the parallel version of DL_MESO_LBE lbout vts and produce a set of linking files lbtout pvts for visualization of the entire system If c is the command for the available C compiler the executable vtk exe can be produced by typing e c o vtk exe lbevtkgather cpp and either run at the command line or via the GUI under Gather LBE Data B 2 DL MESO_DPD 227 All lbout vts files should be copied to the directory including the executable if necessary before running as well as the 1bout info and lbout ext files to give information about the number of processors used for the simulation and the extents of each piece This utility can be run with a command line argument to give the scalar property required e g for Windows and Unix Linux computers respectively e vtk exe 1 e vtk exe 1 where 0 is used for all properties 1 for fluid density 2 for mass fraction 3 for solute concentration and 4 for temperature If the GUI is used this can be se
71. will be required for parallel running and for postcollisional fluid segregation The fCollision Segregation routines used in place of the standard collision routines carry out the achromatic collision of all fluids and D Ortona segregation No solid fluid interactions i e wetting effects are currently available in DL_MESO_LBE using this form of mesoscopic interaction 5 4 Diffusion and heat transfer In a similar fashion to multiple fluid systems the Lattice Boltzmann Equation method can be applied to problems involving diffusion and or heat transfers by using additional distribution functions for each solute and or temperature 27 72 5 4 DIFFUSION AND HEAT TRANSFER 53 For a system consisting of a number of dilute solutes along with a bulk fluid the governing equation for each solute is given as At Ts where g is the distribution function for the solute and 7 the solute relaxation time which is related to its 1 1 Any D x 5 At and the Schmidt number can be determined by diffusivity v 277 1 ad ar Taking the concentration of the solute as C 5 gi the equilibrium distribution function for the solute is given by a simpler form of Equation 3 11 i u gi WCs i 3 5 29 where the velocity used is that of the bulk fluid Heat transfers can be coupled to the system in a similar manner using a thermal distribution function h and a thermal relaxation time 7 which gives th
72. 051 2056 1999 J M V A Koelman and P J Hoogerbrugge Dynamic simulations of hard sphere suspensions under steady shear EPL Europhysics Letters 21 3 363 368 1993 Pierre Lallemand and Li Shi Luo Theory of the lattice Boltzmann method Dispersion dissipation isotropy Galilean invariance and stability Physical Review E 61 6 6546 6562 June 2000 A W Lees and S F Edwards The computer study of transport processes under extreme conditions Journal of Physics C Solid State Physics 5 15 1921 1928 1972 BIBLIOGRAPHY 249 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 S V Lishchuk C M Care and I Halliday Lattice Boltzmann algorithm for surface tension with greatly reduced microcurrents Physical Review E Statistical Nonlinear and Soft Matter Physics 67 3 036701 March 2003 C P Lowe An alternative approach to dissipative particle dynamics EPL Europhysics Letters 47 2 145 151 July 1999 John F Marko and Eric D Siggia Stretching DNA Macromolecules 28 26 8759 8770 1995 G Marsaglia and T A Bray A convenient method for generating normal variables SIAM Review 6 3 260 264 July 1964 George Marsaglia Arif Zaman and Wai Wan Tsang Toward a universal random number generator Statistics and Probability Letters 9 1 35 39 January 1990 C A Marsh G Backx and M H Ernst Static and dynamic p
73. 13 DL MESO DPD PACKAGE REFERENCE e start_module Contains subroutines to initialize and restart DPD calculations e config_module Contains subroutines to read in input files with system and molecule bond data to zero all parameters and accumulators for statistical data and for parallel version only determine 3D domain decomposition e field module Contains subroutines to calculate pairwise forces between particles e integrate module Contains subroutines to integrate the equations of motion using the Velocity Verlet scheme and apply various thermostats and barostats e statistics module Contains subroutines to calculate and write out statistical and trajectory data e run module Contains program loops for different integrators and barostats Most of the above modules and the main program file dlmesodpd 90 are identical for both serial and parallel versions of DL_MESO_DPD The filenames for the serial versions of comms_module and domain_module end with _ser but are referred to in the code by their standard names The module for many body DPD interactions manybody_module may be modified by users to incorporate alternative schemes Additional bond angle and dihedral models can be added to bond module by the user although modifications to config_module are also required to allow DL_MESO to recognise new types of bond interaction For anything else however we recommend that DL_MESO users put any self defined subroutines
74. 4 3 Visualizations of DPD PhaseSeparation test case we for particle type blue for type 2 14 4 Aggregate This simulation consists of 3000 unbonded particles and 30 molecules of 10 particles each with harmonic bonds between them The unbonded particles and molecules are made up of different species with a higher energy parameter for unlike particle interactions This causes the molecules to aggregate which can be seen in Figure 14 4 a snapshot of the simulation 14 5 POLYELECTROLYTE 217 Figure 14 4 Visualization of system at t 2220 from DPD Aggregate test case 14 5 Polyelectrolyte This simulation example consists of a slightly hydrophobic polyelectrolyte molecule of 50 particles each with a relative charge of 0 5 immersed in a salt solution of concentration 0 14M 14 The salt solution consists of 9900 neutral water particles 75 cationic salt particles net charge 1 75 anions of charge 1 and 25 counterions of charge 1 to keep the system neutral A similar simulation is included with the polyelectrolyte replaced with a neutral polymer of the same number of particles and the counterions replaced with water FIELD neutral this should be renamed to FIELD to run the simulation and used with the same CONTROL file Figure 14 5 gives a comparison between the polyelectrolyte and neutral polymer at the final time step which have measured radii of gyration of 4 5 and 2 7 respectively a Polyelectrolyte b Neutral polymer
75. 6 6 7 Headings The headings in this Licence Agreement are for ease of reference only they do not affect its construction or interpretation Assignment etc The Licensee may not assign or transfer this Licence Agreement as a whole or any of its rights or obligations under it without first obtaining the written consent of STFC Illegal unenforceable provisions If the whole or any part of any provision of this Licence Agreement is void or unenforceable in any jurisdiction the other provisions of this Licence Agreement and the rest of the void or unenforceable provision will continue in force in that jurisdiction and the validity and enforceability of that provision in any other jurisdiction will not be affected Waiver of rights If STFC fails to enforce or delays in enforcing an obligation of the Licensee or fails to exercise or delays in exercising a right under this Licence Agreement that failure or delay will not affect its right to enforce that obligation or constitute a waiver of that right Any waiver by STFC of any provision of this Licence Agreement will not unless expressly stated to the contrary constitute a waiver of that provision on a future occasion Entire agreement This Licence Agreement constitutes the entire agreement between the parties relating to its subject matter The Licensee acknowledges that it has not entered into this Licence Agreement on the basis of any warranty representation statem
76. 9 fCheckSteer e Header records int fCheckSteer e Function Checks for the existence of notsteer files if found then reads lbin sys and lbin spa files e Dependencies fInputParameters lbin sys fReadSpaceParameter lbin spa 7 2 6 IbpIOPlot3D fOutputGrid e Header records int fOutputGrid3D const char filename 1bout e Function Outputs grid positions for system in Plot3D format e Dependencies fOutputGrid2D fOutputGrid3D e Arguments filename input array of characters e Comments The default output file name is lbout xyz for 3D systems and lbout xy for 2D systems fOutputQ e Header records int fOutputQ const char filename 1bout e Function Outputs macroscopic mass densities and fractions for all fluids concentrations for all solutes temperature and velocity speeds along x y and z directions at each lattice point for system in Plot3D format e Dependencies fOutputQ2D fOutputQ3D e Arguments filename input array of characters e Comments The default output file name is 1bout prop q with prop substituted by dens frac conc or temp for fluid densities mass fractions solute concentrations or temperature respectively and preceded by the number of the fluid or solute This can be changed by specifying an output file name when calling the routine 80 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE fOutputQP e Header records int fOutputQP const char filename lbout int ipro
77. 9010 9011 JO 1bsy ny lbsy nz J100 9101 Jlbsy nx lbsy ny lbsy nz At each grid point DL_MESO_LBE arranges the particle distribution functions in order of fluid functions solute functions temperature functions and phase field order parameter For example for a D2Q9 lattice with two fluids scalar temperature and phase field the distribution functions are in the order of ida tattoo tatoo Les Ji f To Ti To To Ta To To Tr Ts pf Therefore the number of particle distribution functions at each grid point is lbsitelength lbsy nf lbsy nc lbsy nt x 1bsy nq 1bsy ph where 1bsy nf lbsy nc 1bsy nt 1bsy nq and 1bsy ph are respectively number of fluids number of solutes number of temperature scalars number of discrete speeds and number of the phase field order parameters lbsy nt and lbsy ph can only take the values of 1 or 0 representing systems with or without temperature scalar and phase field Also if 1bsy nc 4 0 lbsy nf cannot be set larger than 1 4 2 2 Storage of space properties The space property is represented by an integer value in DL MESO_LBE For example 1bphi 100 0 represents the 100th grid point as a liquid site and 1bphi 101 12 shows the 101st grid point as an on grid bounce back boundary Table 4 1 lists the categories of space properties The orientation of a solid liquid boundary is also represented by the value of an integer For example a planar surface with normal vector along t
78. CONFIG file ligindex ogical TorF duplications of CONFIG file in x direction nfoldx integer duplications of CONFIG file in y direction nfoldy integer duplications of CONFIG file in z direction nfoldz integer total number of duplications of CONFIG file nfold integer data key for CONFIG file levcfg integer periodic boundary key for CONFIG file imcon integer printout selection for OUTPUT file outsel integer maximum number of particles maxdim integer maximum number of pairwise interactions maxpair integer maximum message buffer size maxbuf integer maximum number of particles per molecule mxmolsize integer maximum number of bonds per molecule mxbond integer maximum number of angles per molecule mxangles integer maximum number of dihedrals per molecule mxdiheds integer maximum number of interaction parameters mxprm integer density variation for non uniform system distributions dvar real KIND dp name of DL_MESO_DPD calculation text character 80 number of time steps for calculation nrun integer interval for writing OUTPUT file nsbpo integer Sul interval for writing CORREL file iscorr integer starting time step for writing HISTORY files straj integer interval for writing HISTORY files ntraj integer restart file export creation interval ndump integer temperature scaling interval nsbts integer number of equilibration time steps nseql integer calculation restart parameter kres integer number of species nspe integer gt 1 number o
79. Comments The default output file name is 1bout q and the concentration of solute 0 is output by default These can be changed by specifying an output file name and solute number up to 1bsy ns 1 when calling the routine fOutputQT e Header records int fOutputQT const char filename lbout e Function Outputs macroscopic temperature and fluid velocity at each lattice point for system in Plot3D format e Dependencies fOutputQT2D fOutputQT3D e Arguments filename input array of characters e Comments The default output file name is lbout q This can be changed by specifying an output file name when calling the routine 7 2 7 lbplOLegacyVTK fOutputLegacyVTK e Header records int fOutputLegacyVTK const char filename lbout e Function Outputs macroscopic mass densities and fractions for all fluids concentrations for all solutes temperature and velocity speeds along x y and z directions at each lattice point for system in Structured Grid Legacy VTK format e Dependencies fOutputLegacyVTK2D fOutputLegacyVTK3D e Arguments filename input array of characters e Comments The default output file name is lbout vtk This can be changed by specifying an output file name when calling the routine fOutputLegacyVTKP e Header records int fOutputLegacyVTK const char filename lbout int iprop 0 82 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE Function Outputs macroscopic mass density and velocity s
80. D FUNCTIONS 63 D3Q19 e Header records int D3Q19 e Function Assign the weight factor lbw speed vector 1bv index for opposite speed vector lbopv MRT transformation matrices 1btr and 1btrinv and tuneable parameters 1bmrts and 1bmrtw for the D3Q19 lattice model e Dependencies None D3Q27 e Header records int D3Q27 e Function Assign the weight factor lbw speed vector 1bv and the index for opposite speed vector lbopv for the D3Q27 lattice model e Dependencies None e Comments No Multiple Relaxation Time MRT scheme is currently available for this lattice 7 2 3 lbpBASIC This package contains general purpose functions which are not directly related to the Lattice Boltzmann Equa tion method These may be replaced with any suitable functions in C standard libraries fCppAbs e Header records template lt class T gt T fCppAbs T a return a lt 0 a a e Function Calculate absolute value of number a e Dependencies None e Arguments a input any datatype fCppAbs output same datatype as a fReciprocal e Header records template lt class T gt T fReciprocal T a return a 0 1 a 0 64 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Function Calculates reciprocal of a for all non zero values returns zero for a 0 e Dependencies None e Arguments a input any datatype fReciprocal output same datatype as a fEvapLimit e Header records template lt class T gt T fEvapLimit T a
81. D particle density For sufficiently large densities p gt 2 g r takes the same form and the equation of state can be well approximated by p pkgT aAp 9 13 4 ct where the parameter a 0 101 0 001 has units equivalent to rf This expression permits the use of fluid compressibilities to obtain conservative force parameters for bulk fluids e g for water A Se Alternative equations of state may be obtained by modifying the functional form of conservative interactions to include localized densities i e many body DPD 46 66 Transport coefficients for a DPD fluid can be derived using the expressions for the drag and stochastic forces 16 32 40 The kinematic viscosity can be found to be MkgT 21 ypr x 9 14 d 4nypr 1575 9 12 while the self diffusion coefficient is given as 45kpT Dx 9 15 2nypr3 The ratio of these two properties the Schmidt number Sc is therefore 1 2mypr Sc x c 9 16 e 5 70875keT vee and for values of the drag coefficient and density frequently used in DPD simulations this value is of the order of unity which is an appropriate magnitude for gases but three orders of magnitude too small for liquids This property of standard DPD does not rule it out for simulations of liquid phases except when hydrodynamics are important It may also be argued that the self diffusion of DPD particles might not correspond to that of individual molecules and thus a Schmidt numb
82. DL_MESO LBE provides the routine fConvectionForceBoussinesq to calculate this force The product of gravitational acceleration and volumetric expansion g8 for each fluid as well as the maximum and minimum temperatures T and T can be included in the 1bin sys file 54 CHAPTER 5 DL_MESO_LBE FEATURES 5 5 Compressible and incompressible fluids The standard Lattice Boltzmann Equation scheme is capable of modelling compressible fluids Incompressible fluids can be modelled by making a simple modification to the local equilibrium distribution function 24 se e A ED fet wi ptm 262 26 3 5 33 2c4 2c where po is the fixed density of the incompressible fluid and the density p becomes an analogue to pressure p While Equation 3 1 is still applicable to calculate p the fluid velocity is now calculated by q poua ys Silica 5 34 i 0 DL_MESO_LBE allows users to select incompressible fluids by means of the variable incompress whose value can be selected using the keyword incompressible_fluids in the lbin sys file Additional collision and equilibrium distribution function routines ending in Incom are included to allow the user to model incompressible fluids All of these routines use a specified constant density for each fluid in the system 1bincp as the value of po Chapter 6 DL MESO LBE Input and Output Files 6 1 Input files All user specified input files for DL MESO_LBE must be in ANSI text format with keyw
83. DL_MESO USER MANUAL M A Seaton and W Smith STFC Daresbury Laboratory Daresbury Warrington Cheshire WA4 4AD United Kingdom Version 2 5 April 2012 Contents Contents 1 DL_MESO General Information 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 2 The 2 1 2 9 2 3 2 4 2 5 3 The 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 5 1 5 2 5 3 5 4 5 5 Description e nse asaran A as amp ee e A A A a A ae ey EE REA F nctionality nd oh ein eee BA we Ae Geass od A ate Ll RA we oS BAA Requirements 2 os a ad te a ee Dee egy er et ests kA bs a oe CEA Bs he he ee ae The DL_MESO Directory Structure 2 2 a Disclaimer aa a see te BO Be She eon g ate Co ee BOP ae BL aS Copyright stages S MLD A A Et Be ha Gee A Authors Sa p At td Bae ha de eee tien Be SE die ey Se ee AA Suggestions and Bug Reports aaau aaa aaa a DL_MESO GUI Getting Started with the DL MESO GUI 0 00 0 000 00000000 Lattice Boltzmann and the DL MESO GUI e Dissipative Particle Dynamics and the DL MESO GUl o o ooo o Compiling and running DE MESO 200 2000 0000000000004 NOTES gt os ee ae apni hy a BA Ae Gods a ate th eg ad Ske ee dd Lattice Boltzmann Equation LBE Lattice Boltzmann Equation Basic Theory INTO UCM cri A E e e aai A A A A A a e AA EA a a Basic Detnitions ono a e A dE PORE ee AR e i Derivation of Equilibrium ea AE A A RP ee ds a a ee A Structural Relaxation and Macroscop
84. FC STFC Daresbury Laboratory Dares bury Warrington Cheshire WA4 4AD United Kingdom version 4 01 0 edition October 2010 S Y Trofimov E L F Nies and M A J Michels Thermodynamic consistency in dissipative parti cle dynamics simulations of strongly nonideal liquids and liquid mixtures Journal of Chemical Physics 117 20 9383 9394 2002 Loup Verlet Computer experiments on classical fluids I Thermodynamical properties of Lennard Jones molecules Physical Review 159 1 98 103 July 1967 P B Warren Vapor liquid coexistence in many body dissipative particle dynamics Physical Review E 68 6 066702 December 2003 John D Weeks David Chandler and Hans C Andersen Role of repulsive forces in determining the equilibrium structure of simple liquids Journal of Chemical Physics 54 12 5237 5247 1971 Dean R Wheeler Norman G Fuller Rowley and Richard L Non equilibrium molecular dynamics simu lation of the shear viscosity of liquid methanol adaptation of the Ewald sum to Lees Edwards boundary conditions Molecular Physics 92 1 55 62 1997 Satoru Yamamoto Yutaka Maruyama and Shi aki Hyodo Dissipative particle dynamics study of sponta neous vesicle formation of amphiphilic molecules Journal of Chemical Physics 116 13 5842 5849 2002 BIBLIOGRAPHY 251 72 M Yoshino and T Inamuro Lattice Boltzmann simulations for flow and heat mass transfer problems in a three dimensional porous structure Intern
85. G file and the value of imcon is greater than zero these will be read on the assumption that the simulation volume is orthorhombic the only possible shape available in DL_MESO_DPD Each particle is represented by a block record with at least two lines of information 1This file is formatted identically to CONFIG files used in DL_POLY 60 65 except that the origin is set as the back bottom left corner of the simulation volume instead of the centre 164 CHAPTER 12 DL MESO DPD INPUT AND OUTPUT FILES e The species name 8 characters or number integer and the global particle number integer optional e The z y and z coordinates for the particle real e The z y and z components of particle velocity real if levcfg gt 0 e The x y and z components of force on the particle real if levcfg gt 1 If global particle numbers are not included or the no index option is invoked in the CONTROL file these are generated automatically for the particles in the order specified by the CONFIG file Care should be taken that any particles belonging to molecules are numbered correctly since the bond information is assigned in an identical fashion to unspecified systems i e numbering after all loose particles in the relative order specified by the FIELD file If the nfold option is invoked in the CONTROL file DL_MESO_DPD will duplicate the given configuration in each Cartesian direction and assign global particle numbers to the enlarged syst
86. Header records INTEGER KIND 1i FUNCTION parseint word e Function Reads the integer contained in the string word e Dependencies None e Arguments word input character LEN parseint output integer KIND li 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 179 parsedble e Header records REAL KIND dp FUNCTION parsedble word e Function Reads the double precision number contained in the string word e Dependencies None e Arguments word input character LEN parsedble output real KIND dp getint e Header records INTEGER KIND 1i FUNCTION getint txt n e Function Reads the nth word of the string txt to obtain an integer e Dependencies parseint e Arguments txt input character LEN n input integer getint output integer KIND li getdble e Header records REAL KIND dp FUNCTION getdble txt n e Function Reads the nth word of the string txt to obtain a double precision number e Dependencies parsedble e Arguments txt input character LEN n input integer getdble output real KIND dp lowercase e Header records SUBROUTINE lowercase word e Function Changes all upper case letters in the string word to lower case e Dependencies None 180 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE e Arguments word input output character LEN n input integer getdble output real KIND dp 13 2 6 surface_module This module requires the variables module to
87. IELD 1 acceleration x component 0 0 2 acceleration y component 0 0 acceleration z component 0 0 SAVE E CANCEL E c External field parameters Figure 2 8 Species interactions and external field pop up windows 6 If a non periodic hard surface is defined the wall repulsion parameter Aa for the species can be specified Figure 2 8 b gives the layout for the interaction pop up window 1 The pair of species can be selected using these pull down boxes the interaction parameters and type currently set for the selected species pair will be displayed 2 The interaction type for the species pair the standard DPD model by Groot and Warren 16 is the de fault but many body density dependent DPD 46 66 Lennard Jones 30 and Weeks Chandler Andersen hard sphere models can also be selected Note that while the Lennard Jones and Weeks Chandler Andersen WCA 69 models are not DPD models the DPD thermostat can be used with them to maintain system temperature 3 The energy parameters for the species pair can be typed into these boxes and set using the button SET I Only one energy parameter is required for standard DPD 4 Lennard Jones and WCA eij while many body DPD can use up to five the exact number required will depend upon the model selected by the user Note that values for these and other interaction parameters for all species pairs will be written to the FIELD file if many b
88. IND dp system electrostatic energy at current step stpee real KIND dp system mean bond length at current step stpbdl real KIND dp system maximum bond length at current step stpbdmx real KIND dp system minimum bond length at current step stpbdmn real KIND dp system mean bond angle at current step stpang real KIND dp system mean bond dihedral at current step stpdhd real KIND dp rolling average system potential energy ravpe real KIND dp rolling average system virial ravvir real KIND dp rolling average system kinetic energy ravtke real KIND dp rolling average system total energy ravte real KIND dp rolling average system pressure ravprs real KIND dp rolling average system volume ravvlm real KIND dp rolling average system temperature ravttp real KIND dp rolling average system bond potential energy ravbe real KIND dp rolling average system angle potential energy ravae real KIND dp rolling average system dihedral potential energy ravde real KIND dp rolling average system electrostatic potential energy ravee real KIND dp stage number for data stack nav integer data stack for potential energy stkpe real KIND dp A nstk data stack for virial stkvir real KIND dp A nstk data stack for kinetic energy stktke real KIND dp A nstk data stack for volume stkvlm real KIND dp A nstk data stack for bond potential energy stkbe real KIND dp A nstk data stack for angle potential energy stkae real KIND dp A nstk data stack for dih
89. If bonds are dealt with locally only the bonds associated with the subdomain are calculated by each process otherwise all processes hold information on all bonds The Cartesian coordinates velocities and forces for the particles are each held in sets of three double precision arrays for x y and z components Particle positions relative to the volume modelled by the individual processor thus not absolute positions unless the serial version of DL_MESO_DPD is used are held in arrays xxx i yyy i and zzz i for particle i Particle velocities are held in vxx i vyy i and vzz i Three sets of arrays for the net forces acting on the particles are available fxx i fyy i and fzz i for forces that remain constant over each time step fvx i fvy i and fvz i for forces that may vary during the time step e g drag forces for DPD Velocity Verlet integration thermostatting force for Stoyanov Groot thermostat and fcfx i fcfy i and fcfz i for corrections to forces between frozen particles particularly long range electrostatic forces The particles modelled by a particular processor have both local and global identity numbers the latter of which are stored in the integer array lab i DL MESO_DPD assigns the lowest local identity numbers i e between 1 and nfbeads to the frozen particles in each processor s subdomain to avoid having to search for and skip over frozen particles during force integration steps while the highest gl
90. Lattice Boltzmann calculations and should not be modified fCollisionMRTGuoSegregation e Header records int fCollisionMRTGuoSegregation e Function Collision and segregation steps for all compressible and incompressible fluids using MRT model with Guo like forcing terms and Lishchuk mesophase interactions e Dependencies fSiteFluidCollisionMRTGuoSegregation fSiteFluidIncomCollisionMRTGuoSegregation fSiteSoluteCollisionBGK fSiteThermalCollisionBGK fGetOneMassSite fGetTotMassSite fGetSpeedSite fGetSpeedIncomSite e Comments This routine is fundamental to Lattice Boltzmann calculations and should not be modified fPropagationTwoLattice e Header records int fPropagationTwoLattice e Function Moves lattice particles distribution functions to neighbouring grid points using the two lattice algorithm e Dependencies None e Comments This routine is fundamental to Lattice Boltzmann calculations and should not be modified This is the least efficient propagation routine available fPropagationSwap e Header records int fPropagationSwap e Function Moves lattice particles distribution functions to neighbouring grid points using the swap algorithm 114 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Dependencies fSwapPair e Comments This routine is fundamental to Lattice Boltzmann calculations and should not be modified Propagation is carried out by systematic swapping of post collisional values for
91. OUTINE scan_config e Function Scans CONFIG file for dimensions of system unit cell e Dependencies CONFIG file getint getdble global_sca_and error e Arguments None read_control e Header records SUBROUTINE read_control e Function Reads in system data from CONTROL file 208 CHAPTER 13 e Dependencies CONTROL file getdble getint getword lowercase error global_sca_and e Arguments None scan_field e Header records SUBROUTINE scan_field e Function Scans FIELD file for numbers of interactions species etc including bonds e Dependencies FIELD file error global_sca_and getword lowercase getint getdble e Arguments None read_field e Header records SUBROUTINE read_field e Function DL_MESO_DPD PACKAGE REFERENCE and sets up arrays for all interaction data Reads in all species and interactions from FIELD file including bonded interactions and molecule config urations e Dependencies FIELD file getdble getint getword lowercase error global_sca_and e Arguments None 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 209 e Comments This routine will determine interaction parameters for species pairs not specified in FIELD file unless any interactions are many body DPD this requires all interaction species pairs to be specified elecgen e Header records SUBROUTINE elecgen e Function Sets up electrostatic parameters for self interaction and charged s
92. S AND FUNCTIONS 111 e Function Collision and segregation steps for all compressible and incompressible fluids using BGK model with Lishchuk mesophase interactions e Dependencies fSiteFluidCollisionBGKSegregation fSiteFluidIncomCollisionBGKSegregation fSiteSoluteCollisionBGK fSiteThermalCollisionBGK fGetOneMassSite fGetTotMassSite fGetSpeedSite fGetSpeedIncomSite e Comments This routine is fundamental to Lattice Boltzmann calculations and should not be modified fCollisionBGKGuo e Header records int fCollisionBGKGuo e Function Collision steps for all compressible and incompressible fluids using BGK model with Guo forcing terms e Dependencies fSiteFluidCollisionBGKGuo fSiteFluidIncomCollisionBGKGuo fSiteSoluteCollisionBGK fSiteThermalCollisionBGK fGetSpeedSite fGetSpeedIncomSite e Comments This routine is fundamental to Lattice Boltzmann calculations and should not be modified fCollisionBGKGuoSegregation e Header records int fCollisionBGKGuoSegregation e Function Collision and segregation steps for all compressible and incompressible fluids using BGK model with Guo forcing terms and Lishchuk mesophase interactions e Dependencies fSiteFluidCollisionBGKGuoSegregation fSiteFluidIncomCollisionBGKGuoSegregation fSiteSoluteCollisionBGK fSiteThermalCollisionBGK fGetOneMassSite fGetTotMassSite fGetSpeedSite fGetSpeedIncomSite 112 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Comments This routine
93. SerialDomainBuffer e Addition of fsBoundPeriodic and fMarkBoundArea immediately before fInitializeSystem e Addition of fsPeriodic inside main loop before calculating interaction forces it does not matter whether this is placed before or immediately after the call for creating output files e Addition of fsIndexPeriodic inside main loop before calculating interaction forces for the Lishchuk algorithm if these are not to be calculated this call can be omitted e Addition of fsForcePeriodic inside main loop after calculating interaction forces if these are not to be calculated this call can be omitted 5 2 Boundary conditions To apply boundary conditions to a Lattice Boltzmann Equation simulation the distribution functions f at boundary lattice points have to be modified or replaced during each time step to give the required fluid velocity or pressure concentration temperature This may take place either between the collision and propagation stages or at the end of each time step the subroutines fPostCollBoundary and fPostPropBoundary respectively are used to invoke the boundary conditions The space property lbphi is used to define the boundary conditions for each lattice node in the system 5 2 1 Periodic Periodic boundaries are used to simulate bulk fluids sufficiently far away from the actual boundaries of a real physical system so that surface effects can be neglected As the fluid moves out of one face of the system volume it
94. T cannot be found in the CONTROL file this is a compulsory parameter for DPD simulations Action Look in the CONTROL file and make sure the temperature directive is included with a non zero value Message 3 time step size not set A valid simulation timestep At cannot be found in the CONTROL file this is a compulsory parameter for DPD simulations Action Look in the CONTROL file and make sure the timestep directive is included with a non zero value Message 4 boundary halo size larger than half subdomain size The size of the boundary halo either specified by the user or determined from required interaction and bond lengths exceeds half the length of at least one dimension of the subdomain volume assigned to each processor The DPD simulation may therefore run less efficiently Action None required to ensure the simulation runs as this is a warning message but the user may wish to reduce the specified boundary halo size or use global bond calculations for future calculations Message 5 too many beads per node The number of particles likely to be assigned to each processor is greater than the calculated maximum value maxdim 231 232 APPENDIX C DL MESO_DPD ERROR MESSAGES Action This error is unlikely to happen as maxdim is calculated according to the numbers of particles and processors available but the user may wish to use the densvar directive in the CONTROL file to increase this value Message 10 cann
95. TER 7 DL MESO _LBE PACKAGE REFERENCE Function Outputs macroscopic mass density of fluid iprop and velocity speeds along x y and z directions at each lattice point for system in Structured Grid XML VTK format Dependencies fOutputVTKP2D fOutputVTKP3D Arguments filename input array of characters iprop input integer Comments The default output file name is lbout vts and the density of fluid 0 is output by default This can be changed by specifying an output file name and fluid number up to 1bsy nf 1 when calling the routine fOutputVTKCA e Header records int fOutputVTKCA const char filename 1bout int iprop 0 Function Outputs mass fraction of fluid iprop and speeds along x y and z directions at each lattice point for system in Structured Grid XML VTK format Dependencies fOutputVTKCA2D fOutputVTKCA3D Arguments filename input array of characters iprop input integer Comments The default output file name is 1bout vts and the mass fraction of fluid 0 is output by default These can be changed by specifying an output file name and fluid number up to 1bsy nf 1 when calling the routine fOutputVTKCB e Header records int fOutputVTKCB const char filename 1bout int iprop 0 e Function Outputs concentration of solute iprop and fluid velocity at each lattice point for system in Structured Grid XML VTK format e Dependencies fOutputVTKCB2D fOutputVTKCB3D e Arguments filename input
96. TK Contains subroutines to write calculation output files in Legacy VTK structured grid format 1bpIOVTK Contains subroutines to write calculation output files in XML VTK structured grid format e 1bpBOUND Contains subroutines for boundary conditions e g calculating the particle distribution function in a shear boundary e lbpFORCE Contains subroutines to calculate non constant forces e g immiscible fluid fluid interactions e 1bpSUB Contains the most important subroutines for Lattice Boltzmann calculations e g particle propagation and site collision e 1bpRUNx Contain the major program loops to carry out Lattice Boltzmann calculations 1bpRUNSER for serial running 1bpRUNPAR for parallel 61 62 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e 1bpMPI Contains all subroutines necessary for parallel computation This package can be left out if the user uses only a single processor workstation or a Windows PC It is recommended that DL_MESO users put self defined subroutines into a package called 1bpUSER so upgrades of DL_MESO will not interfere with their contributions 7 2 DL MESO LBE Subroutines and Functions 7 2 1 main There are two primary versions of the main DL_MESO_LBE program serial slbe cpp and parallel plbe cpp These provide calls to the main loops for Lattice Boltzmann calculations in 1bpRUN and allow the use of input files to select collision forcing and mesophase interaction algorithms as w
97. a utility written in C to gather Plot3D output files produced by the parallel version of DL_MESO_LBE and produce a single structure file lbtout xyz or 1btout xy and a single set of solution files Ibtout q for visualization of the entire system If c is the command for the available C compiler the executable plot3d exe can be produced by typing e c o plot3d exe lbeplot3dgather cpp and either run at the command line or via the GUI under Gather LBE Data All lbout xyz and lbout q files should be copied to the directory including the executable if necessary before running as well as the lbout info file to give information on the sizes of integers and floating point numbers No user input is required although the utility will stop with an error message if no 1bout info file is available No other error messages are produced so care should be taken to ensure no solution files are missing This utility can be run with a command line argument to give the scalar property required e g for Windows and Unix Linux computers respectively e plot3d exe 1 e plot3d exe 1 where 0 is used for all properties 1 for fluid density 2 for mass fraction 3 for solute concentration and 4 for temperature If the GUI is used this can be selected using the pulldown list in the Gather LBE Data panel If the argument is omitted the utility will ask the user to enter the required property No other user input is required but error messages
98. action types in this sub routine as additional cases this would also require changes to read_control in config_module bondforceslocal e Header records SUBROUTINE bondforceslocal e Function Calculates all bond stretching angle dihedral forces between particles in system using locally defined bond lists 188 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE e Dependencies shellsort_list search_list duplicate error global_sca_and bond_force angle force dihedral_force e Comments Assumes that bond lists contain only those bonds in the current node This is the most efficient method for parallel running but runs the risk of losing track of bonded pairs if bond lengths get longer than the subdomain halo size rhalo bondforcesglobal e Header records SUBROUTINE bondforcesglobal e Function Calculates all bond stretching angle dihedral forces between particles in system using globally defined bond lists e Dependencies shellsort_list search_list images error global_sum_dble global_sca_and bond_force angle_force dihedral_force e Comments Assumes that bond lists contain all bonds in the entire system This is less efficient for parallel running than only calculating the bonds in each node but ensures longer bond lengths can be accommodated 13 2 10 domain module This module requires the modules constants variables error_module comms_module if running parallel version and bond_module if running parallel v
99. ader records two cases 3D and 2D inline long fGetNodePosi int xpos int ypos int zpos inline long fGetNodePosi int xpos int ypos 68 e Function CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE Calculates the position of the grid point in a one dimensional array from its Cartesian coordinate e Dependencies None e Arguments xpos input ypos input zpos input fGetNodePosi output e Comments integer integer integer long integer The calculation follows the standard C data structure row major fGetCoord e Header records two cases 3D and 2D int fGetCoord long tpos int amp xpos int amp ypos int amp zpos int fGetCoord long tpos int amp xpos int amp ypos e Function Calculates the Cartesian coordinate of a grid point from its position in a one dimensional array e Dependencies None e Arguments xpos output integer reference ypos output integer reference zpos output integer reference tpos input long integer fGetOneMassSite e Header records three cases double fGetOneMassSite doublex startpos double fGetOneMassSite int fpos long tpos double fGetOneMassSite int fpos int xpos int ypos int zpos e Function Calculates the mass density of one of the fluids at a grid point e Dependencies None e Arguments startpos fpos tpos xpos ypos zpos fGetOneMassSite input input input input input input double pointer integer long integer integer
100. airs that are to be subjected to the Nos Hoover thermostat an additional thermostatting force is included Y kpT Fi ow rij 1 a vig gt ij ei 11 16 with a as a system wide thermostat coupling parameter and w rij as a switching function which by default is equivalent to w rij 1 Tii for standard DPD All other particle pairs are thermostatted using the standard Lowe Andersen method A virial correction of FF Tij is also made for each particle pair This thermostat can produce a wide range of system viscosities and diffusivities with good temperature control and hydrodynamics using the collision frequency I to obtain the required Schmidt number The replicated data strategy is again used for the Lowe Andersen part which requires memory in each processing unit to store the velocities of all particles and the data for particle pair modification using the Lowe Andersen scheme the Nos Hoover scheme calculates the thermostatting forces locally 11 3 Barostats In addition to a thermostat a barostat may be included in simulations to obtain a desired average pressure Po by adjusting the size and shape of the simulation cell DL_MESO_DPD includes two such algorithms a Langevin type barostat 29 and the Berendsen barostat 2 both of which have been coupled to all five available thermostats The isotropic pressure in a system is calculated using the virial theorem P t 70 2 mito DAO 0 11 17 while for an
101. airwise forces calculated plcfor_ The time taken to calculate the forces is determined timchk The second stage of the integrator is applied to calculate the velocities at the end of the time step This may include e g recalculation of dissipative forces or resizing of the system for a barostat Statistical properties for the system are calculated and during equilibration the particle velocities are rescaled for the specified temperature statis After every nsbpo time steps the system clock is consulted timchk and statistical data is printed to the OUTPUT file printout If equilibration has come to an end i e nstep nseql this is also reported equilout If requested by the user after every iscorr time steps statistical data is written to the CORREL file corout and after every ntraj time steps trajectory data is saved to the HISTORY or HISTORY file s The step time is calculated timchk and if the allocated time has expired the job is closed down otherwise restart data is saved revive After all the time steps have been calculated or the allocated time has elapsed The final calculation summary is printed to the OUTPUT file result The duration of the calculation run is determined and printed timchk All remaining output channels for OUTPUT HISTORY files are closed For parallel running only MPI communications are closed down exitcomms 13 2 2 numeric_container This package contains general pu
102. ajectory file export vtf from DL_MESO_DPD restart files export that can be visualized to give a snapshot of the last simulation timestep B 2 DL MESO DPD 229 Since a limited amount of data is included in restart files the FIELD file for the simulation is needed to provide some additional information The source code for this utility exportimage f90 can be used for export or export files created by both the serial and parallel versions of DL_MESO_DPD their endianness is automatically detected so the utility can be run on a different machine to the one used for DPD calculations If the available Fortran90 compiler is invoked by the command 90 the executable export exe can be produced by typing e 90 o export exe exportimage f90 and either run at the command line or by using the GUI in Process DPD Data This utility can be run with a command line argument indicating the number of processes used to generate the restart data e g if 16 processes were used either of the following commands can be used e export exe 16 e export exe 16 If no command line argument is given the utility will ask the user to type in the number of processes The number of processes can be specified in the GUI before running the utility traject The Fortran90 utility traject reads in HISTORY output data files generated by DL_MESO_DPD and produces a VTF format trajectory file traject vtf that can visualize the simulation after equilibra
103. al and Engineering Sciences 360 1792 437 451 2002 U D Ortona D Salin Marek Cieplak Renata B Rybka and Jayanth R Banavar Two color nonlinear Boltzmann cellular automata Surface tension and wetting Physical Review E Statistical Physics Plasmas Fluids and related interdisciplinary topics 51 4 3718 3728 April 1995 Burkhard Diinweg and Wolfgang Paul Brownian dynamics simulations without Gaussian random numbers International Journal of Modern Physics C 2 3 817 827 1991 U Frisch B Hasslacher and Y Pomeau Lattice gas automata for the Navier Stokes equation Physical Review Letters 56 14 1505 1508 April 1986 A Ghoufi and P Malfreyt Mesoscale modeling of the water liquid vapor interface A surface tension calculation Physical Review E 83 051601 May 2011 J B Gibson K Chen and S Chynoweth The equilibrium of a velocity Verlet type algorithm for DPD with finite time steps International Journal of Modern Physics C 10 1 241 261 February 1999 Minerva Gonz lez Melchor Estela Mayoral Maria Eugenia Vel zquez and Jos Alejandre Electro static interactions in dissipative particle dynamics using the Ewald sums Journal of Chemical Physics 125 22 224107 2006 R D Groot Electrostatic interactions in dissipative particle dynamics simulation of polyelectrolytes and anionic surfactants Journal of Chemical Physics 118 24 11265 11277 2003 247 248 16 17 18 19 20 21
104. ameter data type notation many body DPD cutoff radius rg rmbcut real KIND dp square of many body DPD cutoff radius rmbct2 real KIND dp short range electrostatic cutoff re relec real KIND dp square of electrostatic cutoff rel2 real KIND dp surface cutoff length ze srfzcut real KIND dp square of surface cutoff length sr zct2 real KIND dp maximum calculation time timjob real KIND dp calculation close time tclose real KIND dp system volume volm real KIND dp size of system in x dimension dimx real KIND dp size of system in y dimension dimy real KIND dp size of system in z dimension dimz real KIND dp size of unit cell in z dimension dimxcell real KIND dp size of unit cell in y dimension dimycell real KIND dp size of unit cell in z dimension dimzcell real KIND dp number of domain cells in x npx integer gt 1 number of domain cells in y npy integer gt 1 number of domain cells in z npz integer gt 1 list of neighbouring processes map integer A6 x position of domain cell idx integer y position of domain cell idy integer z position of domain cell idz integer position of domain cell origin in system volume x dimension delx real KIND dp position of domain cell origin in system volume y dimension dely real KIND dp position of domain cell origin in system volume z dimension delz real KIND dp domain cell length in x direction sidex real KIND dp domain cell length in y direction sidey real KIND dp domain c
105. an and unit variance The constant o is related to the temperature as is understood from the role of the stochastic force in representing a heat bath Finally the particles are subject to a drag force which depends on the relative velocity between interacting pairs of particles 2 Pere FR qijw riz Fig Ui T 9 7 ij where w r j is once again a switching function and vj vj vj The constant 7 is the drag coefficient It follows from the fluctuation dissipation theorem that for thermodynamic equilibrium to result from this method the following relations must hold oj 2yijkBT 9 8 2 w rij w ri5 9 9 In practice the switching functions are defined through w rig 1 a rij lt re 9 10 9 3 EQUATION OF STATE AND DYNAMIC PROPERTIES 129 which ensures that all interactions are switched off at the range rij re In many DPD simulations the stochastic and drag coefficients are often constant for all interactions i e oij 0 and yi y although this assumption does not have to apply 9 3 Equation of state and dynamic properties The form of the conservative force determines the equation of state for a DPD fluid which can be derived using the virial theorem to express system pressure as follows 1 Li p pkaT 35 Es Fy is 9 11 j gt i pkgT se f rA 1 g r r dr 9 12 0 Te where g r is a radial distribution function for the soft sphere model 16 and p is the DP
106. and standard Plot3D data format in binary format for parallel calculations and ANSI for serial These may be modified by the user as required The utility lbeplot3dgather in the LBE utility directory can combine Plot3D files generated in parallel while Parallel Structured Grid XML VTK files lbtout pvts that refer to the files from each processor can be created using the utility lbevtkgather further details can be found in Appendix B or the README file in the same directory By default all properties for a simulation fluid densities mass fractions solute concentrations and temperatures are written to each output file or to individual output files for Plot3D for each property The customizable version of DL MESO_LBE allows users to select which properties should be written to output files 6 2 OUTPUT FILES 59 Structured Grid XML VTK format lbout vts Structured Grid VTK files written by DL MESO_LBE include the lattice dimensions numbers of grid points in each direction the Cartesian coordinates of the grid points in real life units and the same data as in Legacy VTK files Output files produced in serial include the data between XML tags e g lt DataArray gt while those produced in parallel use the lt DataArray gt tags to refer to the starting point for the data in a stream of binary numbers inside an lt AppendedData gt tag The latter files represent the data in each subdomain and should be retained when plotting the entire
107. and edited afterwards using the text editor option described above 2 3 2 1 Species interactions and external field parameters Examples of the pop up windows for species non bonded interactions and external field parameters can be seen in Figure 2 8 with the rows labelled in red numbering The species pop up window is formatted as in Figure 2 8 a with individual columns for each species 1 The name of each species which can be up to 8 characters long 2 The mass of a particle for the species m 3 The charge of a particle for the species q 4 The number of unbonded particles of the species population unbonded in the system 5 The tickbox indicates whether or not the particles for the species should be frozen 2 3 DISSIPATIVE PARTICLE DYNAMICS AND THE DL_MESO GUI 17 species i 1 Aij 250 3 species j SPEC v Bij interaction type DPD 7 Cij Dij TE bpp species properties abe Eli species 1 interaction length 1 0 4 name SPECl 1 1 dissipative collision parameter 4 5 5 mass 1 0 2 E 0 0 rane paare oo 3 wall species 6 population unbonded 0 4 wall density Tf frozen wall thickness wall repulsion parameter 6 A E 8 SAVE SP CANCEL SP SELL SAVE I CANCEL a Species parameters b Non bonded interaction parameters EJ DPD external field properties SAIA GRAVITATIONAL F
108. and stress tensors that are required to exclude interactions between charged frozen particles these corrections only need to be calculated once if the volume is held constant and thus the frozen particles do not move but have to be recalculated at each time step if a barostat is applied This method can be invoked by using the directives ewald permittivity and smear in the CONTROL file the first is used to set the real space convergence parameter a and k space vector range the second to set the permittivity coupling constant T and the third with the keyword slater used to set the smearing coefficient B 11 6 Bond interactions between particles Molecules of particles bonded together can be included in calculations using a FIELD file to define the properties and topologies of the bonds angles and dihedrals between them These data are used in the start subroutine to add the specified numbers of molecules into the system before DPD calculations commence and to create tables listing the particles that are included in bonds angles and dihedrals 11 6 1 Stretching bonds DL_MESO_DPD can model four forms of bond potential and corresponding force between specified particles all of which are functions of the distance between them The available bond forms between particles and j are as follows 1 Harmonic Hookean Fraenkel bond U rij 5 rij ro 11 63 2 Shifted Finitely Extendible Non linear Elastic FENE bond
109. ange repulsion between species and wall while if frozen bead surfaces are in use the surface directive should be followed by a single line specifying the properties for the walls to be constructed 12 1 INPUT FILES 163 name a8 name of frozen bead species Pwall real density of frozen beads in wall regions Lwall real thickness of wall region External fields are flagged by the directive external followed by a line with a keyword indicating the type of field to be applied and the field parameters A gravitational field can be specified using the keyword grav and three real values representing the x y and z components of gravitational acceleration i e grav Gr Gy Gz If using the Lees Edwards shearing boundary condition the velocity of the walls in dimension a can be specified using the keyword shear and three real values representing the x y and z components for the velocity at Za La i e shear Via Voy Vw z Note that the velocity at a 0 will be equal in magnitude but opposite in direction and that the velocity component for dimension a will be ignored The FIELD file must be closed with the directive close If molecules are to be included in the system the supplied C program molecule generate in the directory DPD utility can be used to either create a new FIELD file with the required data or append it to a pre existing file see Appendix B for more details Example files in the DEMO DPD directory can be examined for this
110. any other way out of the subject matter of this Licence Agreement or the use of the DL_MESO Software will not exceed in total 5000 Nothing in this Licence Agreement limits or excludes STFC s liability for death or personal injury caused by its negligence or for any fraud or for any sort of liability that by law cannot be limited or excluded The express undertakings and given by STFC in this Licence Agreement and the terms of this Licence Agreement are in lieu of all warranties conditions terms undertakings and obligations on the part of STFC whether express or implied by statute 243 common law custom trade usage course of dealing or in any other way All of these are excluded to the fullest extent permitted by law 4 INTELLECTUAL PROPERTY RIGHTS AND ACKNOWLEDGEMENTS 4 1 4 2 5 2 5 3 5 4 Nothing in this Licence Agreement assigns or transfers any Intellectual Property Rights in any of the DL_MESO Software Those rights are reserved to STFC The Licensee will ensure that if any of its employees or students publishes any article or other material resulting from or relating to a project or work undertaken with the assistance of any part of the DL_MESO Software that publication will contain the following acknowledgement DL_MESO is a mesoscale simulation package written by R Qin W Smith and M A Seaton and has been obtained from STFC s Daresbury Laboratory via the website http www ccp5 ac
111. array of characters iprop input integer 7 2 DL MESO _LBE SUBROUTINES AND FUNCTIONS 85 e Comments The default output file name is 1bout vts and the concentration of solute 0 is output by default These can be changed by specifying an output file name and solute number up to 1bsy ns 1 when calling the routine fOutputVTKT e Header records int fOutputVTKT const char filename lbout e Function Outputs macroscopic temperature and fluid velocity at each lattice point for system in Structured Grid XML VTK format e Dependencies fOutputVTKT2D fOutputVTKT3D e Arguments filename input array of characters e Comments The default output file name is lbout vts This can be changed by specifying an output file name when calling the routine Other output routines Subroutines with names fsOutput are suitable for serial running and produce output files for entire systems Unlike the routines listed above these omit any domain boundary lattice points used in calculations Notes regarding q vtk and vts files e lboutzx is the q vtk or vts file at the th saved step during serial running e lboutyatxz is the q vtk or vts file at the xth saved step written by processor y during parallel running e lbout files produced using multiple processors will require gathering or simultaneous plotting see Ap pendix B for more details 7 2 9 IbpBOUND fNextStep e Header records three cases 3D 2D and coord
112. art file s export Each processing unit produces a restart file with a name beginning with export every ndump time steps This binary file contains the following information for the time step e Name of DPD calculation e Numbers of particles bonds angles and dihedrals in the processing unit e Specified temperature number of time steps system volume 12 2 OUTPUT FILES 165 e Current state of random number generators e Particle global identity numbers species and molecule numbers e Bond angle and dihedral tables e Particle Cartesian coordinates velocities forces and virials e Current time step and statistical properties current values cumulative sums and fluctuations rolling averages and stacks In combination the export files can restore a stopped DPD calculation They can also be used to generate a plot at the given time step or a CONFIG file for subsequent simulations using the utilities exportimage and exportconfig respectively in the DPD utility directory Appendix B gives instructions for their use Trajectory file s HISTORY If the trajectory option is specified in the CONTROL file each processing unit will generate a trajectory file with a name beginning with HISTORY every ntraj time steps starting from timestep straj Each binary file contains some of the system properties including an identity number for each molecule followed by the positions and velocities for each particle in the domain
113. ation double startpos double sitespeed double bodyforce double phaseindex e Function Calculates collisions and phase segregation for the Lishchuk algorithm at a grid point using the Bhatnagar Grook Krook BGK model with the Guo forcing term for incompressible fluids e Dependencies fGetAllMassSite fGetTotMassSite fReciprocal fGetEquilibriumFIncom e Arguments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer phaseindex input double pointer e Comments Collisions are carried out on a single achromatic fluid using the BGK single relaxation time 4 with the Guo forcing term 19 also acting on the achromatic fluid fluid segregation takes place using the D Ortona algorithm 9 pa ae ae ab PEL fi z t fi Zt 58 Wi z i Nab P ba P fSiteFluidCollisionMRT e Header records int fSiteFluidCollisionMRT double startpos double sitespeed double bodyforce e Function Calculates collisions at a grid point using Multiple Relaxation Time MRT models for compressible fluids e Dependencies fGetOneMassSite fGetSpeedSite fGetMomentEquilibriumF fGetMRTCollide 106 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Arguments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer e Comments Collisions for each fluid species are carried out using multiple relaxation time MRT schemes 33 8 Os eia a fi T7
114. ational Journal for Numerical Methods in Fluids 43 2 183 198 2003 73 Qisu Zou and Xiaoyi He On pressure and velocity boundary conditions for the lattice Boltzmann BGK model Physics of Fluids 9 6 1591 1598 June 1997
115. ative mesoscale algorithms can be added by the user fInteractionForceShanChen e Header records int fInteractionForceShanChen e Function Calculates interaction forces for all fluids based on the Shan Chen model 55 56 e Dependencies fCalcInteraction_ShanChen e Comments The interaction potentials need to be calculated prior to calling this routine Alternative mesoscale interactions can be applied using similar routines 94 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE fInteractionForceShanChen Wetting e Header records int fInteractionForceShanChenWetting e Function Calculates interaction forces for all fluids based on the Shan Chen model 55 56 with additional wetting forces 41 e Dependencies fCalcInteraction_ShanChenWetting e Comments The interaction potentials need to be calculated prior to calling this routine Alternative mesoscale interactions can be applied using similar routines fCalcPhaseIndex_Lishchuk e Header records int CalcPhaseIndex_Lishchuk e Function a b Calculates phase indices pn ae and first order spatial derivatives Vp for all unlike fluid pairs storing the latter for future use e Dependencies fGetOneMassSite e Comments The Lishchuk model is detailed in 35 20 fCalcInteraction_Lishchuk e Header records int fCalcInteraction Lishchuk int xpos int ypos int zpos e Function Calculates particle interaction forces according to Lishchuk model e A
116. ature at front boundary sets rate of change in temperature at back boundary sets thermal relaxation time 7 sets thermal relaxation frequency 7 sets constant external body force on fluid f n 3f for c component n 3f 1 for y component n 3f 2 for z component sets x component of constant external body force on fluid f sets y component of constant external body force on fluid f sets z component of constant external body force on fluid f sets Boussinesq force constant g8 for fluid f n 3f for z component n 3f 1 for y component n 3f 2 for z component sets z component of Boussinesq force constant 7 8 for fluid f sets y component of Boussinesq force constant g8 for fluid f sets z component of Boussinesq force constant gf for fluid f sets high reference temperature for Boussinesq convection Th sets low reference temperature for Boussinesq convection T sets interaction parameter between fluids f and fo n 1bsy nf x f f2 sets interaction parameter between fluids f and fa sets fluid segregation parameter between all fluids species sets fluid segregation parameter between fluids f and fo n lbsy nf x fi fo sets fluid segregation parameter between fluids f and fa The GUI is recommended for creating the 1bin spa file which stores the data in the following format 58 CHAPTER 6 DL_MESO_LBE INPUT AND OUTPUT FILES X y Z grid property An empty lbin spa file represents all boundaries as peri
117. be used to specify other information such as fluid densities velocities relaxation times or frequencies etc Superfluous parameters can be omitted while new ones would require additions to the parameter recognition loop in the fInputParameters subroutine in 1bpIO Note that if there are duplicate entries for any keyword the value associated with the last one in the 1lbin sys file will be used keyword total_step equilibration_step save_span noise_intensity evaporation_limit sound_speed kinetic_viscosity total_step speed_ini_n speed_top_n speed_bot_n speed_lef_n speed_rig_n speed_fro_n speed_bac_n density _ini_f density_inc_f density_top_f density_bot_f density _lef_f density_rig_f density_fro_f density_bac_f relaxation fluid_f relax _freq_fluid_f meaning sets total number of timesteps for the simulation sets number of timesteps for equilibration of the simulation without solid boundary conditions or external forcing sets interval for writing output files gives maximum variation in initial fluid densities for multiple fluid systems gives minimum fluid density for non continuous fluids when dealing with edge or corner boundaries sets speed of sound for fluid 0 in real life i e non lattice based units sets kinematic viscosity for fluid 0 in real life units sets total number of timesteps for the simulation sets initial velocity for all fluids n 0 for x component n 1 for y component n
118. ble A lbsy nf bulk fluid inverse relaxation time 77 hulk Lbtfbulk double A lbsy nf solute inverse relaxation time 1 lbtc double A lbsy nc temperature inverse relaxation time 7 1btt double A lbsy nt fluid fluid interaction parameter gas lbg double A lbsy nf lbsy nf fluid wall interaction parameter ga wail lbgwall double A lbsy nf fluid segregation parameter 8 lbseg double A lbsy nf 1bsy nf body force lbbdforce double A 3 lbsy nf Boussinesq force 78 lbbousforce double A 3 lbsy nf interaction force lbinterforce double A 3x 1bsy nf 1bdm touter distribution function 1bf double A lbsitelength lbdm touter temporary function 1bft double A 1bdm touter lbsy nf lbsy nc equilibrium distribution lbfeq double A lbsy nq space property lbphi int A lbdm touter neighbouring point property lbneigh int A 6 1bdm touter speed vector for the model lbv int A 3 lbsy nq index for opposing speed lbopv int A lbsy nq weight factor of speed vector lbw double A lbsy nq MRT transformation matrix lbtr double A lbsy nq lbsy nq MRT inverse transformation matrix lbtrinv double A lbsy nq lbsy nq MRT tuneable collision parameters lbmrts double A3 MRT tuneable equilibrium parameters 1bmrtw double A3 number of parameters per grid point lbsitelength int number of grid points in yz plane lbyz int grid spacing 1bdx double time step 1bdt double speed of sound lbsoundv double Reynolds number lbreynolds double pro
119. ble pointer v input double pointer tem input double precision e Comments The equilibrium distribution function calculated here is het wT f ds mm c using the velocity of the bulk fluid 27 This subroutine can be changed for other Lattice Boltzmann models e g 23 fGetMomentEquilibriumF e Header records int fGetMomentEquilibriumF double meq double p double rho e Function Calculates equilibrium distribution function in moment space for compressible fluid 100 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Dependencies None e Arguments meq output double pointer p input double pointer rho input double precision e Comments The equilibrium distribution function in moment space calculated here is Mea T the exact form of which is dependent on the lattice scheme given for D2Q9 by 33 and for D3Q15 and D3Q19 by 8 Parameters for calculating the square of energy e and fourth order moments Taa can be modified by the user in the 1bpMODEL module fGetMomentEquilibriumF Incom e Header records int fGetMomentEquilibriumFIncom double meq double p double rho double rho0 e Function Calculates equilibrium distribution function in moment space for incompressible fluid e Dependencies None e Arguments meq output double pointer p input double pointer rho input double precision rho0 input double precision e Comments The equilibrium distribution function in moment space calculated here
120. briumFIncom fGetMomentForce fGetMRTCollide 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS 109 e Arguments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer e Comments Collisions are carried out using multiple relaxation time MRT schemes coupled with Guo like forcing terms 49 81 eia a fi T7 3 TF Met 1 413 fSiteFluidIncomCollisionMRTGuoSegregation e Header records int fSiteFluidIncomCollisionMRTGuoSegregation double startpos double sitespeed double bodyforce double phaseindex e Function Calculates collisions and phase segregation for the Lishchuk algorithm at a grid point using Multiple Relaxation Time MRT models coupled with Guo like forcing terms for incompressible fluids e Dependencies fGetAllMassSite fGetTotMassSite fReciprocal fGetMomentEquilibriumFIncom fGetMomentForce fGetMRTCollide e Arguments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer phaseindex input double pointer e Comments Collisions are carried out on a single achromatic fluid using multiple relaxation time MRT schemes coupled with Guo like forcing terms 49 fluid segregation takes place using the D Ortona algorithm 9 p pep Pat A Bw s fab P Za P fSiteSoluteCollisionBGK e Header records int fSiteSoluteCollisionBGK double startpos double sitespeed e Function Calculates solute collisions at a
121. ce back type x0 obstacle type yo z0 add obstacle SET AS POROUS MEDIA bounce back type pore fraction 0 8 Figure 2 4 Set LBE Space e fixed V velocity C concentration and T temperature e fixed V and C Neumann T e fixed V and T Neumann C e fixed V Neumann C and T e fixed P pressure or density C and T e fixed P and T Neumann C e fixed P and C Neumann T e fixed P Neumann C and T 2 The bottom boundary condition can be selected using the pull down list 3 The left boundary condition can be selected using the pull down list 4 The right boundary condition can be selected using the pull down list 5 The front boundary condition can be selected using the pull down list This pull down list will be greyed out for two dimensional systems 6 The back boundary condition can be selected using the pull down list This pull down list will be greyed out for two dimensional systems 7 Solid obstacles can be added to the calculation space by selecting the bounce back on grid or mid grid and obstacle types in the pull down lists entering its location on the grid and if necessary entering its size and clicking add obstacle e A single point will be located at x0 y0 z0 e A sphere is centred at x0 yO z0 and has radius r e A two dimensional circle is centred at x0 y0 and has radius r lFor a property DL MESO currently only calculates V 0 by using on grid bounce back on
122. ce code e JAVA containing the GUI source code e MAN containing the DL_MESO user manual e DEMO containing test cases for DL_MESO e WORK an example working directory 1 5 Disclaimer Neither STFC CCP5 nor any of the authors of the DL_MESO package guarantee that the package is free from error Neither do they accept responsibility for any loss or damage that results from its use 1 6 Copyright STFC Daresbury Laboratory 2012 1 7 Authors Dr Michael Seaton and Prof William Smith Scientific Computing Department STFC Daresbury Laboratory Warrington WA4 4AD United Kingdom 1 8 Suggestions and Bug Reports We encourage users to send suggestions for improvements and new features for DL_MESO including bug reports and subroutines as well as any additional test cases that demonstrate its features All of these should be sent to michael seaton stfc ac uk Chapter 2 The DL MESO GUI 2 1 Getting Started with the DL MESO GUI The DL_MESO GUI offers a convenient way of using the DL_MESO package although it is not an essential tool for those who prefer command line operation Appendix A provides details on compiling the DL_MESO program codes manually Working with the GUI requires the availability of Java tools particularly the javac compiler and the java runner for Java 2 version 1 4 or later These may be obtained from the java sun com website To build the GUI proceed as follows e Enter the DL_MESO JAVA d
123. ce links are organised so that the conjugate link j to link i e j is equal to a mt fori 1 m Looping i between 1 and m the post collisional distribution functions for each lattice point f Z are initially swapped with their conjugate values f 7 then at each point the value f 1 is then swapped with f 1 At These sets of swaps can be carried out either in two separate steps or in one go The use of separate swap steps requires two sweeps through the domain but the order in which the distribution functions are swapped does not matter and no boundary domain is necessary for serial calculations Simultaneous swapping cannot make use of automatic periodic boundary conditions thus a non zero domain boundary is required and requires lattice links to be additionally ordered so that the first half are all directed to lattice points that have previously gone through at least the first swap stage but only a single sweep through the domain is required By default the serial version of DL MESO LBE uses the propagation routine that carries out two separate swap steps fPropagationSwap while the parallel version uses the combined swap propagation routine fPropagationCombinedSwap If the user wishes to use the combined swap propagation routine in serial an alternative program slbecombine cpp is available which includes the following notable modifications to slbecustom cpp e Replacement of fSetSerialDomain with fSet
124. ceives data in the form of a double precision array buf 176 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE e Dependencies None e Arguments buf output array of real KIND dp msgtag input integer length input integer msg_receive_unblocked output integer e Comments Since no scalars are received in non blocking calls no scalar version of this function exists msg_send_blocked e Header records SUBROUTINE msg_send_blocked msgtag buf length pe e Function In a blocking call send data from a double precision array buf e Dependencies None e Arguments buf input array of real KIND dp msgtag input integer length input integer pe input integer e Comments For a double precision scalar the alternative SUBROUTINE msg_send_sca_blocked msgtag buf length pe is available msg_wait e Header records SUBROUTINE msg_wait request e Function Causes process to wait for an unblocked message e Dependencies None e Arguments request input integer mynode e Header records INTEGER FUNCTION mynode e Function Returns name of process 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 177 Dependencies None e Arguments mynode output integer e Comments The serial version of this function returns 0 numnodes e Header records INTEGER FUNCTION numnodes e Function Returns total number of processes available e Dependencies None e Arguments numnodes output integer
125. ces Lees Edwards shearing 192 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE import_shear e Header records SUBROUTINE import_shear nlimit mdir begin final shove shovel shove2 sidel side2 e Function Imports particle forces from boundary halos for integration schemes and thermostats that only require one set of forces to be calculated and Lees Edwards shearing e Dependencies error msg_receive_unblocked msg_receive_sca_blocked msg_send_blocked msg_send_sca_blocked msg_wait e Arguments nlimit input output integer mdir input integer begin input real KIND dp final input real KIND dp shove input real KIND dp shovel input real KIND dp shove2 input real KIND dp sidel input real KIND dp side2 input real KIND dp e Comments Only exists in parallel version of DL_MESO_DPD This routine is suitable for thermostats using the standard Velocity Verlet algorithm for force integration and one set of forces this includes the DPD thermostat with MD integration MD VV the Lowe Andersen and Peters thermostats This routine requires information for the two dimensions along the surface of the shearing boundary the variables shovel and shove2 represent the displacement due to shear while side1 and side2 are the domain dimensions importvariable e Header records SUBROUTINE importvariable nlimit mdir mp begin final shove first skip e Function Imports particle forces from boundary halo for integration sc
126. cessor name lbdm rank int total number of processors lbdm size int x coordinate for domain 1bdm xcor int y coordinate for domain 1bdm ycor int z coordinate for domain 1lbdm zcor int number of processors along x axis 1bdm xdim int number of processors along y axis 1bdm ydim int number of processors along z axis 1bdm zdim int x coordinate of domain start position 1bdm xs int x coordinate of domain end position 1bdm xe int y coordinate of domain start position lbdm ys int y coordinate of domain end position lbdm ye int z coordinate of domain start position lbdm zs int z coordinate of domain end position lbdm ze int inner grid points along x 1bdm xinner int 2Excluding boundary points 4 3 THE PARAMETERS AND THEIR FUNCTIONS Table 4 8 DL_MESO_LBE Parameters continued 43 function parameter data type notation outer grid points along x 1bdm xouter int inner grid points along y 1bdm yinner int outer grid points along y 1bdm youter int inner grid points along z 1bdm zinner int outer grid points along z 1bdm zouter int total grid points 1bdm touter int name of neighbouring processor 1bnb rank int position for sending distribution message 1bnb spos unsigned long position for receiving distribution message lbnb rpos unsigned long position for sending boundary message lbnb bspos unsigned long position for receiving boundary message lbnb brpos unsigned long position for send
127. collisional moments are determined by relaxation of the non equilibrium part i e M t M d t A M E t M 4 z t 5 5 where A is the collision matrix which takes the form of a diagonal matrix of m collision parameters represented by 5 A diag s 5 6 Some of the collision parameters can be specified by the user to set both kinematic and bulk viscosities a few others can be tuned to improve simulation stability and the remainder i e those for density and momentum are fixed to conserve macroscopic hydrodynamics If all values of s are set to a the scheme reduces to BGK single relaxation time collisions Since the collisional matrix is diagonal equation 5 5 can be rewritten in terms of each moment i e Mi amp t M E t s M E t ME E 0 5 7 2 Multiplying M Z t by the inverse of the transformation matrix T gives the post collisional distribution functions Interfacial and external forces can be applied either by the addition of rF to the fluid momentum 41 or by the use of a moment transformed source term S whose terms are defined by 49 s u EAF 5 8 and applied by the following to correct the post collisional moments AM I A SAt 5 9 where I as an identity matrix The above equation can be re expressed as AM 1 tsi S At 5 10 The above equations after inverse transformation reduce to equation 5 2 when the collision parameters are set to a All colli
128. coupling parameter a and Langevin barostat with relaxation time f and viscosity parameter fa select NPT ensemble thermostat type Q with Berendsen barostat setting ratio of compressibility to relaxation time to f select NPT ensemble Stoyanov Groot thermostat with coupling parameter o and Berendsen barostat with compressibility relaxation time ratio f equilibrate system for the first n timesteps default n 0 calculate electrostatic forces using Ewald sum with real space convergence pa rameter and reciprocal space k vector range k1 ka k3 close the CONTROL file last data record calculate bonded interactions globally by storing bond data on all processors and sharing bonded particle positions default calculate bonded interactions locally set maximum job time to f seconds set required many body DPD interaction radius rg to f length units default f e write restart data to export files every n timesteps default n 1000 option to create volumetrically expanded version of current system described by CONFIG and FIELD files by replicating CONFIG file s contents i j k times while preserving topology of FIELD file ignore contents of CONFIG file and create initial configuration based purely on FIELD file ignore electrostatics in simulation ignore particles indices as read from CONFIG file and set their indexing accord ing to order of reading switch off isotropy for barostat i e allow uneven contractions and e
129. cubic or orthogonal or whether replication of a CONFIG file is required nfold If specifying a cubic volume the total volume should be specified while orthogonal volumes require the sizes for all three dimensions and the nfold setting requires integer values specifying the number of replications in each dimension The target temperature kgT and pressure Pp for the system The latter is greyed out if no barostat is to be used The maximum interaction cutoff re for pairwise particle interactions and the many body cutoff ra for determining localized particle densities as used for many body DPD If required the electrostatic cutoff re for short range electrostatic interactions and the surface cutoff zc for interactions between particles and solid walls These are greyed out if not required The size of the boundary halo for copying particle data from neighbouring subdomains or across periodic boundaries and the size of each time step At for integrating the equations of motion The total steps required for the DPD simulation and the number of time steps required to equilibrate the system equilibration steps 2 3 10 11 12 13 14 15 16 17 18 DISSIPATIVE PARTICLE DYNAMICS AND THE DL_MESO GUI 13 The numbers of time steps to store system variables for rolling averages stack interval and between rescaling of particle velocities to the desired system temperature duri
130. domain along y axis nlz number of link cells in domain along z axis wdthx link cell size in x dimension wdthy link cell size in y dimension wdthz link cell size in z dimension nlewx number of electrostatic link cells in domain along x axis nlewy number of electrostatic link cells in domain along y axis nlewz number of electrostatic link cells in domain along z axis wdthewx electrostatic link cell size in x dimension wdthewy electrostatic link cell size in y dimension wdthewz electrostatic link cell size in z dimension Table 10 3 Neighbour information parameter meaning map k processor name of neighbour k k 1 left neighbour k 2 right neighbour k 3 lower neighbour k 4 upper neighbour k 5 back neighbour k 6 front neighbour Bond angles and bond dihedrals are stored in similar tables angtb1 i j particles j from 1 to 3 angle type at j 4 and dhdtb1 i j particles j from 1 to 4 dihedral type at j 5 respectively using the second particle in each triple or quadruple as the reference particle Prior to force calculations a list of bonded particles in each process domain and if calculating bond forces locally the surrounding boundary halo is constructed lblclst i j to allow DL_MESO_DPD to find the local number for a particle j 2 from its global number j 1 using a binary search This list may include duplicates for the same global particle number the local numbers giving the shortest distance between pairs of
131. ds i too many few The total number of particles assigned to all processors for a new simulation does not match up with the numbers specified in the FIELD file taking nfold duplication into account if a CONFIG file is used Action For simulations without CONFIG files this error should never occur and the authors of DL_MESO should be contacted if it does If using a CONFIG file check the FIELD file to ensure that the number of particles for each species and numbers of molecules match up with those in the CONFIG file Message 52 cube for molecule i bigger than domain The maximum extent of molecule i which is represented as a cube is larger than the defined size of the system This is particularly important for systems with hard surfaces or frozen walls as molecules cannot cross these boundaries Action If running a simulation with hard surfaces or frozen walls either the system size must be increased to accomodate the defined molecule or the molecule needs to be made smaller If running a simulation without hard surfaces or frozen walls this is only a warning message no action is thus required but the user may wish to consider modifying either the system or molecule sizes in future Message 53 insufficient number of beads per node allocated for required CONFIG file The value of maxdim is not large enough to include the particles assigned to each processor for a new simulation with a CONFIG file Action This error is unlikely
132. e boundary The fluid velocity at the lattice point given by the array uwall is required for this boundary condition fFixed Temperature e Header records int fFixedTemperature long tpos int prop double uwall e Function Calculates the particle distribution function at a fixed temperature boundary e Dependencies Many for different lattice schemes e Arguments tpos input long integer prop input long integer uwall input array of doubles e Comments Planar surface calculations are based on 28 concave edges and corners assume zero speed at the boundary The fluid velocity at the lattice point given by the array uwal1 is required for this boundary condition fPostCollBoundary e Header records int fPostCollBoundary e Function Calculates the particle distribution function at different boundaries after the collision step prior to prop agation e Dependencies Many for different lattice schemes e Comments Algorithms for other boundary conditions can be added by the user although care should be taken as to when they are applied in each time step the conditions invoked in this routine are applied to post collisional distribution functions before propagation takes place fPostPropBoundary e Header records int fPostPropBoundary e Function Calculates the particle distribution function at different boundaries after propagation prior to the next collision step e Dependencies Many for diff
133. e drag force does however depend upon particle velocities and is therefore only approximated using the mid step values this frequently produces a system temperature higher than that specified by the user and requires a small time step At to reduce the offset to tolerable levels 11 2 2 DPD thermostat with DPD Velocity Verlet integration DPD VV dpdvv As with the MD VV scheme this algorithm uses the drag and random forces as the system thermostat which are combined with all other forces before being integrated using the Velocity Verlet scheme The drag force is subsequently recalculated after the second stage using the velocities at the end of the time step 13 The recalculation of drag forces after force integration helps to alleviate the temperature offset produced by the MD VV and hence larger time steps may be used for reasonable temperature control It does require the re use of the linked list cells and inter processor communications to recalculate the drag forces which can significantly increase the time required per time step compared to the MD VV scheme 11 2 3 Lowe Andersen thermostat lowe The Lowe Andersen thermostat 36 is an alternative to the use of drag and random forces in the DPD thermostat which uses a variant of the Andersen thermostat 1 After all other forces conservative bonding etc are integrated using the Velocity Verlet scheme a random sample of particle pairs have their relative velocity replaced by a val
134. e expressed in terms of pairwise interactions taking a form similar to the standard DPD conservative force Equation 9 5 A Op pi OW ps Tij O J Gh VI Fj Ta H F w Cri 11 42 The local density approximation can be defined as a weighted average of instantaneous densities En I AA pi S w rij 11 43 with we r as the weight function vanishing beyond a cutoff rq which can be equal to re or smaller and normalized so that dor Arr w r dr 1 The most frequently used form for the weight function is 15 Tij f wP riz 2nr3 1 s rij lt ra 11 44 which reduces to standard DPD when the excess free energy per particle is set to y 5 45 Ap Multiple component many body DPD is also possible by defining partial local densities e g for component a p Y lr 11 45 jEa j i and generalizing Equation 11 42 FC ee es a e i y m 11 46 a Be OPe i Tij with c i as the component to which particle belongs e g if i a c i a and p as the set of local densities of different components at the position of particle 7 The manybody_module includes a routine local_density to calculate local densities for each species using Equation 11 45 the overall density for each particle can be obtained by a simple sum over all species The user can modify the routines manybody_force and manybody_potential to apply their own choices for many body forces and potentials respectively Up to five many b
135. e governing equation At hi Z At t At hi Zt hi t hj 5 30 Tt The temperature at each lattice point relative to a mean value can be determined as the sum of the distribution functions T hi which can be used to determine the equilibrium distribution function e i u he wT a 5 31 again using the bulk fluid velocity The thermal relaxation time is related to the thermal diffusivity 1 1 Az z T Mt with the Prandtl number for the system determined by a ratio of relaxation times i e 277 1 V PS a It should be noted that if multiple relaxation time MRT schemes are to be used these only apply to fluids all diffusion and heat transfer processes are calculated using the single relaxation time schemes described in this section 5 4 1 Boussinesq approximation The coupling of fluid flows to heat transfer described above only produces heat conduction effects To model convective heat transfer processes an additional force on the fluid is required to link flow to thermal trans port The most common form is the Boussinesq approximation 18 which applies a buoyancy force on fluid a proportional to the temperature difference Fog 7 5 32 where g is gravitational acceleration 6 is the volumetric expansion coefficient for fluid a T and T are respectively the maximum and minimum temperatures of the system and To 5 T T is a reference temperature
136. e launched via a batch job script please consult your machine administrator or documentation for further details Modifications may be made to the customised versions of the code to select routines for e g specific collision propagation and mesophase interaction algorithms For example the Guo forcing scheme can be applied by lif preferred an alternative version that uses a boundary layer slbecombine cpp is available 2 may need to be replaced by on computers running Windows 221 222 APPENDIX A MANUAL COMPILIATION AND RUNNING OF DL_MESO selecting collision routines with Guo e g fCollisionBGKGuo while multiple relaxation time MRT schemes can be used with calls to f CollisionMRT Other possible modifications include modifying tuneable parameters for MRT schemes which are given in lbpMODEL cpp for the required lattice model D2Q9 D3Q15 or D3Q19 Additional boundary conditions should be added to the fPostCollBoundary or fPostPropBoundary routines depending on whether they are applied after collisions and before propagation or after propagation respectively Calls to alternative and or additional output routines can be included in the main loops of the customisable codes provided they are called before the output file number qVersion is increased If no fluid fluid interaction forces are required the calls to routines to zero interaction forces fInteractionForceZero and calculate them e g fInteractionForceShanChen can
137. e left hand side of Equation 3 12 can be expanded as X NE m fi At t At fi t m 1 0 liada fi z t 3 15 Expanding the instantaneous particle distribution function around its equilibrium and retaining only the first order gives fi z t i z t 7 Tf liada ie z t Te O 0 3 16 Substituting Equations 3 15 and 3 16 into the left hand side of Equation 3 12 gives the second order differential equation for the equilibrium distribution Fa fi eq 2 peq 3 0 liada WF 0 liada f O 0 3 17 Tf x At where wf Tf E 26 CHAPTER 3 THE LATTICE BOLTZMANN EQUATION BASIC THEORY Summing Equation 3 17 over i and ignoring the second order deriviative we obtain 0 Op Ogpta Wf0g ons a De feas 0 0 3 18 Summing Equation 3 18 times e over i we obtain 0 pua Og No fi eiaeig wf Oy a 5 fi CiaCiy 08 5 ieee 0 6 3 19 Equation 3 19 shows that the second term in Equation 3 18 is of the third order in the derivative Therefore we have the continuity equation to the second order of the derivative Defining the third and fourth order moments 5 Free Pag puaug 3 21 DE FP eiatigeiy Paguy Payus PgqUa PUAUGUur 3 22 a With these definitions Equation 3 19 leads to the weakly compressible Navier Stokes equation wD as 30 Pa pua Os puaug Og Pag 4 5 ay B gt 20 pun dalpus Os 0
138. e step without requiring recalculation of particle forces or rescaling of particle coordinates 11 3 2 Berendsen barostat berendsen The governing equation for the Berendsen barostat 2 is a simple differential equation for the pressure dP P P Zao aae 11 30 dt Tp which can be solved to give a scaling factor for the simulation volume 7 t BAt Ma t 1 7 Po Palt 11 31 P where is the isothermal compressibility of the system The exact value of this property is not critical to the algorithm since it relies on the ratio P The barostat is implemented using a variant of the Velocity Verlet algorithm after the midstep velocities are determined the scaling factor for time t is used to modify the particle positions and resize the simulation volume Tia t At nalt rija t Atvia t 4At 11 32 La t At nalt La t 11 33 The remainder of the Velocity Verlet algorithm is unchanged although the scaling factor for the beginning of the next time step can be calculated at this point using Equation 11 31 No iteration is required for this barostat 11 4 Particle particle interactions Pairwise particle interaction parameters in DL_MESO_DPD are specified in the FIELD file for each species pair using the directive interactions Interaction parameter values and lengthscales are stored in the array vvv 1 npot 1 mxprm in preparation for DPD calculations the maximum number of parameters mxprm de pendent on the u
139. e to reduce increase its wetting 5 3 2 Lishchuk continuum based model The Lishchuk model 35 20 is a modified form of the chromodynamic model devised by Gunstensen and Rothman 17 which models interactions between multiple components by applying forces based on the exis tence of those components This continuum based model is primarily suited for systems where hydrodynamic interactions dominate and no further fluid separation takes place A phase field is defined between components a and b as NPOP 5 19 Pab pe p noting that A pN First order spatial differentials of this quantity can be determined by means of fourth order accurate isotropic schemes 21 e g for lattice points without neighbouring walls 1 A de V pa AL Ds wi ipap Z At 5 20 52 CHAPTER 5 DL MESO_LBE FEATURES and these can be used to determine the interfacial normal between the phases 5 21 which can subsequently be used to obtain the local curvature from the interface normal in the phase field Ka V 5 ab 5 22 The force acting between the components to give interfacial tension is given by gt a 1 F 3900 Kab V Pat 5 23 Rather than colliding each fluid separately a single achromatic distribution function is defined as the sum of distribution functions for all fluids k f 52a the sum of which is equal to the density of all fluids p This distribution function is collided using any va
140. each dimension and the shape of the system will change over time The parameters for electrostatics can be given in the pop up window shown in Figure 2 6 c 1 The type of electrostatics to be used in the simulation 2 Electrostatic parameters for the Ewald sum with Slater type smearing the system coupling constant T Ewald real space convergence a and charge smearing 8 coefficients need to be specified 3 The Ewald sum method also requires a reciprocal space k vector range 2 3 DISSIPATIVE PARTICLE DYNAMICS AND THE DL_MESO GUI 15 FI DPD thermostat properties mm a oone properties E LANGEVIN de STOYANOV GROOT 1 barostat relaxation time 0 0 2 global coupling parameter 0 0 2 piston drag coefficient 0 0 y isotropic system 3 SAVET CANCEL T SAVE B CANCEL B a Thermostat parameters b Barostat parameters system coupling constant 0 0 2 Ewald real space convergence 0 0 charge smearing 0 0 g g El DPD surface properties SIERS ER be componant o 3 HARD SURFACES WITH SOFT REPULSION iL k vector y component 0 wall directions xyz 2 k vector z component 0 SAVE E CANCEL E SAVE SF CANCEL SF c Electrostatic parameters d Surface parameters Figure 2 6 Thermostat barostat electrostatic and surface pop up windows If non periodic boundaries are to be used the param
141. ecules Potentials standard Groot Warren DPD 16 density dependent many body DPD 46 66 Lennard Jones 30 Weeks Chandler Andersen 69 Electrostatic potentials between charged beads using a modified Ewald summation 14 Boundaries Periodic hard reflecting walls with optional short range repulsions 50 frozen particle walls Lees Edwards periodic shearing boundaries 34 Initial conditions can either be determined by DL MESO_DPD or specified by the user Requirements 1 3 1 Software requirements Standard C Compiler for LBE source code DL_MESO_LBE Standard Fortran90 Compiler for DPD source code DL_MESO_DPD Message Passing Interface if parallel execution required JAVA 2 Version 1 4 or higher if GUI is to be used GNU Make included in standard Unix Linux distributions can be installed for Windows 1 3 2 System requirements DL_MESO is designed to work in both serial and parallel running it can be run on standalone machines clusters and supercomputers The code has been tested on Solaris Windows XP IBM p690 HPCx PowerPC 450 Blue Gene P and Cray XT4 XT6 HECTOR machines 1 4 THE DL MESO DIRECTORY STRUCTURE 3 1 4 The DL_MESO Directory Structure The supplied version of DL_MESO is a gzipped tar file which unpacks as directory dl_meso_2 x where x is a generation number Beneath the top level of this directory are a number of subdirectories e LBE containing the LBE source code e DPD containing the DPD sour
142. edral potential energy stkde real KIND dp A nstk data stack for electrostatic potential energy stkee real KIND dp A nstk duni random number generator state uni integer A 102 mtrnd random number generator state mt integer A 0 624 Chapter 11 DL MESO DPD Features 11 1 Domain decomposition and linked list cell calculations The Domain Decomposition DD strategy is one of several ways to parallelize particle based simulations 57 Its basis is the division of the simulated system into equal sized spatial blocks or domains each of which is allocated to a specific processing unit of a parallel computer The arrays defining the coordinates velocities and forces for all N particles in the system are divided into sub arrays of size x on each of the P processing units with the particles allocated geometrically among them In order for the strategy to work efficiently the simulated system should possess a reasonably uniform density so that each processing unit is allocated as equal a portion of particle data as possible The computation of forces and integration of the equations of motion are shared more or less equally between the processing units and to a large extent can be computed independently on each unit While tricky to program this method is conceptually simple and particularly suited to large scale simulations The DD strategy which underpins DL_ MESO_DPD is based on the link cell algorithm 26 which requires a relatively short ra
143. ees to the terms and conditions of this Licence Agreement the website with the URL http www ccp5 ac uk DL_MESO and any website that from time to time replaces that website any virus worm time bomb time lock drop dead device trap and access code or anything else that might disrupt disable harm or 239 240 APPENDIX D DL_MESO LICENCE AGREEMENT ACADEMIC PURPOSES impede the operation of any information system or that might corrupt damage destroy or render inaccessible any software data or file on or that may allow any unauthorised person to gain access to any information system or any software data or file on it Intellectual Property patents trade marks service marks registered designs copyrights database rights design rights know how confidential information applications for any of the above and any similar right recognised from time to time in any jurisdiction together with all rights of action in relation to the infringement of any of the above the Licence Period the period beginning when the Licensee agrees to the terms and conditions of this Licence Agreement and downloads the DL_MESO Software from the DL_MESO Website and ending on the termination of this Licence Agreement under clause 5 2 2 LICENCE 2 1 STFC grants the Licensee an indefinite non exclusive non transferable royalty free licence to use copy modify and enhance the DL_MESO Software during the Licence Period on
144. elease or version of the DL_MESO Software that would have remedied or mitigated the effects of any error defect bug or deficiency in the DL_MESO Software The Licensee acknowledges that proper use of the DL_MESO Software and any Derived Work is dependent on the Licensee its employees and students exercising proper skill and care in inputting data and interpreting the output provided by the DL_MESO Software or that Derived Work STFC will not be liable for the consequences of decisions taken by the Licensee or any other person on the basis of that output STFC does not accept any responsibility for any use which may be made by the Licensee of that output nor for any reliance which may be placed on that output nor for advice or information given in connection with that output Subject to clause 3 7 STFC s liability or any breach of this Licence Agreement any negligence or arising in any other way out of the subject matter of this Licence Agreement or the use of the DL_MESO Software will not extend to any incidental or consequential damages or losses or any loss of profits loss of revenue loss of data loss of contracts or opportunity whether direct or indirect even if the Licensee has advised STFC of the possibility of those losses arising or if they were or are within STFC s contemplation Subject to clause 3 7 the aggregate liability of STFC for any and all breaches of this Licence Agreement any negligence or arising in
145. ell as output file formats and whether fluids are compressible or incompressible These programs do not need to be modified by the user if the provided code features are to be used Alternative versions of the program slbecustom cpp and plbecustom cpp for serial and parallel running respectively are also provided The user may wish to modify these listings to use user defined routines and functions as well as different outputs and formats alternative collision routines boundary conditions that move through the system etc These versions reduce the number of logic statements required to run and thus may be used if greater computational efficiency is required An additional version of the serial program is available which uses a boundary layer of lattice points slbecombine cpp Appendix A gives more details on using these versions of the program 7 2 2 IbpMODEL D2Q9 e Header records int D2Q9 e Function Assign the weight factor lbw speed vector 1bv index for opposite speed vector lbopv MRT transformation matrices 1btr and 1btrinv and tuneable parameters 1lbmrts and 1bmrtw for the D2Q9 lattice model e Dependencies None D3Q15 e Header records int D3Q150 e Function Assign the weight factor 1bw speed vector 1bv index for opposite speed vector 1bopv MRT transformation matrices 1btr and 1btrinv and tuneable parameters 1bmrts and 1bmrtw for the D3Q15 lattice model e Dependencies None 7 2 DL MESO_LBE SUBROUTINES AN
146. ell length in z direction sidez real KIND dp number of particles in domain cell nbeads integer number of frozen particles in domain cell nfbeads integer number of link cells in domain cell x dimension nlx integer number of link cells in domain cell y dimension nly integer number of link cells in domain cell z dimension nlz integer number of link cells in domain cell and boundary halo x dimension n1x2 integer number of link cells in domain cell and boundary halo y dimension nly2 integer number of link cells in domain cell and boundary halo z dimension nlz2 integer link cell length in x direction wdthx real KIND dp link cell length in y direction wdthy real KIND dp link cell length in z direction wdthz real KIND dp number of link cells for electrostatics in domain cell x dimension nlewx integer number of link cells for electrostatics in domain cell y dimension nlewy integer number of link cells for electrostatics in domain cell z dimension nlewz integer number of link cells for electrostatics in domain cell and boundary halo x dimension nlewx2 integer number of link cells for electrostatics in domain cell and boundary halo y dimension nlewy2 integer number of link cells for electrostatics in domain cell and boundary halo z dimension nlewz2 integer electrostatic link cell length in x direction wdthewx real KIND dp electrostatic link cell length in y direction wdthewy real KIND dp electrostatic link cell leng
147. em in a similar fashion i e unbonded particles precede bonded ones and molecules are ordered according to the FIELD file CONFIG files can be created from restart files of previous simulations using the supplied Fortran90 program exportconf ig in the directory DPD utility see Appendix B for more details Frozen particle walls if specified in the CONTROL file can be added to systems with CONFIG files with or without duplication but users have to ensure that any molecules do not cross boundaries where frozen particle walls will be placed no checks are available to prevent this from happening but CONFIG files could be created from previous simulations involving hard adsorbing surfaces 12 2 Output files General output file OUTPUT This ANSI text file is generated by all DPD calculations and contains e The system and bond angle dihedral properties used for calculations e Domain decomposition details Parallel version only e The starting positions and velocities of a particle sample e The calculation time current values and rolling averages for the total energy potential energy total elec trostatic and from bond stretching angles and dihedrals virial kinetic energy pressure and temperature every nsbpo time steps e Final averages and fluctuations standard deviations over all time steps after equilibration e The final positions and velocities of a particle sample e Elapsed and average times for the calculation Rest
148. ensional system is modelled this will be reset to 1 domain boundary width sets the size of the boundary region if running DL_MESO in serial this is usually reset to 0 Additional keywords can be used to specify the algorithms for collisions forcing and mesophase interac tions the format for output files and whether fluids are compressible or incompressible If these are omit ted DL_MESO_LBE will assume that the fluids are compressible and subjected to BGK single relaxation 1No multiple fluid phase scheme included in DL MESO currently requires this lattice 55 56 CHAPTER 6 DL MESO _LBE INPUT AND OUTPUT FILES time collisions using standard forcing without mesophase interactions If using the customizable versions of DL_MESO_LBE all of these keywords may be omitted except for incompressible_fluids which is required to correctly calculate fluid velocities in initialization and output files and apply boundary conditions keyword collision_type interaction type output_format incompressible_fluids meaning sets the type of collisions and forcing BGK 0 BGKGuo 1 MRT 2 or MRTGuo 3 sets the type of mesophase interactions ShanChen 1 ShanChenWetting 2 or Lishchuk 3 sets the format for output files VTK 0 LegacyVTK 1 Plot3D 2 determines whether or not the fluids should be incompressible set to 0 for compressible fluids 1 for incompressible fluids The following keywords can
149. ensure molecules do not cross non periodic boundaries initialvelocity e Header records SUBROUTINE initialvelocity e Function Initializes particle velocities randomly in system to give required system temperature e Dependencies duni global_sum_dble sort_beads e Header records SUBROUTINE sort_beads e Function Re orders local identity numbers of beads in current processor to place frozen beads at beginning of list e Comments Frozen beads are moved to local bead numbers between 1 and nfbeads while non frozen beads are moved to local bead numbers between nfbeads 1 and nbeads 13 2 12 config_module This module requires the modules constants variables comms_module numeric_container parse_utils domain_module and surface_module to be loaded beforehand 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 207 sysdef e Header records SUBROUTINE sysdef e Function Reads in system data determines simulation properties prints to OUTPUT file and allocates main arrays for calculations e Dependencies scan_config read_control scan_field read_field frozenbead domain_decompose domain_dimensions surfacenodes elecgen error e Arguments None e Comments The routine calculates a maximum size for the main arrays maxdim and a maximum number of pairwise interactions maxpair based on the total number of particles the number of link cells and number of nodes scan_config e Header records SUBR
150. ent agreement or undertaking except those expressly set out in this Licence Agreement The Licensee waives any claim for breach of or any right to rescind this Licence Agreement in respect of any representation which is not an express provision of this Licence Agreement However this clause does not exclude any liability which STFC may have to the Licensee or any right which the Licensee may have to rescind this Licence Agreement in respect of any fraudulent misrepresentation or fraudulent concealment before the signing of this Licence Agreement Amendments No variation of or amendment to this Licence Agreement will be effective unless it is made in writing and Signed by each party s representative Third parties No one who is not a party to this Licence Agreement has any right to prevent the amendment of this Licence Agreement or its termination and no one except a party to this Licence Agreement may enforce any benefit conferred by this 6 8 245 Licence Agreement unless this Licence Agreement expressly provides otherwise Governing law This Licence Agreement is governed by and is to be construed in accordance with English law The English Courts will have exclusive jurisdiction to deal with any dispute which has arisen or may arise out of or in connection with this Licence Agreement except that STFC may bring proceedings against the Licensee or for an injunction in any jurisdiction Bibliography 10
151. ential energy fluctuation flcde real KIND dp system electrostatic potential energy fluctuation flcee real KIND dp system potential energy accumulator zumpe real KIND dp system virial accumulator zumvir real KIND dp system kinetic energy accumulator zumtke real KIND dp system volume accumulator zumvlm real KIND dp system bond potential energy accumulator zumbe real KIND dp system angle potential energy accumulator zumae real KIND dp system dihedral potential energy accumulator zumde real KIND dp system electrostatic potential energy accumulator zumee real KIND dp system potential energy at current step stppe real KIND dp system virial at current step stpvir real KIND dp system kinetic energy at current step stptke real KIND dp system total energy at current step stptke real KIND dp 3These are only allocated if variable forces are required for e g DPD Velocity Verlet integration and Stoyanov Groot thermostat 10 2 THE PARAMETERS AND THEIR FUNCTIONS Table 10 4 DL_ MESO_DPD Parameters continued 139 function parameter data type notation system pressure at current step stpprs real KIND dp system volume at current step stpvlm real KIND dp system temperature at current step stpttp real KIND dp system bond potential energy at current step stpbe real KIND dp system angle potential energy at current step stpae real KIND dp system dihedral energy at current step stpde real K
152. ents nlimit input output integer importdata_dpdvv2_shear Header records SUBROUTINE importdata_dpdvv2_shear nlimit e Function Applies import of variable particle forces from boundary halos of neighbouring domains and or across periodic boundary conditions for the DPD Velocity Verlet algorithm with Lees Edwards shearing e Dependencies importvariable Parallel version only importvariable_shear Parallel version only e Arguments nlimit input output integer importdata_stoyanov e Header records SUBROUTINE importdata_stoyanov nlimit e Function Applies import of particle forces constant and variable from boundary halos of neighbouring domains and or across periodic boundary conditions for the Stoyanov Groot thermostat e Dependencies importvariable Parallel version only e Arguments nlimit input output integer 202 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE importdata_stoyanov_shear e Header records SUBROUTINE importdata_stoyanov_shear nlimit e Function Applies import of particle forces constant and variable from boundary halos of neighbouring domains and or across periodic boundary conditions for the Stoyanov Groot thermostat with Lees Edwards shear ing e Dependencies importvariable Parallel version only importvariable_shear Parallel version only e Arguments nlimit input output integer importdensitydata e Header records SUBROUTINE importdensitydata nlimit e Function Applies
153. eometric property planar surface concave corner or concave edge Boundary orientation one letter for planar surface two letters for concave corners or three letters for concave edges For example a shearing planar surface facing down the y axis with constant composition and temperature i e isothermal is represented as VCBPSD and translated as 322 38 CHAPTER 4 DL MESO _LBE BASIC DEFINITION Table 4 3 Notation of boundary condition VCTPST VCTPSR VCTCCTRB VCTCCDRB VCTCCDLF VCTCETL VCTCETF VCTCERF VCTCEDB VBBPSD VBBPSF VBBCCTLB VBBCCTRE VBBCCDRF VBBCEDL VBBCELF VBBCETB VBBCERB VCBPSL VCBPSB VCBCCDLB VCBCCTLF VCBCETR VCBCEDR VCBCEDF VCBCELB VBTPST VBTPSR VBTCCTRB VBTCCDRB VBTCCDLF VBTCETL VBTCETF VBTCERF VBTCEDB PCTPSD PCTPSF PCTCCTLB PCTCCTRF PCTCCDRF PCTCEDL PCTCELF PCTCETB PCTCERB PBTPSL PBTPSB PBTCCDLB PBTCCTLF 121 124 127 130 133 144 147 150 153 222 225 228 231 234 245 248 251 254 323 326 329 332 343 346 349 352 421 424 427 430 433 444 447 450 453 522 525 528 531 534 545 548 551 554 623 626 629 632 VCTPSD VCTPSF VCTCCTLB VCTCCTRF VCTCCDRF VCTCEDL VCTCELF VCTCETB VCTCERB VBBPSL VBBPSB VBBCCDLB VBBCCTLF VBBCETR VBBCEDR VBBCEDF VBBCELB VCBPST VCBPSR VCBCCTRB VCBCCDRB VCBCCDLF VCBCETL VCBCETF VCBCERF VCBCEDB VBTPSD VBTPSF VBTCCTLB VBTCCTRE VBTCCDRF VBTCEDL VBTCELF VBTCETB VBTCERB PCTPSL PCTPSB PCTCCDLB
154. er of additional particles created during export of particles into boundary halos with Lees Edwards shearing is greater than the current processor can accommodate Action This error message suggests non constant particle densities across the system and poor load balancing The user may wish to use the densvar directive in the CONTROL file to increase the value of maxdim and thus accommodate larger numbers of particles Message 83 cannot correctly export velocities to boundary halos Particle velocities for DPD Velocity Verlet integration cannot be exported correctly to particles already in the boundary halos Action This error should never occur If it does please contact the authors of DL_MESO Message 84 cannot correctly export densities to boundary halos Particle densities for many body DPD cannot be exported correctly to particles already in the boundary halos Action This error should never occur If it does please contact the authors of DL_MESO Message 100 wrong bead total after compression too many few The total number of particles after the first Velocity Verlet integration stage including dealing with boundary conditions etc does not equal the specified total number of particles for the system Action This error should never occur If it does please contact the authors of DL_MESO Message 200 bond too long or cannot be found At least one bond between specified particles is too long e g longer than the ma
155. er of the order 10 is unnecessary for modelling liquids 47 Alternative thermostats are available which can model systems with higher Schmidt numbers 36 62 9 4 Derivation of Equilibrium The derivation of the DPD algorithm is based on the Fokker Planck equation Op C 9 17 a P 9 17 where p is the equilibrium distribution function and is the evolution operator which may be split into conservative and dissipative parts Estel 9 18 130 CHAPTER 9 DISSIPATIVE PARTICLE DYNAMICS BASIC THEORY with INS 3 N AS LA a Lo pee pas Oe 9 19 i 1 tj A a af p op 2 o 0 Lo Yeu ae om i ig gt wh ras isle ae 9 20 e Tis where jj 2 ij When a y 0 then Equation 9 17 becomes ane Lop 9 21 for which the equilibrium solution is evidently N je ix pt E exp EBT 2 om 7 26 rs 9 22 which is of course the Boltzmann distribution function for an equilibrium system Thus it is apparent that for the simulation based on Equation 9 17 to maintain the same distribution function the terms in the operator LP of Equation 9 20 must sum to zero It follows that the conditions given in Equations 9 8 and 9 9 must apply 9 5 Summary of Dissipative Particle Dynamics DPD is a simple method All that is required is a system of spherical particles enclosed in a periodic box undergoing time evolution as a result of the above forces In implementation it differs very little from Molecular Dynamic
156. erent lattice schemes e Comments Algorithms for other boundary conditions can be added by the user although care should be taken as to when they are applied in each time step the conditions invoked in this routine apply to distribution functions after propagation 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS 91 fNeighbourBoundary e Header records int fNeighbourBoundary e Function Determines the existence of solid boundaries in neighbouring lattice points e Dependencies None e Comments Stores results in the lbneigh array currently only covers orthogonal directions i e no diagonals Only needs to be called once if boundary conditions do not change during calculations fsPeriodic e Header records int fsPeriodic e Function Applies periodic boundary condition for serial calculations with non zero boundary domain widths by copying distribution functions from edges of fluid points e Dependencies fsPeriodic2D fsPeriodic3D e Comments Serial equivalent of NonBlockCommunication essential for using the combined swap propagation routine fPropagationCombinedSwap in serial running fsBoundPeriodic e Header records int fsBoundPeriodic e Function Applies periodic boundary condition for serial calculations with non zero boundary domain widths by copying boundary information from edges of fluid points e Dependencies fsBoundPeriodic2D fsBoundPeriodic3D e Comments Serial equivalent of fBoundNo
157. ers and boundary conditions for the solutes must be set by clicking the set solute parameters button see below for more details The using temperature scalar box may be clicked yes if thermal systems are to be studied If checked the thermal parameters must be set by clicking the set thermal parameters button see below for more details valid 1bin sys file already exists in the current working directory the OPEN button can be clicked to load its information into the GUI which can then be viewed and edited Once all the data in this window and any pop up windows for fluid solute and thermal parameters are filled in the SAVE button should be clicked to write the lbin sys file 2 2 1 1 Fluid solute and thermal parameters Examples of the pop up windows for fluid solute and thermal parameters can be seen in Figure 2 3 with the rows labelled in red numbering multiple columns of dialogue boxes are made available for systems with multiple fluids and or solutes For 1 2 3 10 11 fluids the required data are as follows Body force x axis the x component of body force on each fluid Body force y axis the y component of body force on each fluid Body force z axis the z component of body force on each fluid Greyed out for two dimensional systems Boussinesq force x axis the x component of the Boussinesq force parameter 7 5 on each fluid Boussinesq force y axis the y component o
158. ersion to be loaded beforehand domain_decompose e Header records SUBROUTINE domain_decompose e Function Determines 3D domain decomposition for system number of nodes in each direction location for each node in system nearest neighbouring nodes 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 189 e Dependencies parallel version only msg_receive_blocked msg_receive_sca_blocked msg_send_blocked msg_send_sca_blocked e Comments Essential for parallel version of DL _MESO_DPD the serial version of this subroutine sets values for a single processor domain_dimensions e Header records SUBROUTINE domain dimensions e Function Determines dimensions of domain and link cells e Dependencies None e Comments This subroutine is called during setup and if a barostat is used when the volume of the system changes parlnk e Header records SUBROUTINE parlnk numi num2 e Function Constructs the parallel link cells for calculations of pairwise forces between particles e Dependencies None e Arguments numi input integer num2 input integer e Comments Pairwise electrostatic forces typically act over longer lengthscales between charged particles only and are not considered using this subroutine a similar routine for the real space part of Ewald summation is included in ewald_real deport e Header records SUBROUTINE deport nlimit mdir mp begin final shove skip e Function Deports particl
159. ersion only e Arguments nlimit input output integer mdir input integer mp input integer begin input real KIND dp final input real KIND dp shove input real KIND dp skip input logical e Comments The switch skip in the parallel version only prevents particles in the boundary halo of the current domain from being transferred for non periodic boundary conditions e g hard surfaces Lees Edwards shearing export_shear e Header records SUBROUTINE export_shear nlimit mdir begin final shove shovel shove2 sidel side2 196 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE e Function Exports particle data positions velocity to appropriate domains as boundary halos for Lees Edwards shearing e Dependencies error msg_receive_unblocked Parallel version only msg_receive_sca_blocked Parallel version only msg_send_blocked Parallel version only msg_send_sca_blocked Parallel version only msg wait Parallel version only e Arguments nlimit input output integer mdir input integer begin input real KIND dp final input real KIND dp shove input real KIND dp shovel input real KIND dp shove2 input real KIND dp sidel input real KIND dp side2 input real KIND dp e Comments This routine requires information for the two dimensions along the surface of the shearing boundary the variables shovel and shove2 represent the displacement due to shear while side1 and side2 are the domain dimensions exportveloc
160. es double fGetFracSite int fpos double startpos double fGetFracSite int fpos long tpos double fGetFracSite int fpos int xpos int ypos int zpos e Function Calculates the mass fraction of fluid fpos in the site e Dependencies fReciprocal e Arguments startpos input double pointer fpos input integer tpos input long integer xpos input integer ypos input integer Zpos input integer fGetFracSite output double precision 7 2 DL MESO _LBE SUBROUTINES AND FUNCTIONS 71 e Comments The calculation is based on z se re This function operates in a similar way to fGetOneMassSite with the second and third cases slightly slower than the first but more readable fGetOneConcSite e Header records two cases double fGetOneConcSite int cpos long tpos double fGetOneConcSite int cpos int xpos int ypos int zpos e Function Calculates the concentration of solute cpos at the grid point e Dependencies fGetOneMassSite e Arguments tpos input long integer cpos input integer xpos input integer ypos input integer Zpos input integer fGetFracSite output double precision fGetTemperatureSite e Header records two cases double fGetTemperatureSite long tpos double fGetTemperatureSite long xpos long ypos long zpos e Function Calculates the scalar temperature at the grid point e Dependencies fGetOneMassSite e Arguments tpos input long integer xpos input long integer ypos input long integer
161. es from boundary halo to neighbouring domain e Dependencies contract_bndtbl contract_angtbl 190 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE contract_dhdtbl error global_sca and all msg receive_unblocked msg receive_sca_ blocked msg_send_blocked msg_send_sca_blocked msg_wait e Arguments nlimit input output integer mdir input integer mp input integer begin input real KIND dp final input real KIND dp shove input real KIND dp skip input logical e Comments Only exists in parallel version of DL_MESO_DPD The switch skip prevents particles in the boundary halo of the current domain from being transferred this is useful for applying non periodic boundary conditions e g hard surfaces Lees Edwards shearing deport_shear e Header records SUBROUTINE deport_shear nlimit mdir begin final shove shovel shove2 vshovel vshove2 sidel side2 e Function Deports particles from boundary halo to appropriate domains for Lees Edwards shearing e Dependencies contract_bndtbl contract_angtbl contract_dhdtbl error msg_receive_unblocked msg_receive_sca_blocked msg_send_blocked msg_send_sca_blocked msg_wait e Arguments 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 191 nlimit input output integer mdir input integer begin input real KIND dp final input real KIND dp shove input real KIND dp shovel input real KIND dp shove2 input real KIND dp vshovel input real KIND dp vshove2 input real KIND dp
162. eters for surfaces can be entered in the appropriate pop up window Figure 2 6 d 1 The type of surface interactions or boundary conditions to be applied 2 Wall directions if the checkbox for a particular dimension is ticked the boundary condition will be applied to the surfaces orthogonal to the specified axis After filling in all the required values clicking the relevant save button SAVE T SAVE B SAVE E or SAVE SF will store the data in preparation for writing to the CONTROL file The cancel buttons CANCEL T CANCEL B CANCEL E and CANCEL SF will close the pop ups without saving any values 2 3 2 Defining DPD Interactions Figure 2 7 shows the Set DPD Interactions panel with the sections for data entry labelled in red numbering The following data are required 1 The number of species is required to specify all interactions between particles in a DPD simulation The spinner box allows the user to define up to 10 particle species while the button set species opens a pop up window for the user to enter the properties for each species and write them to a new FIELD file see below for more details 2 After the particles species have been defined the button set interactions opens a pop up window to allow the user to define non bonded interactions between particle species and write them to the FIELD file 3 The operating system is required before launching a command line terminal and running the molecule generation utilit
163. f potentials npot integer gt 1 number of defined molecule types nmoldef integer number of defined bond types nbonddef integer lt mxbonddef number of defined bond angle types nangdef integer lt mxbonddef number of defined bond dihedral types ndhddef integer lt mxbonddef size of statistical data stack nstk integer gt 1 total number of particles in system nsyst integer total number of unbonded particles in system nusyst integer total number of frozen particles in system nfsyst integer total number of particles per unit cell nsystcell integer total number of unbonded particles per unit cell nusystcell integer total number of frozen particles per unit cell nfsystcell integer total number of molecules per unit cell nummol integer total number of bonds per unit cell numbond integer total number of bond angles per unit cell numang integer total number of bond dihedrals per unit cell numdhd integer time step number nstep integer force calculation time accumulator timfrc real KIND dp step time accumulator timstp real KIND dp specified system temperature kgT temp real KIND dp size of time step At tstep real KIND dp halo boundary size rhalo real KIND dp interaction cutoff radius re reut real KIND dp gt 0 square of interaction cutoff radius rct2 real KIND dp gt 0 136 CHAPTER 10 DL MESO DPD BASIC DEFINITION Table 10 4 DL _ MESO_DPD Parameters continued function par
164. f the Boussinesq force parameter on each fluid Boussinesq force z axis the z component of the Boussinesq force parameter on each fluid Greyed out for two dimensional systems The initial fluid densities are applied throughout the system and used to initialize LBE calculations The constant fluid density po for incompressible systems this property can also be used to define the reference densities for Shan Chen pseudopotentials and for initialising systems with fluid drops The fluid densities at the top boundary The fluid densities at the bottom boundary The fluid densities at the left boundary 2 2 LATTICE BOLTZMANN AND THE DL_MESO GUI 9 TBE Avid properties 12 13 14 15 16 17 18 fluid O fluid 1 body force x axis 0 o 1 body force y axis o e 2 body force z axis 3 boussinesq force x axis 0 O 4 boussinesq force y axis e 0 5 boussinesq force z axis 6 fluid densities initial 1 1 1 aire merma properties aE constant 1 1 8 initial T K o 1 top 0 0 9 initial dT dt K s 0 2 bottom 0 o 10 boussinesq high T K 0 3 left 0 o 11 boussinesq low T K 0 4 lara 0 o 12 heat relaxation time 1 5 front 13 Ed UBE solute properties ll T K dT
165. fGetOneDirecSpeedSite int dire long tpos float fGetOneDirecSpeedSite int dire int xpos int ypos int zpos e Function Calculates the grid speed for all compressible fluids along direction dire O for x 1 for y and 2 for z 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS 75 e Dependencies fReciprocal e Arguments startpos tpos xpos YPos Zpos dire fGetOneDirecSpeedSite e Comments input double pointer input long integer input integer input integer input integer input double pointer output floating point Mainly used to output grid speed The second and third cases are more readable than the first but also slightly slower fGetOneDirecSpeedIncomSite e Header records three cases float fGetOneDirecSpeedIncomSite int dire double startpos float fGetOneDirecSpeedIncomSite int dire long tpos float fGetOneDirecSpeedIncomSite int dire int xpos int ypos int zpos e Function Calculates the grid speed for all incompressible fluids along direction dire O for x 1 for y and 2 for z e Dependencies fReciprocal e Arguments startpos tpos xpos ypos Zpos dire fGetOneDirecSpeedIncomSite e Comments input input input input input input output double pointer long integer integer integer integer double pointer floating point Mainly used to output grid speed The second and third cases are more readable than the first but also slightly slower 7 2 5 IbpIO fDefineS
166. ger reference ioy input output integer reference ioz input output integer reference ix input integer iy input integer iz input integer fBestGrouping e Header records int fBestGrouping int totalgrid int totalgroup int amp indigrid int amp critigroup e Function Distribute grid points among the processes to give a maximum of one to the differences in the numbers of grid points e Dependencies None e Arguments totalgrid input integer totalgroup input integer indigrid output integer reference critigroup output integer reference e Comments The totalgrid grid points are distributed among totalgroup processes so that the first critigroup processes have indigrid grid points and the others have indigrid 1 fCppMod e Header records two cases int fCppMod int a int b long fCppMod long a long b e Function Ensure that a is in a range between 0 and b 1 so that the value beyond the maximum value equals the minimum and vice versa 66 e Dependencies None e Arguments a input integer long integer b input integer long integer fCppMod output integer long integer e Comments CHAPTER 7 DL_MESO_LBE PACKAGE REFERENCE fCppMod a bwhena gt bor fCppMod a bwhena lt 0 This function is useful for periodic boundary conditions fPrintLine e Header records int fPrintLine e Function Prints a line of 76 characters e Dependencies None fPrintDoubleLine e Header records int fP
167. given wall thickness and bead density and adjusts system dimensions and particle counts to accommodate them e Dependencies None e Comments This routine is only called for new simulations with or without a CONFIG file shearslide e Header records SUBROUTINE shearslide e Function Determines displacement of shearing boundary for Lees Edwards boundary conditions e Dependencies None e Comments The boundary condition is given by 34 Displacement of boundaries only takes place after equilibration 13 2 7 ewald_module This module requires the constant variables numeric_container and comms_module modules to be loaded beforehand ewald_real_slater e Header records SUBROUTINE ewald_real_slater nlimit e Function Calculates real space terms for Ewald summation with Slater type exponential decay charge distribu tions 182 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE e Dependencies erfcdp e Arguments nlimit input integer e Comments Calculates short range Coulombic forces and potential energies for Ewald summation using the following smeared non point charge distribution 14 ro exp 8 mr re ewald_reciprocal e Header records SUBROUTINE ewald_reciprocal e Function Calculates reciprocal space terms for Ewald summation e Dependencies None e Comments Calculates long range Coulombic forces and potential energies using standard Ewald summation including self e
168. grid point using the Bhatnagar Grook Krook BGK model for compress ible fluids e Dependencies fGetOneMassSite fGetEquilibriumC 110 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Arguments startpos input double pointer sitespeed input array of doubles e Comments Collisions for each solute are carried out using the BGK single relaxation time 4 1 e 0 liada gi gi g Ts fSite ThermalCollisionBGK e Header records int fSiteThermalCollisionBGK double startpos double sitespeed e Function Calculates thermal collisions at a grid point using the Bhatnagar Grook Krook BGK model for com pressible fluids e Dependencies fGetOneMassSite fGetEquilibriumT e Arguments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer e Comments Collisions for thermal currents are carried out using the BGK single relaxation time 4 1 Tt Op eiaa hi hi hi fCollisionBGK e Header records int fCollisionBGKO e Function Collision steps for all compressible and incompressible fluids using BGK model e Dependencies fSiteFluidCollisionBGK fSiteFluidIncomCollisionBGK fSiteSoluteCollisionBGK fSiteThermalCollisionBGK fGetSpeedSite fGetSpeedIncomSite e Comments This routine is fundamental to Lattice Boltzmann calculations and should not be modified fCollisionBGKSegregation e Header records int fCollisionBGKSegregation 7 2 DL MESO_LBE SUBROUTINE
169. guments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer phaseindex input double pointer e Comments Collisions are carried out on a single achromatic fluid using the BGK single relaxation time 4 fluid segregation takes place using the D Ortona algorithm 9 p pep FAO fi z t 5 Bw z i Nab P bla P fSiteFluidCollisionBGKGuo e Header records int fSiteFluidCollisionBGKGuo double startpos double sitespeed double bodyforce e Function Calculates collisions at a grid point using the Bhatnagar Grook Krook BGK model with the Guo forcing term for compressible fluids e Dependencies fGetOneMassSite fReciprocal fGetEquilibriumF 104 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Arguments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer e Comments Collisions for each fluid species solute and the thermal lattice are carried out using the BGK single relaxation time 4 with the following Guo forcing term 19 acting on each fluid Cia0a fi gt f 1 wi 3 Cia Va 9 U Fa fSiteFluidCollisionBGKGuoSegregation e Header records int fSiteFluidCollisionBGKGuoSegregation doublex startpos double sitespeed double bodyforce double phaseindex e Function Calculates collisions and phase segregation for the Lishchuk algorithm at a grid point using the Bhatnagar Grook Krook
170. h bead name a8 name of species x real relative x coordinate for bead Y real relative y coordinate for bead 2 real relative z coordinate for bead 12 1 INPUT FILES 161 The relative coordinates are used to define the initial shape of the molecule when it is inserted into the system these are not used if an initial configuration is already available 4 no isomer indicates that the molecule shape should not be reflected or otherwise modified when added to the system This directive is optional and should be left out if no restrictions on molecule insertion are to apply 5 bonds n where n gives the number of flexible bonds in the molecule Each of the subsequent n records contains bond key ad potential key see Table 12 3 index 1 i integer first bead index in bond index 2 j integer second bead index in bond variable 1 real potential parameter see Table 12 3 variable 2 real potential parameter see Table 12 3 variable 3 real potential parameter see Table 12 3 variable 4 real potential parameter see Table 12 3 Note that the bead indices are those arising from numbering each bead in the molecule from 1 to the number specified in the beads directive for this molecule The same numbering scheme applies for all descriptions of the molecule DL MESO_DPD will itself construct the global numbers for all particles in the system 6 angles n where n gives the number of angle bonds in the molecule Each of the n records following con
171. h fluid species are carried out using multiple relaxation time MRT schemes coupled with Guo like forcing terms 49 91 eia a fi T 3 TF Mf 1 315 5 fSiteFluidCollisionMRT GuoSegregation e Header records int fSiteFluidCollisionMRTGuoSegregation doublex startpos double sitespeed double bodyforce double phaseindex e Function Calculates collisions and phase segregation for the Lishchuk algorithm at a grid point using Multiple Relaxation Time MRT models coupled with Guo like forcing terms for compressible fluids e Dependencies fGetAllMassSite fGetTotMassSite fReciprocal fGetMomentEquilibriumF fGetMomentForce fGetMRTCollide e Arguments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer phaseindex input double pointer e Comments Collisions are carried out on a single achromatic fluid using multiple relaxation time MRT schemes coupled with Guo like forcing terms 49 fluid segregation takes place using the D Ortona algorithm 9 a it e z ab PO fi z t het 8 wi 7 ba Nab fSiteFluidIncomCollisionMRTGuo e Header records int fSiteFluidIncomCollisionMRTGuo double startpos double sitespeed double bodyforce e Function Calculates collisions at a grid point using Multiple Relaxation Time MRT models coupled with Guo like forcing terms for incompressible fluids e Dependencies fGetOneMassSite fGetMomentEquili
172. he y axis is denoted by 21 while a concave corner face at the top right front corner is denoted by 31 It must be pointed out that only those space positions located in the surface of a face centered cube have been included and translated in DL_MESO_LBE Points with random orientations e g 47 plane have not been included The boundary condition number can be rather confusing and difficult to understand The GUI in DL_MESO therefore includes a translator which interprets a word as its corresponding integer number The word is made 4 2 DATA STRUCTURE 37 Table 4 2 Boundary condition category letter meaning V Constant Velocity P Constant Pressure Density C Constant Solute Composition T Constant Temperature B Neumann Boundary Condition Solute Composition or Temperature PS Planar Surface CC Concave Corner CE Concave Edge T Normal Vector Pointing to Top D Normal Vector Pointing Downwards L Normal Vector Pointing to Left R Normal Vector Pointing to Right F Normal Vector Pointing to Front B Normal Vector Pointing to Back up of defined letters as listed in Table 4 2 The boundary conditions with combinations of type and orientation are listed in Table 4 3 The letters are in the order of 1 2 3 Fluid property constant speed or constant pressure Solute property constant composition or Neumann boundary Temperature property isothermal constant or heat bath Neumann boundary G
173. hemes and thermostats that require two separate sets of forces to be calculated e Dependencies error global_sca_and_all msg_receive_unblocked msg_receive_sca_blocked msg_send_blocked msg_send_sca_blocked msg_wait 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 193 e Arguments nlimit input output integer mdir input integer mp input integer begin input real KIND dp final input real KIND dp shove input real KIND dp first input logical skip input logical e Comments Only exists in parallel version of DL_MESO_DPD Setting first to true imports both sets of forces constant and variable while setting to false imports just the variable forces This routine is suitable for thermostats where two types of forces need to be kept separate and or recalculated i e the DPD thermostat with DPD Velocity Verlet integration DPD VV and Stoyanov Groot thermostat The switch skip ignores any particles in halos for non periodic boundary conditions e g hard surfaces Lees Edwards shearing importvariable_shear e Header records SUBROUTINE importvariable_shear nlimit mdir begin final shove shovel shove2 sidel side2 e Function Imports particle forces from boundary halos for integration schemes and thermostats that require two separate sets of forces to be calculated and Lees Edwards shearing e Dependencies error msg_receive_unblocked msg_receive_sca_blocked msg_send_blocked msg_send_sca_blocked msg_wait e Arguments
174. his is a 2D simulation of an initially static drop on a 150 x 50 grid undergoing linear shear 21 using Lishchuk continuum based mesophase interactions with Guo forcing The drop and continuous fluid are contained between two solid walls after an equilibration period to allow the drop shape to settle the wall at the top of the system is set to move horizontally while the wall at the bottom is kept stationary Figure 8 7 shows the fluid density pressure field and drop positions at time steps throughout the simulation demonstrating traverse migration lift due to linear shear for a system with droplet Reynolds number of 0 135 and capillary number ratio of inertial to interfacial stresses of 0 147 An AVI video file has been rendered from an example calculation which can be found in the Example Simulations page of the DL_MESO website 122 CHAPTER 8 DL MESO LBE EXAMPLES density 001 2 0008 DY 2 0004 a 2 1 9996 a t 19 000 density 001 2 0008 2 0004 2 1 9996 b t 87 500 density 001 2 0008 2 0004 2 1 9996 c t 390 000 Figure 8 7 Plots of fluid density pressure and drop positions for LBE 2D_DropShear test case 8 8 3D_PhaseSeparation This is a 3D simulation of two fluids on a 100 x 100 x 100 grid with periodic boundary conditions and Shan Chen pseudopotential mesoscopic interactions that cause the fluids to separate Figure 8 8 shows the phase separation process in a number of
175. his method concave edges in three dimensions and concave corners instead use the equilibrium distribution function for the given density velocity and either zero velocity or the density at the nearest fluid grid point An evaporation limit is applied to the density as a minimum limit for constant velocity edges and corners to prevent spurious production of non continuous fluids in multiple fluid systems a default value of 1078 is generally used but this can be overridden by the user in the 1bin sys file 5 2 5 Constant solute concentration temperature To specify constant solute concentrations or temperatures at planar boundaries the Inamuro method 28 27 is used in DL_MESO_LBE This is based upon substituting the unknown distribution functions for a boundary point with local equilibrium values but using an adjusted solute concentration or temperature to produce the correct value for the property at that point This concentration temperature is obtained by substituting the equilibrium distribution function for the unknown populations into the sum of distribution functions equal to the required concentration temperature For example for a top edge with a specified temperature Ty using the D2Q9 lattice scheme TCEDF the adjustment temperature T is given as z 6 E 3Uw y T Tp ho h h2 he h7 hs and the missing populations i 3 4 5 in this case are given by n wr 36 c where Vu is the k
176. ibriumF e Arguments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer phaseindex input double pointer e Comments Collisions are carried out on a single achromatic fluid using the BGK single relaxation time 4 fluid segregation takes place using the D Ortona algorithm 9 p pep fE 2 0 fi 2 04 X bw z Ci fab P bla P fSiteFluidIncomCollisionBGK e Header records int fSiteFluidIncomCollisionBGK doublex startpos double sitespeed double bodyforce e Function Calculates collisions at a grid point using the Bhatnagar Grook Krook BGK model for incompressible fluids e Dependencies fGetOneMassSite 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS 103 fReciprocal fGetEquilibriumFIncom e Arguments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer e Comments Collisions for each fluid species are carried out using the BGK single relaxation time 4 Op 00 fi Ra 0 fSiteFluidIncomCollisionBGK Segregation e Header records int fSiteFluidIncomCollisionBGKSegregation doublex startpos double sitespeed double bodyforce double phaseindex e Function Calculates collisions and phase segregation for the Lishchuk algorithm at a grid point using the Bhatnagar Grook Krook BGK model for incompressible fluids e Dependencies fGetAllMassSite fGetAllMassSite fReciprocal fGetEquilibriumFIncom e Ar
177. ic Equations 0 0 000 ee ee eee Mesoscale Interaction et BPS Re Oe ne hee eee aa BOE eee ER ete AS Summary of Lattice Boltzmann Equation e DL_MESO_LBE Basic Definition Latticeimodels ea GoM feck ean eee go a Boe Se ah a ek iS ik Gn ee Gee a e as Data structure 24 A dee ce Sate ch Wn Sard ete Seth Ai ke ae RS es ee ee ed The Parameters and Their Functions 2 a e ae a e e DL_MESO_LBE Features Collision and Propagation Algorithms sa sek psa te saa ee ee Boutidary conditions s eied ere 6 e ee ee ie od Mesoscale interactions ida a Qo eh oe Roe Dyeing GA eon Gee ee da Diffusion and heat transfer Compressible and incompressible fluids 2 a a ee 12 18 19 21 23 23 23 24 25 26 27 29 29 36 39 ii CONTENTS 6 DL_MESO_LBE Input and Output Files 55 OL input files se eo be i en he eae Sle ae pe aie AS PL Oh Eaves wea ee 55 6225 Output Miles sas ag Ko y A AA AA A Soe oo gd 58 7 DL_MESO_LBE Package Reference 61 Tal OVETVIEW 2 2 2 BEG See eh ES be ae AS EROS ae Goh a ein be ee aed 61 7 2 DL_MESO_LBE Subroutines and Functions 0 0 0 000002 eee ee 62 8 DL_MESO LBE Examples 119 Srl GZDEPRESSULC a he fe ade Paka Mate Gite ee ee Ge Ande Me At okt me ened esa of ae OR we EO we Fe Se 119 O22 2D Shear A e see by ds ele Aceh IS a fh la Nee oe oe 119 8 32 2D Cylinder Flow es a a tie ae ae beh AE Boeck okt eee db duke ah ye eek Ge hd 120 3 4 2D Karman Vortex 1 oe a oe
178. id point 7 2 DL MESO LBE SUBROUTINES AND FUNCTIONS 87 e Dependencies None e Arguments tpos input long integer e Comments This bounce back boundary condition is carried out using f lbopv i 1bv i fMidBounceBackF e Header records int fMidBounceBackF long tpos e Function Performs a mid link bounce back for the fluid distribution function at the tpos th grid point e Dependencies None e Arguments tpos input long integer e Comments This bounce back boundary condition is carried out by exchanging post collisional populations with con jugate values in neighbouring grid points fMidBounceBackC e Header records int fMidBounceBackC long tpos e Function Performs a mid link bounce back for the solute distribution function at the tpos th grid point e Dependencies None e Arguments tpos input long integer e Comments This bounce back boundary condition is carried out by exchanging post collisional populations with con jugate values in neighbouring grid points fMidBounceBackT e Header records int fMidBounceBackC long tpos e Function Performs a mid link bounce back for the temperature distribution function at the tpos th grid point e Dependencies None 88 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Arguments tpos input long integer e Comments This bounce back boundary condition is carried out by exchanging post collisional populations with con jugate
179. import of local densities for particles from boundary halos of neighbouring domains and or across periodic boundary conditions e Dependencies importdensity Parallel version only e Arguments nlimit input output integer e Comments This subroutine is essential for DPD calculations involving many body density dependent interactions importdensitydata_shear e Header records SUBROUTINE importdensitydata shear nlimit e Function Applies import of local densities for particles from boundary halos of neighbouring domains and or across periodic boundary conditions with Lees Edwards shearing e Dependencies importdensity Parallel version only importdensity_shear Parallel version only e Arguments nlimit input output integer e Comments This subroutine is essential for DPD calculations involving many body density dependent interactions 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 203 exportdata e Header records SUBROUTINE exportdata nlimit e Function Applies export of particle properties positions velocities to boundary halos of neighbouring domains and or across periodic boundary conditions e Dependencies export e Arguments nlimit input output integer e Comments Non periodic boundaries either do not require boundary halos or require them to be constructed differently these are thus excluded from the export of particle properties exportdata_shear e Header records SUBROUTINE expor
180. in all the required values clicking the relevant save button SAVE SP SAVE I or SAVE E will write the data to the FIELD file The cancel buttons CANCEL SP CANCEL I and CANCEL E will close the pop ups without saving any values 2 4 Compiling and running DL_ MESO e Compiling the LBE DPD code may be accomplished through the compiler panel which is activated from either of the Compile LBE Code or Compile DPD Code buttons e The Compile LBE Code panel allows you to select the operating system a C compiler compiler flags and the version serial or parallel of the code you wish to build If you require a C compiler that is not included in the pull down list select other and type the command for the required compiler in the neighbouring box Clicking the COMPILE button will start the compilation and a message box will signal its completion e The Compile DPD Code panel allows you to select the operating system a Fortran90 compiler compiler flags and the version serial or parallel of the code you wish to build If you require a Fortran90 compiler that is not included in the pull down list select other and type the command for the required compiler in the neighbouring box The Create Makefile button needs to be clicked first to create a makefile in the working directory which automates compilation and may be edited by the user Clicking the COMPILE button will invoke the makefile to compile the code and a message box will signal its com
181. inate long fNextStep int q int xpos int ypos int zpos long fNextStep int q int xpos int ypos long fNextStep int dx int dy int dz long tpos e Function Finds particle position at the next time step when currently at xpos ypos zpos or tpos and moving along direction q or dx dy dz 86 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Dependencies fCppMod e Arguments q input integer dx input integer dy input integer dz input integer xpos input integer ypos input integer zpos input integer tpos input long integer fNextStep output long integer fBounceBackF Header records int fBounceBackF long tpos Function Performs an on grid bounce back for the fluid distribution function at the tpos th grid point Dependencies None Arguments tpos input long integer Comments This bounce back boundary condition is carried out using f lbopv i f lbv i i e populations are exchanged with conjugate values fBounceBackC Header records int fBounceBackC long tpos Function Performs an on grid bounce back for the solute distribution function at the tpos th grid point Dependencies None Arguments tpos input long integer Comments This bounce back boundary condition is carried out using f lbopv i f 1bv i fBounceBackT e Header records int fBounceBackC long tpos e Function Performs an on grid bounce back for the temperature distribution function at the tpos th gr
182. ing channel flow past an infinitely long cylinder that eventually produces a von Karman vortex street between two solid walls Figure 8 4 shows the flow field at the final time step an AVI video file has been rendered from the calculation and can be found in the Example Simulations page of the DL_MESO website Figure 8 4 Velocity magnitude plot from LBE 2D KarmanVortex test case scale blue to red 8 5 2D_LidCavity This is a 2D simulation of a single incompressible fluid on a 128 x 128 grid with a shear boundary condition at the top and solid walls surrounding the other edges of the system resulting in lid driven cavity flow Figure 8 5 8 6 2D RAYLEIGHBENARD 121 shows the fully developed velocity field for a Reynolds number of 100 at the final time step velocity X 05 0 04 0 02 0 015 Figure 8 5 Magnitude plot of x component velocity and velocity vector plot from LBE 2D_Lidcavity test case 8 6 2D RayleighBenard This is a 2D simulation of a single fluid undergoing natural Rayleigh B nard convection on a 102 x 51 grid The fluid is contained between two solid walls the wall at the bottom of the system is maintained at a higher temperature than that at the top Figure 8 6 shows the fully developed temperature field at the final time step for a Prandtl number of 1 and a Rayleigh number of 21250 Figure 8 6 Plot of fluid temperature for LBE 2D_RayleighBenard test case scale blue to red 8 7 2D_DropShear T
183. ing force message lbnb fspos unsigned long position for receiving force message lbnb frpos unsigned long position for sending phase index message lbnb ispos unsigned long position for receiving phase index message lbnb irpos unsigned long message type 1bmsg2x MPL Datatype message type 1bmsg2y MPI Datatype message type 1bmsg3x MPI Datatype message type lbmsg3y MPI_Datatype message type 1bmsg3z MPL Datatype message type 1bbmsg2x MPL Datatype message type 1bbmsg2y MPI Datatype message type 1bbmsg3x MPI Datatype message type 1bbmsg3y MPL Datatype message type 1bbmsg3z MPL Datatype message type lbfmsg2x MPL Datatype message type lbfmsg2y MPI Datatype message type 1lbfmsg3x MPI_Datatype message type lbfmsg3y MPI_Datatype message type 1b msg3z MPL Datatype message type lbimsg2x MPI_Datatype message type lbimsg2y MPI Datatype message type lbimsg3x MPI_Datatype message type lbimsg3y MPI_Datatype message type lbimsg3z MPI_Datatype endianness of system bigend int total calculation time totaltime double output file number qVersion int collision type parameter collide int interaction type parameter interact int incompressible fluid parameter incompress int 1 or O output file type outformat int 3Including boundary points Chapter 5 DL MESO LBE Features 5 1 Collision and Propagation Algorithms The collision and propagation routines are a fundamental part of Lattice Boltzmann Equation calculations Implementat
184. input input input input input 13 2 3 comms_module real KIND dp real KIND dp real KIND dp real KIND dp real KIND dp real KIND dp integer integer integer real KIND dp real KIND dp real KIND dp CHAPTER 13 DL MESO_DPD PACKAGE REFERENCE This module is essential for parallel running and does not require detailed knowledge for its use depending on the version and implementation of MPI available the user may wish to select between the lines USE MPI and INCLUDE mpif h for loading the necessary routines The serial version of the comms_module primarily consists of dummy routines to satisfy the required calls in the rest of the code initcomms e Header records SUBROUTINE initcomms e Function Starts Message Passing Interface MPI e Dependencies None exitcomms e Header records SUBROUTINE exitcomms e Function Closes Message Passing Interface MPI in a controlled manner e Dependencies None abortcomms e Header records SUBROUTINE abortcomms e Function Terminates Message Passing Interface MPI e Dependencies None 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 173 gsync e Header records SUBROUTINE gsync e Function Pauses running until all processes are synchronized e Dependencies None global_and e Header records SUBROUTINE global_and iii nnn nod idnode e Function Finds global logical AND from a Boolean array iii of size nnn
185. integer begin input real KIND dp final input real KIND dp shove input real KIND dp skip input logical e Comments In serial running this routine can automatically deal with non periodic boundary conditions The switch skip in the parallel version only prevents particles in the boundary halo of the current domain from being transferred for non periodic boundary conditions e g hard surfaces Lees Edwards shearing exportdensity_shear e Header records SUBROUTINE exportdensity_shear nlimit mdir mp begin final shove skip Parallel ver sion SUBROUTINE exportdensity nlimit mdir begin final Serial version e Function Exports particle data local densities to neighbouring domain as boundary halo for calculation of many body DPD interaction forces e Dependencies error msg_receive_unblocked msg_receive_sca_blocked msg_send_blocked msg_send_sca_blocked msg_wait e Arguments 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 199 nlimit input output integer mdir input integer begin input real KIND dp final input real KIND dp shove input real KIND dp shovel input real KIND dp shove2 input real KIND dp sidel input real KIND dp side2 input real KIND dp e Comments Only exists in parallel version of DL_MESO_DPD This routine requires information for the two dimensions along the surface of the shearing boundary the variables shove1 and shove2 represent the displacement due to shear while side1 a
186. inus concentration of anions per unit volume p 7 the local polarizability relative to a reference medium e g water and I the coupling constant for the reference medium The latter is given by e2 T kBT eg rre with e as the electron charge ey the dielectric constant of a vacuum and e the relative permittivity of the 1 reference medium For water at room temperature 298K with Nm molecules per DPD particle T 20 00Nim Alternatively the total electrostatic potential energy can be expressed as a sum of Coulombic energies which also include periodic images i e r 9 95 gt 11 U EZ pas iral 11 50 i gor 11 5 1 Standard Ewald sum with exponential charge smearing ewald The method currently used in DL_MESO_DPD to determine the electrostatic potential is an Ewald summation 14 U a ur y y y pee y gee 11 51 where U is a short range potential energy term that sums quickly in real space U is a long range term that sums quickly in Fourier or reciprocal space U is a self energy correction term and U is a correction for systems with a net charge While the original form of the short range electrostatic potential uses point charges this cannot be used un modified for DPD simulations soft beads used in combination with unlike point charges would collapse on top of each other forming infinitely strong ion pairs The charges are therefore spread out over a finite volume using a smeari
187. ion involves the calculation of post collisional values for the distribution functions at each lattice point at time t For the generalized form of the Lattice Boltzmann Equation with the collision operator C normally in the form of a matrix ABO fi Z t Ci and movement of these distribution functions to neighbouring lattice nodes Ji Z iAt t At fi z t which combine to give the governing equation for calculations 5 1 1 Collision algorithms The forms of collision currently available in DL MESO LBE are the Bhatnagar Gross Krook BGK single relaxation time 4 and Multiple Relaxation Time MRT schemes 5 1 1 1 BGK single relaxation time The BGK collision operator is defined by Ci fi t F 5 1 E where Ty is the relaxation time related to the kinetic shear viscosity of fluid by E 1 Az A 173 with the kinematic bulk viscosity of the fluid v set equal to 3v 7 This reduces the equation for post collisional distribution functions to fi zt f Et Fi Z t F At Tf the same as Equation 3 12 Interfacial and external forces are dealt with either by adding uE to the velocity of the fluid 41 when calculating the equilibrium distribution function fj or by adding a forcing term to the collisional distribution function 19 1 Bie coma F Wi z2 A eij F 5 2 46 CHAPTER 5 DL MESO_LBE FEATURES where 7 is defined as equal to t ap and used
188. iprop input integer 7 2 DL MESO _LBE SUBROUTINES AND FUNCTIONS 83 e Comments The default output file name is 1bout vtk and the concentration of solute 0 is output by default These can be changed by specifying an output file name and solute number up to 1bsy ns 1 when calling the routine fOutputLegacy VTKT e Header records int fOutputLegacyVTKT const char filename 1bout e Function Outputs macroscopic temperature and fluid velocity at each lattice point for system in Structured Grid Legacy VTK format e Dependencies fOutputLegacyVTKT2D fOutputLegacyVTKT3D e Arguments filename input array of characters e Comments The default output file name is lbout vtk This can be changed by specifying an output file name when calling the routine 7 2 8 IbpIOVTK fOutputVTK e Header records int fOutputVTK const char filename lbout e Function Outputs macroscopic macroscopic mass densities and fractions for all fluids concentrations for all so lutes temperature and velocity speeds along x y and z directions at each lattice point for system in Structured Grid XML VTK format e Dependencies fOutputVTK2D fOutputVTK3D e Arguments filename input array of characters e Comments The default output file name is lbout vts This can be changed by specifying an output file name when calling the routine fOutputVTKP e Header records int fOutputVTKP const char filename 1bout int iprop 0 84 CHAP
189. irectory e Type javac java to compile the source code e Type jar cfm GUI jar manifest mf class to create the GUI jar executable JAR file e Move to your working directory e Launch the GUI A Unix Linux script called makegui that performs the build of the GUI can be found in the JAVA subdirectory Your working directory is the directory from which you wish to work when running DL_MESO Working there will keep any files you generate separate from the DL_MESO source files Note in the current version of DL_MESO the working directory should be at the same directory level as the JAVA direction i e within the DL_MESO top directory and contain the executables of any external utilities required to set up input files and gather or process output files from simulations An example of such a working directory called WORK is present under the DL_MESO top directory this includes a makefile to compile all of the external utilties which can be invoked by the command make f Makefile utils In your working directory you can start the GUI with the command e java jar JAVA GUI jar You may consider saving this command in a script for simple execution An example script for Unix Linux called rungui is present in the WORK subdirectory Figure 2 1 shows the DL_MESO GUI when it is started Clicking the LBE and DPD buttons will produce the Lattice Boltzmann and Dissipative Particle Dynamics panels respectively which will guide you through setting
190. isotropic orthorhombic systems the pressure in dimension a related to the instantaneous stress tensor component dqa t is defined as 1 2 P t Vi 2 MiV q t T 2 Falat 11 18 In both equations the instantaneous values required for barostats include only the interaction forces e g soft pairwise interactions bonds electrostatics they do not include virial contributions from thermostatting which are included in reported values of system pressure All barostat definitions are expressed for the more general anisotropic case these can be applied for isotropic systems by setting P t Py t and P t all equal to P t The barostat can be selected in the CONTROL file using the directive ensemble npt the barostat type should be specified after the coupled thermostat The target system pressure can also be specified in the same file using the directive pressure By default the barostat is assumed to act isotropically although the CONTROL file directive no isotropy can be used to apply anisotropy Frozen particles are moved when a barostat is applied but their positions relative to the dimensions of the system remain constant during calculations 11 3 1 Langevin barostat langevin The governing equation for the Langevin barostat on an orthorhombic simulation cell 29 is the force exerted by the piston expressed as the time derivative of its momentum Py a WgUg a 1 1 Paja V Pa Po N 2 MiV YpPg a Opp aAt 11
191. ist e Function Reorders the global local particle number list in terms of global particle number using a Shell sort e Dependencies None search_list e Header records INTEGER FUNCTION search_list aim e Function Determines the index for the global local particle number list for a specified global particle number aim using a binary search e Dependencies None e Arguments aim input integer search_list output integer e Comments This function returns a negative value if the global particle number cannot be found in the list If it is not the only entry for the global particle number the function returns the index plus the value of nlist number of list items to flag up duplicate entries 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 185 duplicate e Header records SUBROUTINE duplicate global1 global2 indi ind2 e Function Determines the indices out of duplicate entries from the global local particle number list for a pair of specified global particle numbers global1 and global2 that produce the shortest distance between the particles e Dependencies None e Arguments global1 input integer global2 input integer ind1 input output integer ind2 input output integer contract _bndtbl e Header records SUBROUTINE contract_bndtbl e Function Strips out all bond pairs from bond table that have been reassigned to neighbouring processors e Dependencies None e Comments Only called for paral
192. iting OUTPUT file nwrite integer I O channel for reading export files nrtin integer I O channel for writing export files nrtout integer I O channel for writing CORREL file nsave integer I O channel for writing HISTORY files nhist integer number of bytes per real number lword1 integer number of bytes per double precision number lword2 integer value of 7 pi real KIND dp value of yr rtpi real KIND dp conversion factor from degrees to radians degrad real KIND dp conversion factor from radians to degrees raddeg real KIND dp conversion factor from energy to temperature fkt real KIND dp square root of 12 for random force calculations tti real KIND dp convergence error for Langevin barostat langeps real KIND dp name of processing unit idnode integer number of processing units nodes integer filename for restart files exportname character 10 switch for temperature scaling ltemp ogical TorF switch for reading CONFIG file lconfig ogical TorF switch for writing CORREL file lcorr ogical TorF switch for writing HISTORY files ltraj ogical T or F switch for modelling bonds lbond ogical TorF switch for modelling bond angles langle ogical TorF switch for modelling bond dihedrals ldihed ogical TorF switch for global holding of bond information lgbnd ogical TorF switch for defining variable force arrays lvarfc ogical TorF switch for isotropic variations of volume with pressure lisoprs ogical TorF switch for ignoring global bead numbers in
193. ition in FIELD file for molecule i A bond dihedral definition has been found in the FIELD file for the i th molecule that was not detected during the initial scan of the input file Action This error should never occur If it does please contact the authors of DL_MESO Message 40 non existent species given in FIELD file for unbonded interaction i An undefined species has been found in the i th unbonded interaction definition in the FIELD file Action Check the FIELD file particularly the th interaction type and the species definitions to ensure the species in the interaction are defined Message 41 non existent species given in FIELD file for surface interaction i An undefined species has been found in the th hard surface interaction definition in the FIELD file Action Check the FIELD file particularly the i th surface interaction and species definitions to ensure the species in the interaction are defined Message 42 non existent species given in FIELD file for frozen wall interaction An undefined species has been found in the definition for frozen particle walls in the FIELD file Action Check the FIELD file particularly the frozen particle wall and species definitions to ensure the required frozen particle species is defined Message 43 incomplete many body DPD interaction data in FIELD file Not all species pairs have defined interaction parameters in the FIELD file this is vital for systems with a
194. ity e Header records SUBROUTINE exportvelocity nlimit mdir mp begin final shove skip Parallel version SUBROUTINE exportvelocity nlimit mdir begin final Serial version e Function Exports particle velocities to neighbouring domain as boundary halo for recalculation of dissipative forces as required for DPD Velocity Verlet algorithm e Dependencies error global_sca_and_all Parallel version only msg_receive_unblocked Parallel version only msg_receive_sca_blocked Parallel version only msg_send_blocked Parallel version only msg_send_sca_blocked Parallel version only msg_wait Parallel version only e Arguments 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 197 nlimit input output integer mdir input integer mp input integer begin input real KIND dp final input real KIND dp shove input real KIND dp skip input logical e Comments In serial running this routine can automatically deal with non periodic boundary conditions The switch skip in the parallel version only prevents particles in the boundary halo of the current domain from being transferred for non periodic boundary conditions e g hard surfaces Lees Edwards shearing exportvelocity_shear e Header records SUBROUTINE exportvelocity_shear nlimit mdir begin final shove shovel shove2 sidel side2 e Function Exports particle velocities to appropriate domains as boundary halo for recalculation of dissipative forces as required fo
195. larger time steps than the standard DPD thermostat but with similarly low system viscosities As for the Lowe Andersen thermostat its implementation in parallel running uses a replicated data strategy to carry out the velocity corrections which requires additional memory per processing unit for storing the velocities of all particles in the system and the data required to modify them The efficiency of the Peters thermostat therefore depends upon the total number of particles in the system since all particle pairs are modified calculation times for this thermostat may be comparable to those for the Lowe Andersen thermostat when At x 1 11 2 5 Stoyanov Groot thermostat stoyanov The Stoyanov Groot thermostat 62 is a combination of the Lowe Andersen thermostat and a Galilean invariant Nos Hoover thermostat which acts locally and on pairs of particles During force calculations after the first Velocity Verlet stage the choice to use either the Lowe Andersen or Nos Hoover thermostats for each particle pair is made at random the Lowe Andersen thermostat is selected with a probability of TAt The system temperature is also determined in terms of relative velocities for all particle pairs i e Ding WT rij ag 3 ae YT rij kpT 11 15 11 3 BAROSTATS 145 where 1 7 rij is a smearing function for the temperature chosen to reduce to zero when rj gt re by default this is set as 7 rij 1 for r lt re For all particle p
196. lected using the pulldown list in the Gather LBE Data panel If the argument is omitted the utility will ask the user to enter the required property No other user input is required but error messages will be produced if either of the files Lbout info and 1bout ext are missing No other error messages are produced so care should be taken to ensure no VTK files for the pieces are missing particularly since these files are required for plotting as the linking files do not include the data B 2 DLMESO_DPD convert input convert input is a utility written in C to read DPD input files created for earlier versions of DL_MESO up to version 2 4 and create CONTROL and FIELD files formatted in the style for versions 2 5 and later This utility can be compiled to produce the executable convert exe with the command e c o convert exe convert input cpp if c is the command for the available C compiler This utility can be run with up to three optional command line arguments specifying the names of the CONTROL FIELD and MOLECULE files in that order if they have alternative names If the standard names are used the old CONTROL and FIELD are renamed after being read to prevent them being overwritten with the new versions of those files The MOLECULE file is no longer required and therefore does not need to be renamed molecule generate molecule generate is a utility written in C to generate the input files required for modelling particles in
197. lel version of DL_MESO_DPD when bond tables include only local bonds in each processor contract _angtbl e Header records SUBROUTINE contract_angtbl e Function Strips out all bond angle triples from angle table that have been reassigned to neighbouring processors e Dependencies None e Comments Only called for parallel version of DL MESO_DPD when angle tables include only local angles in each processor contract _dhdtbl e Header records SUBROUTINE contract_dhdtbl 186 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE e Function Strips out all bond dihedral quadruples from dihedral table that have been reassigned to neighbouring processors e Dependencies None e Comments Only called for parallel version of DL_MESO_DPD when dihedral tables include only local dihedrals in each processor bond_force Header records SUBROUTINE bond force bondtype r a b c d force potential e Function Determines the stretching force and potential energy between a pair of bonded particles Dependencies None e Arguments bondtype input integer r input real KIND dp a input real KIND dp b input real KIND dp c input real KIND dp d input real KIND dp force output real KIND dp potential output real KIND dp e Comments If required the user can add extra stretching bond interaction types in this subroutine as additional cases this would also require changes to read_control in config_module angle_f
198. lid method with all interaction forces combined together and collision operators interpolated according to local 1 1 2 Y 5 25 TE PT After the achromatic fluid is collided the fluids are segregrated to produce post collisional distribution functions mass fraction e g for each fluid This is achieved using the D Ortona algorithm 9 which gives a non zero boundary thickness between the fluids and reduces non physical effects such as pinning of drops to the lattice spatial anisotropy in interfacial tension and spurious microcurrents The equation for the post collisional segregated distribution function for fluid a 61 is given as p pep ft 3 00 Ef 2 00 8 w F hab 5 26 P ba P where 5 is a segregation parameter that controls the width of the diffuse boundary between phases and pra Ba This method can directly simulate a specified interfacial tension Gab which is related to the lattice based parameter gay by Agavv po ct 277 1 Az using the mean density po kinematic viscosity v and relaxation time Tf of a reference fluid e g the 5 27 Cab continuous fluid for the system The subroutine CalcPhaseIndex_Lishchuk calculates and stores the first derivatives of the phase indices which are subsequently used for force calculations values from neighbouring lattice points are required for calculations of interface curvature and the additional fIndexBlockCommunication routine
199. list currently available options include no interactions Shan Chen pseudopotential interactions Shan Chen interactions with surface wetting and Lishchuk continuum based interactions The number of grid points sets the size of the system For 2D systems the number of grid points in the z direction must equal 1 selecting a two dimensional lattice model greys out this box The total steps and the equilibration steps for the simulation the save span number of timesteps between system outputs and the boundary width for running the parallel version of DL_MESO_LBE are given in this row The serial version by default automatically resets the boundary width to zero The output format for system snapshots is set using this pull down list VTK Legacy VTK and Plot3D The sound speed c and kinetic viscosity v are real life quantities for the first main fluid These do not influence calculations at all but allow conversions between lattice and real units the time step and y v _ v3v lattice spacing are given by At HD and Ag 5 respectively The specified top boundary speed in lattice units i e at the maximum y value for the grid This and similar properties only need to be specified if the boundary includes a fixed velocity any specified value will be ignored for periodic bounce back and fixed density conditions Note that the z component will be greyed out for two dimensional systems The specified b
200. local variation of f in the system density of particles useful for non homogeneous or non equilibrium simulations default f 0 set required short range electrostatic cutoff radius re to f length units default f e select NVT ensemble DPD thermostat with standard MD like Velocity Verlet integration default ensemble if otherwise not specified select NVT ensemble DPD thermostat with DPD Velocity Verlet integration select NVT ensemble Lowe Andersen thermostat select NVT ensemble Peters thermostat select NVT ensemble Stoyanov Groot thermostat with coupling parameter o 157 158 ensemble npt Q langevin f fo ensemble npt langevin fi fo ensemble npt Q berendsen f stoyanov a ensemble npt stoyanov a berendsen f equilibration steps n ewald sum a ky ka kg finish global bonds job time f manybody cutoff f ndump n nfold i j k no config no electrostatics no index no isotropy permittivity constant f pressure f print every n rcut f restart restart noscale restart scale scale temperature every n smear slater f stack size n stats every n steps n surface cutoff f surface hard 7 CHAPTER 12 DL MESO DPD INPUT AND OUTPUT FILES select NPT ensemble thermostat type Q i e mduv dpdvv lowe or peters with Langevin barostat setting relaxation time 7 and viscosity parameter Yp as f and f2 respectively select NPT ensemble Stoyanov Groot thermostat with
201. lue of a is equal to vee The long range term for the Ewald sum requires the reciprocal vector k which for an orthogonal periodic simulation box of dimensions L x Ly x Lz is given by Qrky Ly 21 ka Ly 27k3 Lz w II where k ka and kg are integers positive and negative from zero to large values specified by the user as KE k3 and kz respectively for x y and z dimensions the maximum reciprocal vector Emaz using the maximum k values can also be defined Adjustments can be made to this vector to account for shearing boundaries 70 The long range potential energy term for the entire system is given by Emas ezp ee A y ieg exp E E C aV J z2 J qj exp ik 5 11 57 k 0 j where is the imaginary constant y 1 Differentiation of the potential gives the long range electrostatic force on a particle q BY Sika A EL Eoo w RAO Charged frozen particles may interact with non frozen particles but interactions between frozen particles must be excluded While the real space electrostatic potential and forces between charged frozen particles can be ignored pairwise correction terms are required to remove their contributions in reciprocal space The potential energy to be removed between a pair of charged frozen particles with Slater like charge distributions is given as rqiq Ug a erflar 1 1 Brij exp 28r 5 11 59 ij while the pairwise force is PEineorr FHM erfforyg Z exp
202. ly import_shear Parallel version only e Arguments nlimit input output integer e Comments This subroutine is applicable for integrators thermostats using single sets of particle forces i e standard Velocity Verlet Lowe Andersen Peters importdata_dpdvv1 e Header records SUBROUTINE importdata_dpdvvi nlimit e Function Applies import of particle forces constant and variable from boundary halos of neighbouring domains and or across periodic boundary conditions for the DPD Velocity Verlet algorithm e Dependencies importvariable Parallel version only e Arguments nlimit input output integer importdata_dpdvv1_shear e Header records SUBROUTINE importdata_dpdvvi_shear nlimit e Function Applies import of particle forces constant and variable from boundary halos of neighbouring domains and or across periodic boundary conditions for the DPD Velocity Verlet algorithm with Lees Edwards shearing 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 201 e Dependencies importvariable Parallel version only importvariable_shear Parallel version only e Arguments nlimit input output integer importdata_dpdvv2 e Header records SUBROUTINE importdata_dpdvv2 nlimit e Function Applies import of variable particle forces from boundary halos of neighbouring domains and or across periodic boundary conditions for the DPD Velocity Verlet algorithm e Dependencies importvariable Parallel version only e Argum
203. masses in parallel running fPrintSystemMass would be needed 7 2 DL MESO _LBE SUBROUTINES AND FUNCTIONS 77 fPrintDomainMomentum e Header records int PrintDomainMomentum e Function Calculates and prints the total fluid momentum in domain e Dependencies int fGetTotMomentDomain double momentum e Comments This routine only produces the entire system momentum if running in serial to obtain system momentum in parallel running fPrintSystemMomentum would be needed fOutput e Header records int fOutput const char filename lbout e Function Outputs all system data in required format e Dependencies int fOutputPlot3D int fOutputLegacyVTK int fOutputVTK e Comments This routine is used to write output files in parallel running a serial version of this routine fsOutput also exists fInput Parameters e Header records int fInputParameters const char filename lbin sys e Function Reads system parameters in from 1bin sys data file e Dependencies lbin sys data file e Arguments filename input array of characters e Comments The default file name is 1bin sys to use different file names the argument for this routine can be changed by the user fReadSpaceParameter e Header records int fReadSpaceParameter const char filename lbin spa 78 CHAPTER 7 DL_MESO_LBE PACKAGE REFERENCE Function Reads 2D or 3D space parameters from data file 1bin spa Depe
204. mbforce e Function Calculates many body DPD interaction force and non density dependent potential energies between par ticles i and j using parameter set k and inter particle distance rrr e Dependencies None e Arguments i input integer j input integer k input integer rrr input real KIND dp mbforce output real KIND dp e Comments The default form for the many body DPD interaction force is a two term style suitable for modelling vapour liquid mixtures 68 a re ri Fs ES A 2 Bi pi pj 1 3 n Te Td Tij This subroutine may be changed by users who wish to use different many body interaction functional forms 184 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE manybody_potential e Header records SUBROUTINE manybody_potential e Function Calculates the self energy for every particle resulting from density dependent many body interactions e Dependencies None e Comments The default form is based on the two term vapour liquid interactions used for many body forces 68 although only the density dependent potential energies are calculated using this routine the rest are calculated in manybody force Users may wish to modify this routine to use their own many body interaction models 13 2 9 bond_module This module requires the modules constants variables error_module comms_module and numeric_container to be loaded beforehand shellsort_list e Header records SUBROUTINE shellsort_l
205. me of the simulation up to 80 characters in the first line this file contains a number of directives each indicating the type and number of interactions to follow The species information must be provided first as this will be required to specify interaction data which can be included in any order using the directive species n This indicates that data for n species are to follow each species given in a single line using the following format name a8 name of species mass real particle mass for species charge real particle charge for species populations integer unbonded population of species frozen integer determines whether particles of this species are frozen 1 or not 0 The unbonded population can be omitted for species which are wholly contained in molecules as can the frozen particle parameter for unfrozen species 160 CHAPTER 12 DL MESO DPD INPUT AND OUTPUT FILES Non bonded interactions are specified with the directive interactions n with n pairwise interactions to follow each is given in a single line using the format species 1 a8 name of species 1 species 2 a8 name of species 2 key a4 interaction key see Table 12 2 variable 1 real interaction parameter see Table 12 2 variable 2 real interaction parameter see Table 12 2 variable 3 real interaction parameter see Table 12 2 variable 4 real interaction parameter see Table 12 2 variable 5 real interaction parameter see Table 12 2 variable 6 real interactio
206. ms with periodic boundary conditions DL_MESO_DPD uses the Ewald sum to calculate Coulombic interactions see Section 11 5 Calculation of the real space component in routine ewald_real_slater uses the same link cell algorithm as for other pairwise interactions albeit using a larger cutoff radius re and requires a larger boundary halo than for standard pairwise interactions 11 2 Thermostats and integration algorithms The integration algorithms in DL_MESO_DPD are based on the second order Velocity Verlet VV scheme 67 which yields the positions velocities and forces of particles at the same time and is generally used in molecular dynamics simulations This algorithm has two stages The first stage advances the particle velocities to time t At by integrating the forces and uses the new half step velocities to advance the position to time t At A a At F t Ti t At F t Atv t 4At 11 2 The positions at the end of the time step allow the forces to be recalculated before the second stage of the algorithm is applied to advance the half step velocities to the end of the time step by integrating with the new force 5 0 t At 0 t At poaa 11 3 Mi Five thermostatting algorithms are currently available in DL_MESO_DPD two variants of the standard DPD thermostat and three alternative schemes which apply velocity corrections to the particles after force integration The algorithm can be selected in the CONTROL file u
207. n 73 concave edges and corners use equilibrium boundary con ditions with the density on the edge and at the grid point assumed to be equal to the values at their nearest neighbours in the bulk fluid The array uwal1 is the velocity at the grid point for all fluids which is subsequently used for solute concentration and temperature boundary conditions fFixedDensityFluid e Header records int fFixedDensityFluid long tpos int prop double uwall e Function Calculates the particle distribution function at a fixed density boundary e Dependencies Many for different lattice schemes e Arguments tpos input long integer prop input long integer uwall output array of doubles e Comments Planar surface calculations are based on 73 concave edges and corners assume zero speed at the boundary The array uwall is the velocity at the grid point for all fluids which is subsequently used for solute concentration and temperature boundary conditions fFixedSoluteConcen e Header records int fFixedSoluteConcen long tpos int prop double uwall e Function Calculates the particle distribution function at a fixed composition boundary e Dependencies Many for different lattice schemes e Arguments tpos input long integer prop input long integer uwall input array of doubles 90 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Comments Planar surface calculations are based on 28 concave edges and corners assume zero speed at th
208. n dimension a by the factor Ha 1 BAP a Po Tp with the option of keeping the system isotropic by using equal values of P for all dimensions This may be switched off if imposing constant surface tensions at given planar surfaces Rescaling of the simulation volume takes place in the first stage while calculation of the rescaling factor Ha takes place in the second stage after force integration 13 2 15 statistics module This module requires the modules constants variables start module comms _module and numeric_container to be loaded beforehand printout e Header records SUBROUTINE printout time lbegin e Function Writes summary of simulation at the current time step to OUTPUT file e Dependencies None e Arguments time input real KIND dp lbegin input logical e Comments The logical 1begin indicates whether or not the column titles should be printed before the data corout e Header records SUBROUTINE corout time e Function Writes statistical data to CORREL data file e Dependencies None e Arguments time input real KIND dp 214 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE histout e Header records SUBROUTINE histout time e Function Writes trajectory data particle positions and velocities to HISTORY data files e Dependencies None e Arguments time input real KIND dp result e Header records SUBROUTINE result e Function Writes final summary of simulation to OUTPUT
209. n parameter see Table 12 2 variable 7 real interaction parameter see Table 12 2 If any interactions are many body DPD the interactions for all possible species pairs must be specified in the FIELD file and values for all parameters must be given even if not all of them are required for the many body DPD model in use Otherwise only like like same species i e i j interactions are required as any missing interaction data can be derived using mixing rules If using the Lowe Andersen or Stoyanov Groot thermostats the dissipative factor yi should be replaced with the bath collision frequency Tij Table 12 2 Non bonded interactions key interaction type Parameters 1 7 lj Lennard Jones Eij Cig Vij S 7 A J wca Weeks Chandler Andersen j Gij Vig dpd Groot Warren DPD Aij Teij Vag z z a j mdpd Many body DPD Aij Big Ci Dig Ei Seijo Tij Molecules are specified using the directive molecules n with data for n molecule types to follow Immediately after this directive the following records are included to define each molecule type 1 Molecule name which can be a character string of up to 8 characters in length 2 nummols n where n is the number of times a molecule of this type appears in the system This is followed by the data for the molecule type 3 beads n where n gives the number of beads particles in this molecule type A number of records follow for eac
210. n the data type for the array indicates that it is allocatable 4 3 THE PARAMETERS AND THEIR FUNCTIONS Table 4 8 DL_MESO_LBE Parameters 41 function parameter data type notation system information lbsy structure domain information 1bdm structure neighbour information 1bnb structure A6 space dimension lbsy nd int number of discrete speeds lbsy nq int number of fluids lbsy nf int gt 1 number of solutes lbsy nc int temperature scalars lbsy nt int 1 or 0 phase field order parameter lbsy pf int 1 or 0 grid points in x direction lbsy nx int grid points in y direction lbsy ny int grid points in z direction lbsy nz int domain boundary width lbsy bwid int gt 1 system dimension along x lbxsize double total calculation steps lbtotstep int equilibration calculation steps lbequstep int data save interval lbsave int current calculation step lbcurstep int steering lbsteer int lor 0 noise intensity lbnoise double evaporation limit lbevaplim double initial system velocity lbiniv double A3 top boundary velocity lbtopv double A3 bottom boundary velocity lbbotv double A3 front boundary velocity lbfrov double A3 back boundary velocity lbbakv double A3 left boundary velocity lblefv double A3 right boundary velocity lbrigv double A3 constant incompressible fluid density po lbincp double A lbsy nf initial fluid density lbinip double A lbsy nf top boundary fluid density lbtopp double A lbsy nf bottom bou
211. nBlockCommunication may be required for using the combined swap prop agation routine fPropagationCombinedSwap in serial running fsForcePeriodic e Header records int fsForcePeriodic 92 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Function Applies periodic boundary condition for serial calculations with non zero boundary domain widths by copying interaction forces from edges of fluid points e Dependencies fsForcePeriodic2D fsForcePeriodic3D e Comments Serial equivalent of fForceNonBlockCommunication may be required for using the combined swap propa gation routine fPropagationCombinedSwap in serial running for any system requiring non constant forces fsIndexPeriodic e Header records int fsIndexPeriodic e Function Applies periodic boundary condition for serial calculations with non zero boundary domain widths by copying phase index spatial derivatives from edges of fluid points e Dependencies fsIndexPeriodic2D fsIndexPeriodic3D e Comments Serial equivalent of fIndexNonBlockCommunication may be required for using the combined swap prop agation routine fPropagationCombinedSwap in serial running with the Lishchuk mesophase algorithm 7 2 10 IbpFORCE fInteractionForceZero e Header records int fInteractionForceZero e Function Resets all interaction forces to zero prior to calculations e Dependencies None e Comments This routine should be called before any non constant forces e g
212. nbonded potential models in use If interaction parameters between different particle species are not specified in the FIELD file these can be determined by mixing rules Energy and dissipative parameters e g Aag and Yag for DPD can be determined for unlike particle pairs as geometric means of these parameters for same species interactions e g Aap Y Ano Age while interaction lengths are set to the arithmetic mean e g Te aa T Tc BB 2 Teab It should be noted that interaction lengths have to be less than or equal to the maximum interaction cut off radius re which applies for dissipative and random force interactions if the maximum interaction cut off radius is not specified in the CONTROL file the maximum specified value of reag will be used Frozen particles are included in all interactions but the resultant forces on these particles are not subsequently integrated Four types of pairwise interactions between particles are available in DL_ MESO_DPD Lennard Jones Weeks Chandler Andersen Groot Warren standard DPD and many body density dependent DPD In the case that many body DPD interactions are used for any particle pair mixing rules cannot be used and thus interaction parameters for all particle pairs must be specified by the user 148 CHAPTER 11 DL MESO DPD FEATURES 11 4 1 Lennard Jones 1j The Lennard Jones potential 30 is a mathematically simple model that approximates interactions both attrac tive a
213. nctions sitting on each wall node Zw i e filEw t fj Ew t 5 11 where j is the opposite lattice link to 7 i e The reflection of distribution functions occurs on grid On grid bounce back is a first order approximation of the boundary condition 45 i e the error is proportional to the lattice spacing Az but it is completely local i e only uses distribution functions at the wall node 5 2 3 Mid grid bounce back Like the on grid version the mid grid bounce back condition applies a no slip condition at a boundary halfway between lattice points 63 This is applied by assigning post collisional distribution functions to the wall node based on those values at neighbouring points i e filGw t fi Ew EAt tt 5 12 This method essentially applies the actual reflection halfway between timesteps and is a spatially second order method although it is weakly non local due to its use of distribution functions from neighbouring nodes 5 2 4 Constant pressure velocity To specify either velocities or densities pressures at planar boundaries the Zou He method 73 is available in DL_MESO_LBE This is based upon applying the bounce back rule to the non equilibrium distribution functions 1 e EOS Gas 5 13 where qa fi fj with the equilibrium distribution function ff as a function of density and velocity This function can be used to determine the missing wall velocity or density along with the known dist
214. nd repulsive between pairs of neutral atoms or molecules U rij 4eij 2 as 2 11 34 where is the depth of the potential well and g is the finite distance at which the potential is zero between particles i and j This potential and its related force are calculated for all interparticle distances r less than the interaction cutoff radius re Long range system wide corrections to the potential and virial are required g ur SPR 5ap NaN peas Fe 11 35 a B gt a 12013 20 a a wr A 2 dap Na Nocas ao os 773 11 36 a B gt a where dag is the Kronecker delta 1 when a 8 0 when a 4 B and Na the total number of particles of species a These corrections multiplied by the volume are stored in the array clr to eliminate the need to adjust them if the system volume is changed by a barostat 11 4 2 Weeks Chandler Andersen wca The Weeks Chandler Andersen potential 69 is a modification of the Lennard Jones potential to produce purely repulsive short range interactions R O U rij 4 ij om 0 H ij 11 37 ij ij 1 This interaction is applied for interparticle distances up to 280 which should be less than or equal to the interaction cutoff radius re No long range corrections to potential energy or virials are required 11 4 3 Standard DPD dpd The Groot Warren standard form of DPD 16 uses the following purely repulsive soft potential 1 ea NS U rij gis
215. nd side2 are the domain dimensions deportdata e Header records SUBROUTINE deportdata nlimit e Function Applies deport of particles from boundary halos to neighbouring domains and or periodic boundary conditions e Dependencies deport Parallel version only e Arguments nlimit input output integer deportdata_shear e Header records SUBROUTINE deportdata_shear nlimit e Function Applies deport of particles from boundary halos to neighbouring domains and or periodic boundary conditions with Lees Edwards shearing e Dependencies deport Parallel version only deport_shear Parallel version only e Arguments nlimit input output integer importdata e Header records SUBROUTINE importdata nlimit e Function Applies import of particle forces from boundary halos of neighbouring domains and or across periodic boundary conditions 200 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE e Dependencies import Parallel version only e Arguments nlimit input output integer e Comments This subroutine is applicable for integrators thermostats using single sets of particle forces i e standard Velocity Verlet Lowe Andersen Peters importdata_shear e Header records SUBROUTINE importdata_shear nlimit e Function Applies import of particle forces from boundary halos of neighbouring domains and or across periodic boundary conditions with Lees Edwards shearing e Dependencies import Parallel version on
216. ndary fluid density lbbotp double A lbsy nf front boundary fluid density lbfrop double A lbsy nf back boundary fluid density lbbakp double A lbsy nf left boundary fluid density lblefp double A lbsy nf right boundary fluid density lbrigp double A lbsy nf initial composition lbinic double A lbsy nc top boundary composition lbtopc double A lbsy nc bottom boundary composition lbbotc double A lbsy nc front boundary composition lbfroc double A lbsy nc back boundary composition lbbakc double A lbsy nc left boundary composition lblefc double A lbsy nc right boundary composition lbrigc double A 1bsy nc initial temperature lbinit double top boundary temperature lbtopt double bottom boundary temperature lbbott double front boundary temperature lbfrot double back boundary temperature lbbakt double left boundary temperature lbleft double right boundary temperature lbrigt double system heating rate lbsysdt double top boundary heating rate lbtopdt double 42 CHAPTER 4 DL MESO LBE BASIC DEFINITION Table 4 8 DL_MESO_LBE Parameters continued function parameter data type notation bottom boundary heating rate lbbotdt double front boundary heating rate lbfrodt double back boundary heating rate lbbakdt double left boundary heating rate lblefdt double right boundary heating rate lbrigdt double Boussinesq high temperature lbbousth double Boussinesq low temperature 1bboustl double fluid inverse relaxation time Fe lbtf dou
217. ndencies lbin spa data file fReadSpace2D fReadSpace3D Arguments filename input array of characters Comments The default file name is lbin spa this can be changed by the user if the space data file has a different name If system is to be equilibrated on grid bounce back is initially and temporarily used in place all boundary conditions specifying fixed values for fluid velocities densities solute concentrations and temperatures fReadInitialState Header records int fReadInitialState const char filename lbin init Function Reads initial velocities densities concentrations and temperatures from data file lbin init and calculates initial distribution functions Dependencies lbin init data file fReadInitialState2D fReadInitialState3D Arguments filename input array of characters Comments The default file name is lbin init this can be changed by the user if the initial state data file has a different name This routine will replace the default values of all properties at specified points and should be called after fInitializeSysten fSetoffSteer e Header records int fSetoffSteer e Function Creates a file called notsteer to prevent DL_MESO_LBE from creating new 1bin sys and 1bin spa files which occurs if notsteer is missing e Dependencies None e Comments If the user has changed the input datafiles the code will run with new parameters 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS 7
218. ndex This algorithm requires a modification to the collision step at each lattice point all fluids are collided as a single fluid which is then segregated back out into the individual fluids 3 6 Summary of Lattice Boltzmann Equation Lattice Boltzmann is an established numerical methodology for handling hydrodynamics in fluid It is particu larly suited to simulating systems with complex boundary conditions and is also suitable for systems with phase transitions since mesoscale interactions can be merged into the method easily Chapter 4 DL MESO LBE Basic Definition 4 1 Lattice models DL_MESO LBE utilizes a right handed Cartesian coordinate system with the x axis from left to right in the horizontal direction the y axis from low to high in the vertical direction and z axis from back to front D2Q9 D3Q15 D3Q19 and D3Q27 lattice models have been included The speed vectors and weight factors are arranged to allow the use of swap algorithms for propagation 43 The transformation matrices T for Multiple Relaxation Time MRT schemes are included for each lattice except D3Q27 along with the equilibrium moments M 41 expressed for the incompressible case for the compressible case pg is substituted with p gt collision operators 5 definition of bulk viscosity 1 and forcing source terms 5 D2Q9 Weight factor 2 Wi 0 4 2 4 6 8 i 153 957 z Speed
219. ne to compile both sets for use with the GUI The latter can be invoked using the command e make f Makefile utils Some further details on these utilities can be found in the README files in the source directories B 1 DL_MESO LBE lbeinitcreate lbeinitcreate is a utility written in C to create initialisation files lbin init to override the default initial conditions This utility can add fluid drops to the system either circular in 2D or spherical in 3D and rectangular sources of specified solute concentrations or temperature to a system If c is the command for the available C compiler the executable init exe can be produced by typing e c o init exe lbeinitcreate cpp and run at the command line init exe or init exe A pre existing 1bin sys file needs to exist in the directory where the utility is run as this provides information on the dimensions and size of the simulation system the numbers of fluids and initial and constant densities for each fluid the number of solutes whether or not a thermal lattice is included and the default initial velocity This information is displayed on the screen when the utility is run if no 1bin sys file can be found an error message will be displayed and the utility will terminate If more than one fluid is specified in the lbin sys file the utility will then attempt to determine the continuous fluid for the system from the initial densities and if necessary ask the u
220. nergy corrections for charged systems ewald_frozen_slater e Header records SUBROUTINE ewald_frozen_slater e Function Calculates corrective forces potential energies virials and stress tensors to remove electrostatic interac tions between charged frozen particles in the Ewald summation e Dependencies erfdp images e Comments This routine uses a replicated data strategy to determine all electrostatic interactions between charged frozen particles If a simulation does not use a barostat only one call prior to force calculations is required it otherwise has to be called whenever the simulation volume changes 13 2 8 manybody_module This module requires pre loading of the constants and variables modules local_density e Header records SUBROUTINE local_density 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 183 e Function Calculates local densities for many body DPD interactions e Dependencies weight_rho e Comments Uses the parallel link cell structure to calculate local densities for each component Pi 5 wP rij A omitting self contributions for each particle 66 weight_rho e Header records REAL KIND dp FUNCTION weight_rho rrr e Function Calculates normalized weight function for local densities e Dependencies None e Comments The default weight function 68 is which may be changed by the user manybody_force e Header records SUBROUTINE manybody_force i j k rrr
221. ng charge distribution f r The current approach uses a Slater type distribution i e q 2r Fr e 7 11 52 where A is the decay length of the charge This gives a potential energy between charged particles and j of Paid U rij 2 1 1 Brij exp 26ri 11 53 Arr 11 5 LONG RANGED ELECTROSTATIC COULOMBIC POTENTIALS 151 and the corresponding electrostatic force is Pag rig Ex rig 37 2 L exp 26rig 1 28ra Bray 2 11 54 ij ij e where 6 For large particle separations these expressions reduce down to the standard expressions for point charges and thus the reciprocal space part of the Ewald sum can be calculated without modification The real space terms for the Ewald sum are modifications of the above expressions evaluated for particle pairs when the separation is less than the electrostatic short range real space cutoff re The short range potential energy between particles i and j is given as Taig ust PU erfe ari 1 1 Brij exp 28ri 11 55 3 4TTij and the pairwise force is FPES Tuay 20785 exp a r erfe arj 1 exp 26r 1 28r 1 Br yy 5 11 56 ij 4rr yT ij ij a ij ij Tij 2 where a is a convergence parameter that controls the real space contribution chosen to give negligible contribu tions beyond the real space cutoff If a calculational precision of e is required for the Ewald sum the required In ere va
222. ng equilibration temp scaling interval The latter can be set to zero if no temperature rescaling is required The starting time step save start and the number of time steps between saves save interval of trajectory data to HISTORY files for later visualization The latter can be set to zero if no trajectory data are required The numbers of time steps between printing summaries in the OUTPUT file print interval and outputs of statistical data system energy potential energies pressure temperature etc to a plottable CORREL file plot interval The latter value can be set to zero if no plot file is required The number of time steps between dumps of system configurations to export files for simulation restarts dump interval and the percentage variation in particle density density var to allow for unevenly distributed systems The job time is the maximum real time that can be spent carrying out the DPD simulation the close time gives the time needed to write restart files and shut down the calculation in a controlled manner The restart key for the simulation this can either be set to none for a new simulation a full restart to continue a previous run using export files a new run which takes a starting state particle positions and velocities for a new simulation from export files and rescaled does the same as a new run but additionally rescales the particle velocities to give the specified system temperature The
223. nged cutoff for interparticle potentials and forces There is a need for processing units to exchange halo data i e sending the contents of link cells at the boundaries of each domain to neighbouring units so each may have all the necessary information to compute pairwise forces acting on the particles in its allotted domain Similarly the force and virial contributions from particles in boundary halos need to be returned to their original processing units for summation The link cell algorithm is also applied in serial by duplicating system data to create the boundary halo across periodic boundaries The size of the boundary halo which can be specified by the user in the CONTROL file should not be greater than the minimum system dimension per domain for good parallel performance it is recommended that the halo size should be no larger than one third of the smallest subdomain dimension The value of maxdim calculated after reading the input files in config_module gives the maximum sizes of force velocity and position arrays This value should be large enough to hold all particles in each domain plus any particles in boundary halos including duplicates when running in serial or using smaller numbers of processing units If the density of the system is likely to be uneven the user can increase the size of maxdim by specifying an additional density variation in the CONTROL file 11 1 1 Intramolecular interactions Intramolecular interac
224. nown or calculated velocity for all fluids at the same boundary DL MESO LBE includes implementations of the Inamuro boundary condition for all four lattice schemes Only planar surfaces can be dealt with using this method as for constant pressure boundaries concave edges and corners use the equilibrium distribution function for the required concentration temperature and the known or calculated velocity On grid bounce back is used for Neumann zero gradient conditions of solute concentrations and or temperature to keep this type of boundary condition entirely local 5 3 Mesoscale interactions DL_MESO_LBE includes a number of algorithms that can be used to apply interactions between fluid compo nents at the mesoscale most commonly to model immiscible fluids The user should take care to ensure the correct model is used for the type of system being modelled If 1bin init files are used to insert fluid drops into the simulation domain DL MESO LBE includes the option of carrying out equilibration to allow the shapes of drops to settle by modelling the system without external 5 3 MESOSCALE INTERACTIONS 51 body forces and boundaries imposing specific velocities densities solute concentrations or temperatures This option can be selected using the equilibration_step keyword in the lbin sys file 5 3 1 Shan Chen pseudopotential model The Shan Chen model 55 56 models interactions between multiple phases and components by calculating
225. ny many body DPD interactions as universal mixing rules are unavailable for many body DPD parameters 234 APPENDIX C DL MESO _DPD ERROR MESSAGES Action Check the FIELD file to ensure that unbonded interactions between every possible species pair is defined Message 44 no interaction data in FIELD file for single species i Unbonded interaction data between particle pairs of the same species are unavailable in the FIELD file mixing rules to determine any missing interaction data thus cannot be applied Action Check the FIELD file to ensure that unbonded interactions exist for same species pairs Message 45 zero reciprocal vector range for ewald sum The maximum reciprocal vector Mili has not been defined for systems requiring Ewald sum electrostatics Action Look in the CONTROL file and make sure the ewald directive includes the convergence parameter and the extents of the maximum reciprocal vector k ka and ks Message 50 insufficient number of beads per node allocated for required initialization The value of maxdim is not large enough to include the unbonded particles assigned to each processor for a new simulation without a CONFIG file Action This error is unlikely to happen as maxdim is calculated according to the numbers of particles and processors available but the user may wish to use the densvar directive in the CONTROL file to increase this value Message 51 discrepency in total number of starting bea
226. o 1 2 0 20 ul de 3 7 270 3 4 STRUCTURAL RELAXATION AND MACROSCOPIC EQUATIONS 25 Using Gaussian quadrature Equation 3 7 changes into v20p Ena gt ww 2 vee sae 1 2 2 0 2 2 u 3 8 Let os Da CE wes 3 9 276 and fit wip 1 2 E0 2 0 ul 3 10 The value of w c can be obtained from Gauss Hermite integration Equation 3 10 is the equilibrium particle distribution function in the discrete regime w is called the weight factor for speed vector ci Equation 3 10 can also be written as 3 11 fo wip E _ Gi 9 a a T c2 2c4 2c where c v30 4 Shed is the modulus of the basic lattice vector and equivalent to the fluid speed of sound e g for water at 20 C c 367 8 m s 3 4 Structural Relaxation and Macroscopic Equations The Lattice Boltzmann method often uses the BGK Bhatnagar Gross and Krook approximation 4 to describe the structural relaxation The single particle distribution function evolves to the equilibrium state via fi 2 At t At fi z t fs 8 F 3 12 where Ty is called the relaxation time and is related to the kinetic viscosity of fluid This evolution equation can be divided into two separate processes of collision where tt denotes a time after collision has taken place A fi t 7 3 13 and propagation or free streaming fi Z At t At fi 2 4 3 14 To derive the macroscopic equations th
227. o Gaussian random variables with zero mean and unity variance sclsum e Header records REAL KIND dp FUNCTION sclsum n a i e Function Calculates the scalar sum of an array e Dependencies None 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 171 e Arguments n input integer a input array of real KIND dp i input integer sclsum output real KIND dp erfcdp e Header records REAL KIND dp FUNCTION erfcdp x e Function Calculates the complementary error function for x erfc x e Dependencies None e Arguments x input real KIND dp erfcdp output real KIND dp e Comments This approximation for the function is based on a Chebyshev polynomial fitting 22 erfdp e Header records REAL KIND dp FUNCTION erfdp x e Function Calculates the error function for x erf x e Dependencies None e Arguments x input real KIND dp erfdp output real KIND dp e Comments This approximation for the function is based on a Chebyshev polynomial fitting 22 images e Header records SUBROUTINE images dx dy dz 1x ly lz shearx sheary shearz sldx sldy sldz e Function Calculates the minimum distance between two particles in a periodic orthogonal box adjusting for Lees Edwards shear if necessary e Dependencies None 172 e Arguments dx dy dz 1x ly 1z shearx sheary shearz sldx sldy sldz input output input output input output input input input input
228. obal identity numbers from nusyst 1 to nsyst are assigned to particles belonging to molecules When particles are copied into boundary halos the processor numbers and local particle numbers in their original processors are stored in the integer arrays 131 132 CHAPTER 10 DL MESO DPD BASIC DEFINITION Table 10 1 System information parameter meaning text name of calculation nsyst total number of particles nusyst total number of unbonded particles nfsyst total number of frozen particles nspe number of particle species nmoldef number of molecule types temp specified system temperature kgT prszero specified system pressure Po rcut interaction cutoff radius re rmbcut many body interaction cutoff radius r relec short range electrostatic interaction cutoff radius re sr zcut surface repulsion cutoff distance ze rhalo size of boundary halo nrun number of calculation timesteps nseql number of equilibration timesteps tstep duration of calculation timestep At timjob maximum time available to run calculation tclose time required to shut down calculation kres calculation restart parameter nsbpo interval for printing data to OUTPUT file ltraj switch for saving trajectory data to HISTORY file s straj starting timestep saving trajectory data to HISTORY file s ntraj interval for saving trajectory data to HISTORY file s nstk size of statistical data stack ltemp switch for temperature scaling bef
229. odic Define initial condition lbin init This optional file cannot currently be created by the GUI the user must create this file or use the utility lbeinitcreate if it is required The following format is required for each lattice point whose default velocity fluid densities solute concentrations or temperature needs replacing 0 lbsy nf 1 0 lbsy nc 1 X Y Z Uz Uy Uz p p Y A add T Note that three values for each grid position and velocity must be included the values for z components in two dimensional simulations must be set to zero At each grid point specified density concentration temperature values must be included for all lattices used in calculations the total number of values in each line must be equal to 6 1bsy nf lbsy nc lbsy nt 6 2 Output files DL_MESO_LBE prints information about the simulation to the screen or standard output e welcome messages a description of the simulation to be carried out e details of domain decomposition if running in parallel e reports on the masses and momentum of fluids in the system at user specified intervals a final summary including a calculation efficiency measure and a reminder to cite DL_MESO for any published results This information can be directed to a file specified at the command line e g by launching DL MESO_LBE using the command e lbe exe gt OUTPUT Snapshots of the simulation can be written in Structured Grid XML VTK Structured Grid Legacy VTK
230. odule requires preloading of the constants variables domain module surface module comms_module error module numeric_container and field module modules Like the field module different versions of the subroutine mdvv dpdvv lowe peters stoyanov are available for each thermostat integrator verlet_ e Header records SUBROUTINE verlet_ stage e Function Solves the equations of motion using the Velocity Verlet scheme 67 e Dependencies hardreflect deportdata error exportvelocitydata DPD VV only dragforces_dpdvv DPD VV only importforcedata DPD VV only global_sca_sca_int global_sca_sca_dble global_sum_int Lowe Peters Stoyanov e Arguments stage input integer e Comments All versions of this subroutine use the standard Velocity Verlet algorithm to integrate the equations de _ F dt mi dj _ a Both the MD VV and DPD VV algorithms use dissipative and random forces as the thermostat with the DPD VV algorithm repeating the calculation of dissipative forces at the end of the time step The Lowe Andersen Peters and Stoyanov Groot thermostats are applied after all other forces are integrated 212 verlet_ _lang e Header records SUBROUTINE verlet_ _lang stage Function CHAPTER 13 DL MESO DPD PACKAGE REFERENCE Solves the equations of motion using the Velocity Verlet scheme coupled with a Langevin barostat 29 Dependencies hardreflect deportdata frozenbead error exportveloci
231. ody DPD interactions are not included and mixing rules are to be used between unlike species the file can subsequently be edited to remove extraneous definitions 4 The maximum interaction length between the two species 7 or cij can be typed into this box and set using the button SET I 5 The dissipative factor 7 or collision frequency I for the species pair i e the parameter for the selected thermostat can be typed into this box and set using the SET I button 18 CHAPTER 2 THE DL_MESO GUI 6 If a non periodic frozen bead surface is defined the species of beads making up the walls can be selected using this pull down box 7 The wall density of frozen beads can be typed into this box This is greyed out if frozen bead walls are not specified 8 The wall thickness of frozen beads can be typed into this box This is greyed out if frozen bead walls are not specified The parameters for external force fields can be given in the pop up window shown in Figure 2 8 c 1 The type of external field to be used in the simulation 2 External field parameters for constant gravitational fields or similar constant external force fields the x y and z components of gravitational acceleration G need to be specified For linear shear boundaries the x y and z components of the boundary velocity V need to be defined although the component orthogonal to the wall will be ignored in simulations After filling
232. ody interaction parameters per species pair can be specified in the FIELD file The many body DPD example provided with DL_MESO_DPD produces a van der Waals like equation of state and can be used to model vapour liquid interfaces 68 The potential excess free energy per particle is given by 4 ee To _ Tr E Y7 p 39 Ais 30 Pub 11 47 150 CHAPTER 11 DL MESO DPD FEATURES where P is equivalent to p but with the cutoff set to re instead of rg The associated pairwise force is equal to FS As 1 ES Bi pi p3 1 13 T 11 48 Tc ij Pa Tij In the routine provided the terms with A for both force and potential are calculated as though they are standard DPD By setting A lt 0 and Bij gt 0 a vapour liquid mixture can be modelled and its equation of state for a single component is given as p pkgT aAp 20 Br p cp d where a 0 101 c and d are numerical offsets Parameters A and B for each interacting pair of species can be specified in the FIELD file 11 5 Long ranged Electrostatic Coulombic Potentials Compared to other interactions in DPD electrostatic interactions act over considerably longer ranges which can also include periodic images of the system The governing equation for finding the electric potential is the Poisson equation shown here in dimensionless form 15 V PVY Tp 11 49 where y is the electric potential p the charge density concentration of cations m
233. of particle 7 Additional pairwise forces may be BD and ES are the conservative drag and random or stochastic pair forces respectively Each included for more complicated systems such as those involving chains of particles bonded together 52 The conservative interactions are usually soft i e weakly interacting so that the particles can pass by each other or even through each other relatively easily so that equilibrium is achieved quickly A common form of interaction potential is an inverse parabola 2 1 Taj V rij Aijle 1 a 2 9 4 2 Te where rj r Til re is a cutoff radius and Aj is the interaction strength A may be the same for all particle pairs or may be different for different particle types Equation 9 4 gives rise to a repulsive force of the form RO Cip Tii Tij Tig Fg Arg rij Aij 1 man 9 5 ij c ij This is the deterministic or conservative force ES exerted on particle i by particle j Note the switching function w rij and the force are zero when rj gt re and thus the particles have an effective diameter of 1 in units of the cutoff radius re The stochastic forces experienced by the particles is again pairwise in nature and takes the form R 1 ij OijWw rij Cig At 2 Tij BR bij 9 6 in which At is the time step and w r j is a switching function which imposes a finite limit on the range of the stochastic force is a random number with zero me
234. on engsic real KIND dp charged system correction qfixv real KIND dp Slater charge smearing coefficient 8 betaew real KIND dp bond interaction parameter a aabond real KIND dp A nbonddef bond interaction parameter b bbbond real KIND dp A nbonddef bond interaction parameter c ccbond real KIND dp A nbonddef bond interaction parameter d ddbond real KIND dp A nbonddef angle interaction parameter a aaang real KIND dp A nbonddef angle interaction parameter b bbang real KIND dp A nbonddef angle interaction parameter c ccang real KIND dp A nbonddef angle interaction parameter d ddang real KIND dp A nbonddef dihedral interaction parameter a aadhd real KIND dp A nbonddef dihedral interaction parameter b bbdhd real KIND dp A nbonddef dihedral interaction parameter c ccdhd real KIND dp A nbonddef dihedral interaction parameter d dddhd real KIND dp A nbonddef bond types bdtype integer A nbonddef bond angle types angtype integer A nbonddef bond dihedral types dhdtype integer A nbonddef molecule isomer switch moliso logical A nbonddef bond table bndtbl integer A numbond 3 bond angle table angtbl integer A numang 4 bond dihedral table dhdtbl integer A numdhd 5 global local particle number list lblclst integer A maxdim 2 number of bonds in table nbonds integer number of bond angles in table nangles integer number of bond dihedrals in table ndiheds integer number of entries in global local particle number list nli
235. onvective flow fields at the final time step for a Prandtl number of 1 and a Rayleigh number of 10000 Es Figure 8 10 Plot of fluid temperature for LBE 3D_RayleighBenard test case scale blue to red with streamlines depicting convective flow Part II Dissipative Particle Dynamics DPD 125 Chapter 9 Dissipative Particle Dynamics Basic Theory 9 1 Introduction Dissipative Particle Dynamics DPD is an off lattice discrete particle method for modelling mesoscopic systems It has little in common with Lattice Boltzmann methods except in its application to systems of similar length and time scales The DPD method inherits its methodology from classical Molecular Dynamics MD particularly from Brownian Dynamics BD It differs from BD however in an important way it is Galilean invariant and for this reason conserves hydrodynamic behaviour while the BD method does not Many systems are crucially dependent on hydrodynamic interactions and it is essential to retain this feature in the model DPD is particularly useful for simulating systems on the near molecular scale such as polymers biopolymers lipids emulsions and surfactants systems in which large scale structure evolves on a time scale that is too long to be modelled effectively by MD DPD may also be used when such systems experience shear and flow gradients The DPD algorithm can be summarized by the following A condensed phase system may be modelled as a s
236. or wall normal to z axis npzfwz integer frozen bead density of walls frzwdens real KIND dp width of frozen bead wall normal to x axis frzwxwid real KIND dp width of frozen bead wall normal to y axis frzwywid real KIND dp width of frozen bead wall normal to z axis frzwzwid real KIND dp x component of external body acceleration per particle bdfrcx real KIND dp 138 CHAPTER 10 DL MESO DPD BASIC DEFINITION Table 10 4 DL _MESO_DPD Parameters continued function parameter data type notation y component of external body acceleration per particle bdfrcy real KIND dp z component of external body acceleration per particle bdfrez real KIND dp x component of Lees Edwards shearing velocity shrvx real KIND dp y component of Lees Edwards shearing velocity shrvy real KIND dp z component of Lees Edwards shearing velocity shrvz real KIND dp x component of Lees Edwards shearing displacement shrdx real KIND dp y component of Lees Edwards shearing displacement shrdy real KIND dp z component of Lees Edwards shearing displacement shrdz real KIND dp force x component on particle xx real KIND dp A maxdim force y component on particle fyy real KIND dp A maxdim force z component on particle fzz real KIND dp A maxdim variable force z component on particle fvx real KIND dp A maxdim variable force y component on particle fvy real KIND dp A maxdim variable force z component on particle fvz real KIND dp A ma
237. orce e Header records SUBROUTINE angle force angtype theta rab rcb a b c d force potential virial dfab dfcb e Function Determines the bond angle force potential energy and virial across a triple of bonded particles e Dependencies None 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 187 e Arguments angtype input integer theta input real KIND dp rab input real KIND dp rcb input real KIND dp a input real KIND dp b input real KIND dp c input real KIND dp d input real KIND dp force output real KIND dp potential output real KIND dp virial output real KIND dp dfab output real KIND dp dfcb output real KIND dp e Comments If required the user can add extra bond angle interaction types in this subroutine as additional cases this would also require changes to read_control in config_module dihedral_force e Header records SUBROUTINE dihedral_force dhdtype phi pb pc a b c d force potential e Function Determines the bond dihedral force and potential energy across a quadruple of bonded particles e Dependencies None e Arguments dhdtype input integer phi input real KIND dp pb input real KIND dp pc input real KIND dp a input real KIND dp b input real KIND dp c input real KIND dp d input real KIND dp force output real KIND dp potential output real KIND dp e Comments If required the user can add extra bond dihedral and improper dihedral inter
238. ords where necessary and numerical values separated from each other with spaces or tabs Define system lbin sys The use of the DL_MESO GUI is recommended for producing 1bin sys although existing files of that name can also be edited Its format consists of a keyword and an associated numerical parameter on each line separated by spaces or tabs No allowances are made for typographical errors or abbreviations in keywords which must be included in full and in the form described below Ten keywords are compulsory for all LBE simulations as these determine the lattice scheme to be used the number of lattices to use and the sizes of the system and boundary regions keyword meaning space dimension sets the number of dimensions in the system 2 or 3 discrete_speed sets the number of lattice links per grid point 9 15 19 or 27 number_of fluid sets the number of fluid lattices for the system if modelling solutes this must be set to 1 number of solute sets the number of solutes to be modelled temperature_scalar determines whether or not a lattice is needed to model heat transfers set to 1 if needed 0 if not phase_field determines whether or not a lattice is needed to represent phase fields set to 1 if needed 0 if not grid number_x sets the number of grid points in the z dimension grid_number_y sets the number of grid points in the y dimension grid_number_z sets the number of grid points in the 2 dimension if a two dim
239. ore equilibration nsbts interval for temperature scaling lcorr switch for saving statistical data to CORREL file iscorr interval for saving statistical data to CORREL file itype integrator thermostat selection btype barostat selection etype electrostatic algorithm selection srftype surface boundary selection lbond switch for modelling bonds between particles langle switch for modelling bond angles ldihed switch for modelling bond dihedrals lgbnd switch for globally storing all bond data lisoprs switch for isotropic variation of system dimensions with pressure Imp i and loc i respectively Numbers representing species and molecule types are stored in arrays 1tp i and 1tm i which are used to assign particle masses and the names of particles and molecules respectively to the arrays weight i atmnam i and molnam i All of these arrays are allocatable and their sizes set equal to maxdim which is an estimate of the maximum possible number of particles likely to be stored in each processor based on the total number of particles the numbers of available link cells and the number of processors available Since the calculation for this parameter makes the assumption that the particle density is constant throughout the system possible variations in density can be specified by the user and taken into account when calculating maxdim A similar parameter maxpair is also calculated to determine the maximum possible number of particle pai
240. os ypos zpos The latter two are more readable to the user but a bit slower to carry out fGet Tot MassSite e Header records two cases double fGetTotMassSite double startpos double fGetTotMassSite long tpos e Function Calculates the total mass density of all fluids at a grid point e Dependencies None e Arguments startpos input double pointer tpos input long integer fGetTotMassSite output double precision e Comments Mass density is calculated according to the definition p gt gt fi The second case carries out the same calculation as the first but using tpos for the grid point 70 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE fGetOneMassDomain e Header records double fGetOneMassDomain int fpos e Function Calculates the total mass of fpos th fluid in the domain e Dependencies None e Arguments fpos input integer fGetOneMassDomain output double precision e Comments The total mass of the domain does not include boundary areas used for message passing or nodes used to apply boundary conditions fGet TotMassDomain e Header records double fGetTotMassDomain e Function Calculates the total mass of all fluids in the domain e Dependencies None e Arguments fGetTotMassDomain output double precision e Comments The total mass of the domain does not include boundary areas used for message passing or nodes used to apply boundary conditions fGetFracSite e Header records three cas
241. ot read CONFIG file The supplied CONFIG file cannot be read by DL_MESO_DPD it might have been corrupted Action Check the CONFIG file to ensure it is complete and in ANSI text format Message 20 missing CONTROL file No input file named CONTROL can be found Action Make sure there is a CONTROL file in the same directory as the DL_MESO_DPD executable Message 21 cannot read CONTROL file The supplied CONTROL file cannot be read by DL_MESO_DPD it might have been corrupted Action Check the CONTROL file to ensure it is complete and in ANSI text format Message 30 missing FIELD file No input file named FIELD can be found Action Make sure there is a FIELD file in the same directory as the DL_MESO_DPD executable Message 31 cannot read FIELD file The supplied FIELD file cannot be read by DL _MESO_DPD it might have been corrupted Action Check the FIELD file to ensure it is complete and in ANST text format Message 32 unrecognised bond type defined in FIELD file A bond type not included in Table 12 3 has been found in the FIELD file Action Check the FIELD file to ensure all bond types are valid if adding a new bond type to DL_MESO_DPD the scan field and read field routines in config_module need to be modified Message 33 unrecognised bond angle type defined in FIELD file A bond angle type not included in Table 12 4 has been found in the FIELD file Action Check the FIELD file to ensure all bond angle types are valid
242. ottom boundary speed in lattice units i e at the minimum y value for the grid The specified left boundary speed in lattice units i e at the minimum x value for the grid The specified right boundary speed in lattice units i e at the maximum zx value for the grid The specified front boundary speed in lattice units i e at the maximum z value for the grid For two dimensional systems this can be omitted and is thus greyed out 14 15 16 17 18 Ka CHAPTER 2 THE DL_MESO GUI The specified back boundary speed in lattice units i e at the minimum z value for the grid For two dimensional systems this can be omitted and is thus greyed out The noise magnitude only has an effect for initializing multiple phase simulations DL_MESO_LBE may include either a phase field parameter or no phase field parameter for systems with multiple phases neither mesophase algorithm requires it and thus this option is currently disabled The number of fluids phases can be increased if a multiple fluid system is to be studied up to 6 fluids may be modelled in DL MESO_LBE The parameters and boundary conditions for the fluid s must then be set by clicking the set fluid parameters button see below for more details The number of solutes needs changing if solute parameters are required if the number of solutes is greater than zero and up to 6 the number of fluids in the above row must be set to 0 or 1 If used the paramet
243. ource terms are to be used the vector S for this lattice scheme is defined as 0 6 uz Fs uy Fy 6 uz Fr uy Fy Fo F Fy f 2 Ua Fy UyFy Ug Fy Uy Py Y II Similar schemes are available for the D3Q15 and D3Q19 lattices there is currently no MRT scheme available for D3Q27 The MRT schemes without source terms can be applied using fCollisionMRT while the schemes with Guo like moment transformed source terms can be invoked using fCollisionMRTGuo 5 1 2 Propagation algorithms The simplest implementation the two lattice algorithm involves the use of a temporary array 1bft to copy post collisional distribution functions to their new positions which are subsequently copied back to the main distribution function array 1bf While this particular method is clear easy to understand and can be applied throughout the system s lattice points in any order its drawbacks include the use of two loops for propagation 48 CHAPTER 5 DL MESO_LBE FEATURES and array copying two large arrays for the distribution functions at each lattice node and significant amounts of time expended in memory access If the user wishes to use this method the routine fPropagationTwoLattice is available An alternative more efficient implementation of propagation is the swap algorithm 43 whereby this process is carried out by systematic swapping of pairs of collided distribution function values To make this easier to implement the latti
244. p 0 e Function Outputs macroscopic mass density of fluid iprop and velocity speeds along x y and z directions at each lattice point for system in Plot3D format e Dependencies fOutputQP2D fOutputQP3D e Arguments filename input array of characters iprop input integer e Comments The default output file name is 1bout q and the density of fluid O is output by default This can be changed by specifying an output file name and fluid number up to 1bsy nf 1 when calling the routine fOutputQCA e Header records int fOutputQCA const char filename 1bout int iprop 0 e Function Outputs mass fraction of fluid iprop and speeds along x y and z directions at each lattice point for system in Plot3D format e Dependencies fOutputQCA2D fOutputQCA3D e Arguments filename input array of characters iprop input integer e Comments The default output file name is 1bout q and the mass fraction of fluid 0 is output by default These can be changed by specifying an output file name and fluid number up to 1bsy nf 1 when calling the routine fOutputQCB e Header records int fOutputQCB const char filename lbout int iprop 0 e Function Outputs concentration of solute iprop and fluid velocity at each lattice point for system in Plot3D format e Dependencies fOutputQcB2D fOutputQCB3D 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS 81 e Arguments filename input array of characters iprop input integer e
245. p interval ooo density var bo 11 job time s 3600 0 close time s Roo 12 restart key 13 thermostat barostat electrostatics surface e v o gt F QEJEJEJE O global bonds ignore CONFIG override index 00 Figure 2 5 Define DPD System 2 3 1 1 Thermostat barostat electrostatic and surface parameters Examples of the pop up windows for thermostat barostat electrostatic and surface parameters can be seen in Figure 2 6 with the rows labelled in red numbering multiple columns of dialogue boxes are made available for systems with multiple species The thermostat pop up window is formatted as in Figure 2 6 a 1 The type of thermostat to be used in the simulation 2 Thermostat parameters for the Stoyanov Groot thermostat currently the only type that requires an additional parameter a global coupling parameter for the Nos Hoover part a is required Figure 2 6 b gives the layout for the barostat pop up window 1 The type of barostat to be used in the simulation 2 Barostat parameters for the Langevin barostat a barostat relaxation time 7 and piston drag coefficient yp are required while the Berendsen barostat requires the compressibility relaxation o 8 ratio i 3 This check box determines whether or not an isotropic system i e one where pressure acts uniformly in all dimensions should be modelled If unchecked the barostat will act differently in
246. particles are selected and used 134 CHAPTER 10 DL MESO DPD BASIC DEFINITION 10 2 The Parameters and Their Functions Table 10 4 lists all the globally used parameters defined in DL_MESO_DPD as given in the constants variables and numeric_container modules Because DL_MESO is an ongoing project and new parame ters might be added to the package in the future it is strongly recommended that users of DL_MESO check the names of any self defined variables whenever the package is updated to reduce the possibility of duplications causing unexpected errors The notation column in Table 10 4 gives the restrictions applicable on the parameters A indicates an array of data followed by the number of elements in the array For example A maxdim means the parameter is actually an array with maxdim elements numbered from 1 to maxdim gt 1 means the number must be greater or equal to one while for a Boolean parameter T or F means its value can either be true or false An asterisk in the data type for the array indicates that it is allocatable and defined during the run 10 2 THE PARAMETERS AND THEIR FUNCTIONS Table 10 4 DL_MESO_DPD Parameters 135 function parameter data type notation kind parameter for double precision numbers dp integer kind parameter for long integers di integer maximum word length mxword integer I O channel for reading input files nread integer I O channel for wr
247. party and that third party needs to use the DL_MESO Software in connection with that collaboration or if the Licensee wishes to make the DL_MESO Software available online to any third party for Academic Purposes the Licensee must direct that third party to the DL_MESO Website That third party may use the DL_MESO Software and any Derived Work whether obtained from STFC or from the Licensee only if it has completed the registration process on the DL_MESO Website and agreed to the terms and conditions of the Licence Agreement for the use of the DL_MESO Software for Academic Purposes that then appear on the DL_MESO Website This Licence Agreement allows the Licensee to use only the release or version of the DL_MESO Software downloaded by the Licensee from the DL_MESO Website immediately after the Licensee agrees to the terms and conditions of this Licence Agreement the Licensee must acquire a new licence for any future release or version of the DL_MESO Software that it wishes to use The Licensee will not tamper with or remove any copyright or other proprietary notice or any disclaimer that appears on or in any part of the DL_MESO Software and will reproduce the same in all copies of any of the DL_MESO Software and in all Derived Works 3 WARRANTIES AND LIABILITY 3 1 3 2 The DL_MESO Software is provided for Academic Purposes free of charge Therefore STFC gives no warranty and makes no representation in relation to the DL_MESO Soft
248. peeds along x y and z directions at each lattice point of compressible fluid iprop for system in Structured Grid Legacy VTK format Dependencies fOutputLegacyVTKP2D fOutputLegacyVTKP3D Arguments filename input array of characters iprop input integer Comments The default output file name is lbout vtk and the density of fluid 0 is output by default This can be changed by specifying an output file name and fluid number up to 1bsy nf 1 when calling the routine fOutputLegacyVTKCA e Header records int fOutputLegacyVTKCA const char filename lbout int iprop 0 Function Outputs mass fraction of fluid iprop and speeds along x y and z directions at each lattice point for system in Structured Grid Legacy VTK format Dependencies fOutputLegacyVTKCA2D fOutputLegacyVTKCA3D Arguments filename input array of characters iprop input integer Comments The default output file name is lbout vtk and the mass fraction of fluid 0 is output by default These can be changed by specifying an output file name and fluid number up to 1bsy nf 1 when calling the routine fOutputLegacy VTKCB e Header records int fOutputLegacyVTKCB const char filename lbout int iprop 0 e Function Outputs concentration of solute iprop and fluid velocity at each lattice point for system in Structured Grid Legacy VTK format e Dependencies fOutputLegacyVTIKCB2D fOutputLegacyVTKCB3D e Arguments filename input array of characters
249. periodic walls orthogonal to i axis x y z if specified a single wall can be specified and only the first specified dimension will be used set required simulation temperature kgT to f target temperature for con stant temperature ensembles write trajectory data to HISTORY file s with controls start timestep for dumping configurations default equilibration time j timestep interval between configurations timestep f set timestep to f time units volume f f2 f3 set system size to either cubic volume f or orthorhombic dimensions fi fa fs While not every directive has to be included in the CONTROL file for a valid simulation and many hold default values if unspecified the following are mandatory and must be set to values greater than zero cutoff temperature timestep volume if no CONFIG file is available Superfluous parameters and switches for particular systems e g specified pressure for constant volume simu lations can be safely omitted from the CONTROL file without causing runtime problems If the user wishes to include new directives in the CONTROL file modifications to the parameter recognition loop in the read_config subroutine config module will be required Define interactions FIELD The FIELD file contains the species and force field information required for both bonded and unbonded interac tions and is read by the read_field and scan_field subroutines in config_module Apart from the na
250. placing the result on processor nod e Dependencies None e Arguments iii input output array of logical nnn input integer nod input integer idnode input integer e Comments For Boolean scalars the alternative SUBROUTINE global_sca_and iii nod idnode is available global_and_all e Header records SUBROUTINE global_and_all iii nnn e Function Finds global logical AND from a Boolean array iii of size nnn and broadcasts result to all processors e Dependencies None e Arguments iii input output array of logical nnn input integer e Comments For Boolean scalars the alternative SUBROUTINE global_sca_and_all iii is available global_sum_dble e Header records SUBROUTINE global_sum_dble aaa nnn e Function Globally sums double precision array aaa of size nnn 174 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE e Dependencies None e Arguments aaa input output array of real KIND dp nnn input integer e Comments For double precision scalars the alternative SUBROUTINE global_sca_sum_dble aaa is available global_sum_int e Header records SUBROUTINE global_sum_int iii nnn e Function Globally sums integer array iii of size nnn e Dependencies None e Arguments iii input output array of integers non input integer e Comments For integer scalars the alternative SUBROUTINE global_sca_sum_int iii is available global_sca_max_dble e Header records SUBROUTINE global_sca_ma
251. pletion e If the compilation fails you may need to edit the code An editing panel is available for this purpose using either the Change LBE Code or Change DPD code buttons Its function is similar to the compilation panel in operation with a choice of text editors including one packaged with the DL_MESO GUL The files in the LBE code that can be edited include the parallel and serial main files the lattice model file the boundary condition file the core routines for LBE calculations the file for user defined routines the main head file and the head file for user defined routines Others can be edited by selecting other and typing the name of the file in the neighbouring box The files in the DPD code that may be edited include the main program constants global variables and the modules configuration start for system initialization field for force calculations bond interactions many body DPD surfaces and statistics Other code files can be edited by selecting other and typing the name in the neighbouring box 2 5 NOTES 19 2 5 Running the LBE DPD code is made possible through the Run LBE Program or Run DPD Program button which activates a panel that allows you to select the required submission command and then submit the job You may need to create a suitable run script in your working directory beforehand if running the job in parallel Collecting data from multiple processors and processing it for visualization i
252. put would be welcome nevertheless 1 2 1 Lattice Boltzmann Equation DL_MESO_LBE can simulate lattice gas systems using the Lattice Boltzmann Equation LBE The following properties and features are currently available e Multiple fluid components solutes and coupled heat transfers 72 e Collisions Bhatnagar Gross Krook BGK single relaxation time 4 or Multiple Relaxation Time MRT 33 8 e Boundary conditions Periodic bounce back including stationary objects constant pressure velocity at planar surfaces 73 CHAPTER 1 DL MESO GENERAL INFORMATION Mesoscale interactions Shan Chen pseudopotential method 55 56 Lishchuk continuum based method 35 Initial conditions can either be determined by DL_MESO_LBE or specified by the user 1 2 2 Dissipative Particle Dynamics DL_MESO_DPD can model DPD particles beads with soft or hard potential fields along with thermostatting dissipative and random forces The following properties and features are currently available 1 3 Choice of integrators thermostats standard Velocity Verlet DPD Velocity Verlet 13 Lowe Andersen 36 Peters 47 and Stoyanov Groot 62 Constant volume NVT or constant pressure NPT simulations with Berendsen 2 or Langevin 29 barostats User selection of interaction lengths conservative and dissipative force parameters for each species and between unlike species Bond stretching angles and dihedrals between beads in user defined mol
253. r DPD Velocity Verlet algorithm with Lees Edwards shearing e Dependencies error msg_receive_unblocked msg_receive_sca_blocked msg_send_blocked msg_send_sca_blocked msg_wait e Arguments nlimit input output integer mdir input integer begin input real KIND dp final input real KIND dp shove input real KIND dp shovel input real KIND dp shove2 input real KIND dp sidel input real KIND dp side2 input real KIND dp e Comments Only exists in parallel version of DL_MESO_DPD This routine requires information for the two dimensions along the surface of the shearing boundary the variables shove1 and shove2 represent the displacement due to shear while side1 and side2 are the domain dimensions exportdensity e Header records SUBROUTINE exportdensity nlimit mdir mp begin final shove Parallel version SUBROUTINE exportdensity nlimit mdir begin final Serial version 198 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE e Function Exports particle data local densities to neighbouring domain as boundary halo for calculation of many body DPD interaction forces e Dependencies error global_sca_and_all Parallel version only msg_receive_unblocked Parallel version only msg_receive_sca_blocked Parallel version only msg_send_blocked Parallel version only msg_send_sca_blocked Parallel version only msg_wait Parallel version only e Arguments nlimit input output integer mdir input integer mp input
254. r interactions and used to define the maximum sizes of arrays for storing information for thermostats that correct particle velocities after force integration i e Lowe Andersen Peters and Stoyanov Groot Bonded particles are listed by global identity numbers in the integer array bndtb1 i j for bond i with j 1 representing the first particle in the pair j 2 for the second and j 3 giving the user defined bond type The location of the first particle in each bond pair determines the processing unit which holds this data thus movement of this reference particle across processes also causes the bond list entry to be transferred with it 10 1 DATA STRUCTURE 133 Table 10 2 Domain information parameter meaning idnode name of the processor nodes number of processors idx x coordinate of the processor idy y coordinate of the processor idz z coordinate of the processor npx number of processors along x axis npy number of processors along y axis npz number of processors along z axis volm volume of system dimx size of system in x dimension dimy size of system in y dimension dimz size of system in z dimension sidex size of domain in x dimension sidey size of domain in y dimension sidez size of domain in z dimension delx absolute x coordinate of domain origin dely absolute y coordinate of domain origin delz absolute z coordinate of domain origin nlx number of link cells in domain along x axis nly number of link cells in
255. ractions between particles 2 aa 152 TET Suttace interactions toa la e a A e al ee A a a a aa 155 12 DL_MESO_DPD Input and Output Files 157 Pa Input les tf hc AA A a a a AS A E ARA A A a F 157 122 Output tiles r esisi ek A AA ee i ee ee a 164 13 DL_MESO_DPD Package Reference 167 ABs CVCLVICWS o ONS heen ete eS onda DAR OD eee a ee tee eh eS 167 13 2 DL_MESO_DPD Subroutines and Functions e 168 14 DL_MESO DPD Examples 215 14 1 Mixture_Small CONTENTS 111 C D 14 2 Maxtur liarge dc ari aa A AA A a aE a a A we dd Das 215 14 3 PhaseSeparation 24 04 a ca a A da a a da a ee ala 216 TAA APOT a A a A A ed ene bt E E A aS 216 145 Polyelectrolyte E mi nuk dd ta a A A a a ee et 217 14 6 AmphiphileMesophases 2 0 0 ee 217 14 7 VesicleFormation io a ee a e ee eee A Po ae ee 218 14 8 PoiscuilleFloW e aoa a Re ok ba ede FOR eh ane eh ee ee RO 219 14 9 Shear Elow sa iaa BR Bo ed he BAG i eee ele tae Bo ae Oe ee GA 219 14 10 Vapour liquids lt s 25 os Boe o A tok A ee Boe ie he ak eg et 220 Manual compiliation and running of DL_MESO 221 Ant SDE MES OU BES to a AE A Bae a a ae ome lene de o ELE A 221 AQ DE MESO DPD ii way ee ee a Se bol BR A ee ee Re a 222 DL_MESO Utilities 225 BL DE MESOLUBE amp 222408 Site ae a BAe ws aoe SYP A eee i GS A ke ee di 225 B 2 DLMESO DPD a i Sak Sh ae ee ha es ee RS AS yt o Reh Geta ek Bo 227 DL_MESO_DPD Error Messages 231 DL_MESO Licence Agreement Academic Purposes
256. replicated data strategy to carry out the velocity corrections this requires additional memory on each processing unit for the velocities of all particles and the data required to modify the velocities of particle pairs The efficiency of the Lowe Andersen thermostat thus decreases with increasing numbers of particles in the entire system and I 11 2 4 Peters thermostat peters The Peters thermostat 47 is a modification of the Lowe Andersen thermostat that reduces to standard DPD as the time step tends to zero After integrating all forces using the Velocity Verlet scheme all particle pairs have their velocities modified in a random order using I Vi Ui AS ass s 4 Vij At F big Gig V At i 11 10 Mi 1 Uj Uj Ti as tes d Tiz At Tr big Gig V At Ci 1 11 where the coefficients as and b are chosen so that A bij 2kgTaij 1 is Z 215 To ensure that the thermostat both reduces to the DPD thermostat as the time step reduces to zero and is not restricted by the choice of time step the coefficients are chosen as follows Hg Yijw rij At tij Ai 1 exp 11 12 kBT hi 27 50 rij At bi 1 11 1 i FH 1exp 11 13 The above velocity corrections give an equivalent thermostatting force of gt Ra bis Giz a Fi mas es Uiz se Cij 11 14 and a correction to the virial of FE Tij is also applied for each particle pair This thermostat can be used with
257. return a lt lbevaplim 0 a e Function Returns zero for values of a less than the specified evaporation limit 1bevaplim e Dependencies None e Arguments a input any datatype fEvapLimit output same datatype asa e Comments This function is used to eliminate spurious production of non continuous fluids at boundary edges and corners The default value of lbevaplim 1078 can be overridden by the user fSwapPair e Header records template lt class T gt void fSwapPair T a T amp b e Function Swaps pair of numbers a and b e Dependencies None e Arguments a input output any datatype b input output any datatype fGet NumberOrdered e Header records two cases int fGetNumberOrdered int amp iox int amp ioy int amp ioz int fGetNumberOrdered int amp iox int amp ioy e Function Rearrange the integers in descending order e Dependencies None 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS 65 e Arguments iox input output integer reference ioy input output integer reference ioz input output integer reference fGet Number OrderFixed e Header records two cases int fGetNumberOrderFixed int amp iox int amp ioy int amp ioz int ix int iy int iz int fGetNumberOrderFixed int amp iox int amp ioy int ix int iy e Function Rearrange a set of integers so they appear in the same order as another set of integers e Dependencies GetNumberOrdered e Arguments iox input output inte
258. rguments xpos input integer ypos input integer zpos input integer e Comments Further details can be found in 35 20 fInteractionForceLishchuk e Header records int fInteractionForceLishchuk e Function Calculates interaction forces for all fluids based on the Lishchuk model 35 20 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS 95 e Dependencies fCalcInteraction_Lishchuk e Comments The phase indices need to be calculated prior to calling this routine fCalcForce_Boussinesq e Header records int fCalcForce Boussinesq long tpos double temph double templ e Function Calculates buoyancy driven thermal convection force according to the Boussinesq approximation e Dependencies fGetOneMassSite fGetTemperatureSite e Arguments tpos input long integer temph input double precision templ input double precision e Comments The buoyancy force for compressible fluids calculated by this routine is na gt 24 T To 7 00 7 h with the reference temperature To gt Tn T The expression for incompressible fluids is similar with the constant fluid density po substituted for p fConvectionForceBoussinesq e Header records int fConvectionForceBoussinesq double temph double templ e Function Calculates Boussinesq thermal convection forces for all fluids based on 18 e Dependencies fCalcForce Boussinesq e Arguments temph input double precision templ input double precision 7 2
259. ribution function values For instance for a top edge with a known velocity 7 using the D2Q9 lattice scheme V CEDF the wall density and missing distribution functions all for the boundary node at Zw are given as fot f2 fet2 fi t fr t fs 1 Voy 20w0 fi i ie aw s fr fo fe PV Dilo fs fi fo f2 H Pb PwUw y 1 denotes any valid letters for the solute composition and temperature 50 CHAPTER 5 DL MESO_LBE FEATURES The other form specifying the wall fluid density requires the calculation of the wall velocity which can be simplified by setting non orthogonal velocity components to zero For the analogous example at the top wall for D2Q9 P CEDF the same equations for f4 f3 and fs can be used together with PwUVw x 0 Pu Uwy fo fo fe 2 fi fz fs Pw One complication for three dimensional lattices is the requirement to apply the non equilibrium bounce back to all unknown distribution functions which ordinarily overspecifies the system but can be counteracted using transverse momentum corrections for directions other than orthogonal to the boundary which are non zero for e g shearing flows It should be noted that if the wall velocity is set to zero the boundary condition reduces to on grid bounce back DL_MESO_LBE includes implementations of the Zou He boundary condition for all four lattice schemes D2Q9 D3Q15 D3Q19 and D3Q27 Only planar surfaces can be dealt with using t
260. rintDoubleLine e Function Prints a line of 76 characters e Dependencies None fRandom e Header records double fRandom e Function Creates a double precision random number between 1 and 1 e Dependencies None e Arguments fRandom output double precision e Comments There is a built in seed in the function which is only activated when the function is initially called 7 2 DL MESO _LBE SUBROUTINES AND FUNCTIONS 67 fBigEndian e Header records int fBigEndian e Function Determines endianness for machine returns 1 for big endian 0 for little endian e Dependencies None fByteSwap e Header records void fByteSwap void data int len int count e Function Converts between endian types by swapping byte order of array data with byte size per entry len and count entries e Dependencies None e Arguments data input output void len input integer count input integer e Comments Primarily required for writing binary files where a specific endianness is required e g vtk files are required in big endian fCheckTimeSerial e Header records double fCheckTimeSerial e Function Outputs time in seconds since initial call e Dependencies None e Arguments fCheckTimeSerial output double e Comments Obtains calculation time based on system clock parallel calculations may obtain greater timing accuracy with fCheckTimeMPI 7 2 4 IbpGET fGetNodePosi e He
261. roperties of dissipative particle dynamics Physical Review E 56 2 1676 1691 August 1997 Nicos S Martys and Hudong Chen Simulation of multicomponent fluids in complex three dimensional geometries by the lattice Boltzmann method Physical Review E 53 1 743 750 January 1996 Makoto Matsumoto and Takuji Nishimura Mersenne twister a 623 dimensionally equidistributed uniform pseudo random number generator ACM Transactions on Modeling and Computer Simulation 8 1 3 30 1998 Keijo Mattila Jari Hyv luoma Tuomo Rossi Mats Aspn s and Jan Westerholm An efficient swap algorithm for the lattice Boltzmann method Computer Physics Communications 176 3 200 210 February 2007 Philip M Morse Diatomic molecules according to the wave mechanics II Vibrational levels Physical Review 34 1 57 64 July 1929 David R Noble Shiyi Chen John G Georgiadis and Richard O Buckius A consistent hydrodynamic boundary condition for the lattice Boltzmann method Physics of Fluids 7 1 203 209 1995 I Pagonabarraga and D Frenkel Dissipative particle dynamics for interacting systems Journal of Chemical Physics 115 11 5015 5026 2001 E A J F Peters Elimination of time step effects in DPD EPL Europhysics Letters 66 3 311 317 May 2004 Igor V Pivkin and George Em Karniadakis A new method to impose no slip boundary conditions in dissipative particle dynamics Journal of Computational Physics 207 1 114 128 2005 Kannan N
262. rostat velocity At Fo a t Ug a t 3At ug a t z m 11 24 before the positions and simulation box dimensions are updated Tia t At exp uga t 4At At ria t Atvi a t 5At 11 25 Lo t At exp uga t At At La t 11 26 At this point the forces at the end of the time step are calculated including thermostatting forces along with the system pressure Since the the barostat force requires correct velocities for both the particles and barostat an iterative procedure is required which begins by calculating an initial guess for the barostat velocity at the end of the time step 2F a t At g u t At uga t At 4 g 0 Each iteration starts by calculating the particle velocities in a slightly modified second Velocity Verlet step exp g a t 3At At via E 340 LESS 11 27 1 ul At uit t At The barostat force is then calculated using the same Gaussian random numbers for each iteration 1 2 FY t At V Pa Po N Y mi of tD of oppa 11 28 and the barostat velocity is recalculated FA t At At 11 29 UD t At uga t ZAt 11 4 PARTICLE PARTICLE INTERACTIONS 147 Equations 11 27 to 11 29 are repeated until convergence in particle velocities is achieved i e when 2 Es at t At a t At 3N lt with e as a numerical tolerance set to 107 by default This normally takes a few iterations per tim
263. rpose functions which may be replaced with any suitable functions in Fortran90 standard libraries as well as bookkeeping subroutines for the global local particle number list duni Header records REAL KIND dp FUNCTION duni idnode Function Creates a double precision random number between 0 and 1 Dependencies None 170 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE e Arguments idnode input integer duni output real KIND dp e Comments The random number generator is an implementation of the Universal Random Number Generator 39 The processor name idnode is used as a seed which is activated the first time the function is called mtrnd e Header records REAL KIND dp FUNCTION mtrnd idnode e Function Creates a double precision random number between 0 and 1 e Dependencies None e Arguments idnode input integer mtrnd output real KIND dp e Comments The random number generator is an implementation of the Mersenne Twister random number generator 42 The processor name idnode is used as a seed which is activated the first time the function is called gaussmp e Header records REAL KIND dp FUNCTION gaussmp idnode e Function Creates a Gaussian random number e Dependencies mtrnd e Arguments idnode input integer gaussmp output real KIND dp e Comments This is an implementation of the Marsaglia polar method 38 to convert linear random numbers generated by the Mersenne Twister method t
264. rtical position Figure 8 1 Results from LBE 2D_Pressure test case 8 2 2D_Shear This is a 2D simulation of a single fluid on a 42 x 42 grid with a shear boundary condition The vector plot in Figure 8 2 demonstrates the ability of the applied boundary conditions to generate a linear shearing Couette flow throughout the grid which is confirmed by the plot of horizontal velocity component as a function of vertical position at the last time step for the simulation 119 120 CHAPTER 8 DL MESO LBE EXAMPLES 0 001 _ 0 0005 4 E L S k 5 F J E F E 3 3 L a 0 0005 4 Dm a a a a oe ee ooog 0 0001 0 0002 Vertical position a Vector plot of system b Variation of horizontal velocity with vertical posi tion Figure 8 2 Results from LBE 2D_Shear test case 8 3 2D_CylinderFlow This is a 2D simulation of a single fluid on a 125 x 50 grid with a constant horizontal body force and a circular obstacle of radius 12 representing channel flow past an infinitely long cylinder Figure 8 3 shows this flow against a density map of the system with solid black lines representing the solid boundaries both walls and the cylinder Figure 8 3 Density scale blue to red and velocity vector plot from LBE 2D_CylinderFlow test case 8 4 2D KarmanVortex This is a 2D simulation of a single fluid on a 250 x 50 grid with a constant horizontal body force and a circular obstacle of radius 8 represent
265. s Since a limited amount of data is included in restart files the FIELD file for the simulation is needed to provide some additional information The source code for this utility exportconfig f90 can be used for export or export files created by both the serial and parallel versions of DL_MESO_DPD their endianness is automatically detected so the utility can be run on a different machine to the one used for DPD calculations If the available Fortran90 compiler is invoked by the command 90 the executable config exe can be produced by typing e 90 o config exe exportconfig f90 and either run at the command line or by using the GUI in Process DPD Data after entering the number of processes used in the required field and selecting the required CONFIG file key in the pulldown list This utility can be run with two command line arguments the first indicating the number of processes used to generate the restart data and the second denoting the CONFIG file key levcfg 0 positions only 1 positions and velocities 2 positions velocities and force e g if 16 processes were used and the particle positions and velocities are required either of the following commands can be used e export exe 16 1 e export exe 16 1 If no command line argument is given the utility will ask the user to type in the number of processes and the CONFIG file key exportimage exportimage is a utility written in Fortran90 to produce a VTF format tr
266. s It should be noted that all computed interactions are pairwise which means that the principle of the conservation of momentum in the system or Galilean invariance is preserved The conservation of momentum is required for the preservation of hydrodynamic forces Chapter 10 DL MESO DPD Basic Definition 10 1 Data structure 10 1 1 Storage of running information DL_MESO_DPD contains storage for information on the system being modelled the domain and neighbour information for parallel running The parameters for these aspects of calculations can be found in Tables 10 1 10 2 and 10 3 It should be noted for the parameters in Table 10 1 that the fundamental units for the simulation are those of mass M length L and energy E the DPD unit of time is equivalent to ic ea while temperature in the form kgT is defined as two thirds of the kinetic energy per particle 10 1 2 Storage of particle and bond properties The total number of particles in a system is nsyst of which nusyst particles are loose i e not bonded to other particles and nfsyst are frozen i e remain fixed in position but still interact with other particles DL_MESO_DPD divides up the particles and total system volume volm between the processing units available At any given time each process holds nbeads particles including nfbeads frozen particles Each process also has nbonds bonds nangles bond angles and ndiheds bond dihedrals to deal with
267. s Simulations with frozen bead walls can be restarted but these walls must already be included in the restart export files and cannot subsequently be added 11 7 3 Shearing periodic walls shear Shearing walls moving at a specified velocity are applied using the Lees Edwards boundary condition 34 each particle that moves through the otherwise periodic boundary has its velocity modified and is shifted by a distance related to the wall velocity i e AZo Vot 11 91 where Vo is the velocity of the moving boundary Interactions between pairs of particles across the periodic boundary taking the positional shift into account are still calculated but pairwise thermostats are not applied across this boundary to avoid quenching the modification of particle velocities particularly with high values for dissipative force coefficients y or collision frequencies T and maintain the correct shear rate 5 The directive surface is used in the CONTROL file to specify which boundaries should move while the external directive in the FIELD file is used to specify the velocity of the moving walls This boundary condition is only applied after equilibration has taken place Chapter 12 DL_MESO_DPD Input and Output Files 12 1 Input files All user specified input files for DL_ MESO_DPD must be in ANSI text format with keywords where necessary and numerical values separated from each other with spaces or commas tabs are currently not recognised b
268. s follows 1 Cosine torsion U ijx1 A L cos m ijr 11 79 2 Harmonic U Qijr1 5 dista do 11 80 3 Harmonic cosine U ijki 5 cos hijri cos bo 11 81 where A and are dihedral force constants m is the multiplicity the dihedral at minimum potential and o an equilibrium bond dihedral The dihedral angle across all four particles or between planes ij and kl is given by Qijri cos B Fiz Fit Fes 11 82 where Fig X Tik Tin X Tri Fij X Pol Pim X Fil B Tij Tjk Tki 11 83 which gives a negative value for 4 if the vector Tij X Fix Tjk X Tki is in the same direction as the bond vector Fi and positive if in the opposite direction 11 7 SURFACE INTERACTIONS 155 The force on particle acting in the a direction is given by a Fe gz U ij 11 84 1 a O a ee i B T a m j 11 85 sin di Ipizki Uo ijkl 5 are Figs Fito Pet Using the following definition k gu n B the derivative of B fij Tjk Tkl is given by 1 talas Bo aoe Da ijs gt ij XTik ik X AN TELE OI COS Piz Kl 1 o 3 1 0 of 5 ig X ik X 11 86 2 iz x Fil Org Fag Fn Ta x Fal Ore Tje Tea with Bra Fig Fin gt Fe PRD T lFpeF jel ek da Feet ex de5 2 ro FigP ikl Ser See Fin Tio 005 5ei re Fig Pyle Sex Sej Fikira Ses 0e5 arse TigTktlg Ser Sek 11 87
269. s possible using the Gather LBE Data and Process DPD Data buttons Note that the utilities need to be compiled in the working directory prior to use details on this and their functions can be found in Appendix B The results of LBE and DPD calculations may be plotted using the Plot LBE Results and Plot DPD Results buttons which allows the user to select plotting and visualization applications including those not available in the pull down lists Note that these need to be already installed on the workstation in use before being invoked by the GUI if they require running from a command line tick the run in terminal box before launching the application Notes There are some inactive buttons reserved for later use The GUI does not produce initial state files 1bin init for LBE CONFIG for DPD prior to simulations although there are utilities available to do this see Appendix B for further details Click EXIT to close down the GUI Part I Lattice Boltzmann Equation LBE Chapter 3 The Lattice Boltzmann Equation Basic Theory 3 1 Introduction The Lattice Boltzmann Equation LBE method is based on modelling a fluid consisting of fictional particles which collide and move over a discrete lattice grid This method is similar to its ancestor Lattice Gas Cellular Automata LGCA but the main difference is that while LGCA represents the existence or otherwise for each particle at a grid point LBE describes the physical state of
270. s the end of details for a molecule type Each subsequent molecule type can be entered after this directive beginning with its name and ending with the finish directive Table 12 3 Bond potentials key potential type Variables 1 4 functional form harm Harmonic K ro E U r 3x r roy 2 fene Shifted FENE To tinae U r 0 5krmae In i 1512 oe U r 00 7 gt max 70 wle Worm like chain Ap maz U r e E E gt T lt Tmaz U r 00 7 gt mar mors Morse De ro B U r De 1 exp B r ro Table 12 4 Bond angle potentials key potential type Variables 1 4 functional form harm Harmonic Kk A U 0 8 0 hcos Harmonic cosine k 09 U cos cos 6 cos Cosine A m U A 1 cos m Table 12 5 Bond dihedral potentials key potential type Variables 1 4 functional form cos Cosine torsion Ajim 8 U 6 A 1 cos mo 6 harm Harmonic kK bdo U irlo do hcos Harmonic cosine k do U 4 cos cos bp Surface interactions can be specified using the directive surface If hard adsorbing surfaces are to be used this directive should be followed by entries specifying the soft short range repulsions for all species name a8 name of species Awall real soft short r
271. ser to identify it The utility will then ask for the number of drops to be added to the system for each drop the user will need to specify the fluid its radius and where its centre is located on the lattice grid Note that it is possible for a drop to extend beyond the grid boundaries if periodic boundaries are in use lif using the GUI and the utilties are to be compiled manually or in their source directories copies of the executables are required in the directory from which the GUl is to be launched e g WORK 225 226 APPENDIX B DL_MESO UTILITIES If any solutes are to be included the utility will ask for the number of solute sources i e regions of constant solute concentration for each source it will then ask for the solute number the required concentration the location of one corner of the rectangular source and its extent in each dimension which can extend beyond periodic boundaries Similarly if a temperature grid is included in the system the utility will ask for the number of temperature sources followed by the required temperature and the location of the corner and the extent of the source Once all of the above information is obtained the utility will then create the 1bin init file which specifies the grid points velocities fluid densities solute concentrations and temperatures for any locations in the system that require non default initial conditions lbeplot3dgather lbeplot3dgather is
272. sing the directive ensemble with the keyword nvt for constant volume simulations or npt for constant pressure simulations Dissipative force parameters and collision frequencies can be specified for each interacting species pair in the FIELD file Frozen particles are involved in thermostatting algorithms due to the contributions they make to system virials and pressure however they are excluded from the force integration algorithm and their velocities are reset to their previous values usually zero 11 2 1 DPD thermostat with standard Velocity Verlet integration MD VV mdvv This algorithm uses the drag dissipative and random forces FP and FR respectively as described in Chapter 9 as the system thermostat i e the thermostatting force FE FP FR This thermostatting force is combined with all other forces between particles pairwise conservative standard and or density dependent bonding electrostatic planar surface external body forces and integrated using the standard Velocity Verlet integrator This is the first referenced particle in stretching bonds and the second for bond angles and dihedrals 11 2 THERMOSTATS AND INTEGRATION ALGORITHMS 143 The combination of the DPD thermostat with the standard MD type VV algorithm is the simplest and least time consuming thermostatting algorithm available in DL_MESO_DPD If no ensemble type is selected in the CONTROL file DL_MESO_DPD will use this algorithm by default Th
273. sion parameters for conserved moments should be set to unity when applying external forces 5 1 COLLISION AND PROPAGATION ALGORITHMS AT An example can be given for the D2Q9 lattice system 33 the moment vector is p y T M 1 pP 46150 qy P Pey with p as the density e the energy e the square of energy j momentum q energy flux Pax the diagonal stress tensor component and pz the off diagonal stress tensor component The transformation matrix is 1 1 1 1 1 1 T chy 4 2 1 2 1 2 1 2 I 4 1 2 1 2 1 2 1 2 0 1 1 1 0 1 1 1 0 T 0 1 2 1 0 1 2 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 2 1 0 1 2 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1l 0 1 O The equilibrium moment vector is T Jaz gt A 5 ig E Ht tee p p 3p 3p with we and wej as adjustable parameters for convergence to the single relaxation time BGK scheme these are set equal to 1 and 3 respectively Of the 9 collision parameters available sy s3 and ss have no effect except when applying external forces when they should be set equal to one as the associated moments are preserved and sa s4 and sg are tuneable parameters for calculational stability with the condition that s4 sg The remaining parameters represent the viscosities of the fluid i e 1 1 SEN Na 1 1 ANA 1 1 Ar Tr Sep 2 De als 2 DE aL 2 A ibn La 2 Ax 1 Esmas 5 Ax 6 s 2 At 6 2 At Le Te x and Tf bulk A If the moment transformed s
274. snapshots two AVI video files have been rendered from an example calculation one giving a 3D view of the system the other showing a plane normal to the y axis which can be found in the Example Simulations page of the DL_MESO website Lg 7 i i i a t 400 b t 1200 c t 2000 Figure 8 8 Progressive density plots in plane normal to y axis from LBE 3D_PhaseSeparation test case red for fluid 0 blue for fluid 1 8 9 3D_Shear This is a 3D simulation of a single fluid on a 40 x 30 x 25 grid with a shear boundary condition Figure 8 9 shows a vector plot for this system demonstrating that linear shear is generated and maintained by the moving 8 10 3D RAYLEIGHBENARD 123 boundaries in the planes normal to the y axis and a plot of the horizontal component of fluid velocity against vertical position at the last time step 0 001 0 0005 4 Fluid velocity x component o 0 0005 0 001 0 0 0001 Vertical position a Vector plot of system b Plot of horizontal velocity with vertical position Figure 8 9 Results from LBE 3D_Shear test case 8 10 3D_RayleighBenard This is a 3D simulation of a single fluid undergoing natural Rayleigh B nard convection on a 80 x 40 x 80 grid The fluid is contained between two solid walls the wall at the bottom of the system is maintained at a higher temperature than that at the top Figure 8 10 shows the fully developed temperature and c
275. st primary chain the user will also be asked for a pre existing bead number as the starting point for the chain After this the default species for the beads in the molecule will be requested the user will then be asked enter the bead numbers for each of the other species 0 can be entered to finish specifying bead numbers If more than one bond type is to be included the user will be asked to select the default bond type and then select the bonds that are of different types by typing the index bead number and optionally the destination bead if more than one is available Bond angles and or dihedrals can also be selected by typing in the index bead number and then selecting the required bead triple or quadruple if more than one is available The molecules will be appended to the FIELD file in the correct format see Section 12 1 for more details with positions for the beads relative to each molecule s centre of mass Note that this file will not be quite complete after running this utility data for unbonded interactions and external force fields may be required if the FIELD file is created using the utility and a close directive will be required at the end exportconfig exportconf ig is a utility written in Fortran90 to produce a configuration file in DL_POLY format CONFIG from DL_MESO_DPD restart files export which can be used as a starting point for new simulations including restarting simulations on different numbers of processe
276. st integer species population of unbonded particles nspec integer A nspe species population of bonded particles nspecmol integer A mxspe molecule type population nmol integer A nmoldef bead numbers in molecule types nbdmol integer A mxmoldef molecule name nammol character 8 A O nmoldef species number for molecule insertion mlstrtspe integer A nmoldef mxmolsize x coordinate for molecule insertion mlstrtxxx real KIND dp A nmoldef mxmolsize y coordinate for molecule insertion mlstrtyyy real KIND dp A nmoldef mxmolsize z coordinate for molecule insertion mlstrtzzz real KIND dp A nmoldef mxmolsize cube size for molecule insertion cbsize real KIND dp A nmoldef number of bonds for molecule type nbond integer A nmoldef number of bond angles for molecule type nangle integer A nmoldef number of bond dihedrals for molecule type ndihed integer A nmoldef bond table storage for molecule insertion bdinp1 integer A nmoldef mxbonds bond table storage for molecule insertion bdinp2 integer A nmoldef mxbonds bond table storage for molecule insertion bdinp3 integer A nmoldef mxbonds angle table storage for molecule insertion anginp1 integer A nmoldef mxbonds angle table storage for molecule insertion anginp2 integer A nmoldef mxbonds angle table storage for molecule insertion anginp3 integer A nmoldef mxbonds angle table storage for molecule insertion anginp4 integer A nmoldef mxbonds dihedral table storage for molecule insertion dhdinp1
277. step to be written in the trajectory file This version of the utility cannot be invoked using the GUI local local is a utility written in Fortran90 that can read in HISTORY output data files generated by DL_MESO_DPD and produce series of VTK format files containing statistical properties number of beads density compositions per particle and molecule types temperature and mean velocity in cuboidal subdivisions of the simulation volume for plotting and or visualization 230 APPENDIX B DL_MESO UTILITIES The source code for this utility local 90 can read both HISTORY and HISTORY files generated by the serial and parallel versions of DL_MESO_DPD respectively their endianness is automatically detected so the utility can be run on a different machine to the one used for DPD calculations If 90 is the command for the available Fortran90 compiler the executable local exe can be produced by typing e 90 o local exe local f90 and either run at the command line or via the GUI in Process DPD Data after entering both the number of processes used in simulations and the number of divisions required in each dimension This utility can be run with four command line arguments the first denoting the number of processes and the others giving the number of divisions required in x y and z directions respectively If these arguments are omitted the user will be asked to enter these values Files named local_ vtk are produced for
278. t cij 1 eo a 11 38 Te ij This conservative interaction is applied for interparticle distances up to r ij which should be less than or equal to the maximum value re 11 4 4 Many body DPD mdpd The conservative force in standard DPD depends only upon the species interacting and the interparticle sepa ration which yields a quadratic equation of state Many body DPD 46 66 is a method of providing alternative thermodynamic behaviours to DPD particles by making conservative forces additionally dependent on local densities The free energy of an inhomogeneous system with density p r can be defined as the following in both continuous and ensemble averaged discrete forms F II J oE 11 39 E aa ay 11 4 PARTICLE PARTICLE INTERACTIONS 149 where Y p is the free energy per particle in a homogeneous system and p 7 is a function related to the density at and near the position of particle i r The latter can be approximated by a function dependent on the positions of particles close to particle 6 to allow the calculation of an instantaneous free energy F dvi The effective conservative force on particle can be obtained from the spatial derivative of the free energy although only the excess part equivalent to the potential energy U is required since the kinetic motion of particles automatically accounts for the ideal contribution FO OPE 225 OY Nes OF Or 11 41 The force can also b
279. tMassDomain fGetOneMassDomain fGlobalValue fPrintSystemMomentum e Header records int fPrintSystemMomentum e Function Calculates and prints the total fluid momentum in entire system e Dependencies fGetTotMomentDomain fGlobalValue 117 Chapter 8 DL MESO LBE Examples Test cases for Lattice Boltzmann Equation simulations using DL_MESO including the required input and sample output files can be found in the DEMO LBE subdirectory They can be run using either the serial or parallel versions of DL_MESO_LBE Images of all test cases and videos for some can be found in the Example Simulations page of the DL_MESO website a link to it can be found at www ccp5 ac uk DL_MESO 8 1 2D Pressure This is a 2D simulation of a single fluid on a 42 x 42 grid with fixed pressure density boundary conditions on the left and right boundaries and solid walls represented by bounce back at the top and bottom A visualization with vector glyphs and a plot of fluid speed against vertical position can be seen in Figure 8 1 which show the boundary conditions result in a laminar flow with a parabolic velocity profile 0 0025 0 002 gt HE gt z 0 0015 gt E yyy Y Fluid speed 0 001 0 0005 o n y y l y ror y 0 0 0001 0 0002 Vertical position a Vector plot of system b Variation of fluid speed with ve
280. table for square lattices Other lattice models e g FHP 11 would require modification or alternative versions of this routine fGetEquilibriumFIncom e Header records int fGetEquilibriumFIncom double feq double v double rho double rho0 e Function Calculates equilibrium distribution function for incompressible fluid e Dependencies None e Arguments feq output double pointer v input double pointer rho input double precision rho0 input double precision e Comments Equilibrium distribution function calculated here is pisu form which is only suitable for square lattices Further details can be found in 24 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS 99 fGet EquilibriumC e Header records int fGetEquilibriumC double feq double v double rho e Function Calculates equilibrium distribution function for solute e Dependencies None e Arguments feq output double pointer v input double pointer rho input double precision e Comments The equilibrium distribution function calculated here is gl wiC i A using the solute concentration C and the velocity of the bulk fluid 27 This subroutine can be changed for other Lattice Boltzmann models e g free energy model 64 fGetEquilibriumT e Header records int fGetEquilibriumT double feq double v double tem e Function Calculates equilibrium distribution function for temperature e Dependencies None e Arguments feq output dou
281. tains angle key ad potential key see Table 12 4 index 1 i integer first bead index in bond angle index 2 j integer second bead index in bond angle central site index 3 k integer third bead index in bond angle variable 1 real potential parameter see Table 12 4 variable 2 real potential parameter see Table 12 4 variable 3 real potential parameter see Table 12 4 variable 4 real potential parameter see Table 12 4 Angle based parameters e g 99 should be given in degrees This directive and associated data records need not be specified if the molecule contains no bond angles 7 dihedrals n where n gives the number of dihedral interactions in the molecule Each of the following n records contains dihedral key ad potential key see Table 12 5 index 1 i integer first bead index in bond dihedral index 2 j integer second bead index in bond dihedral central site index 3 k integer third bead index in bond dihedral index 4 1 integer fourth bead index in bond dihedral variable 1 real potential parameter see Table 12 5 variable 2 real potential parameter see Table 12 5 variable 3 real potential parameter see Table 12 5 variable 4 real potential parameter see Table 12 5 162 CHAPTER 12 DL MESO DPD INPUT AND OUTPUT FILES Angle based parameters e g fp should be given in degrees This directive and associated data records need not be specified if the molecule contains no bond dihedrals 8 finish indicate
282. tdata shear nlimit e Function Applies export of particle properties positions velocities to boundary halos of neighbouring domains and or across periodic boundary conditions with Lees Edwards shearing e Dependencies export export_shear e Arguments nlimit input output integer exportvelocitydata e Header records SUBROUTINE exportvelocitydata nlimit e Function Applies export of particle velocities to boundary halos of neighbouring domains and or across periodic boundary conditions for recalculation of dissipative forces e Dependencies exportvelocity e Arguments nlimit input output integer e Comments Non periodic boundaries either do not require boundary halos or require them to be constructed differently these are thus excluded from the export of particle velocities 204 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE exportvelocitydata_shear e Header records SUBROUTINE exportvelocitydata_shear nlimit e Function Applies export of particle velocities to boundary halos of neighbouring domains and or across periodic boundary conditions with Lees Edwards shearing for recalculation of dissipative forces e Dependencies exportvelocity exportvelocity_shear Parallel version only e Arguments nlimit input output integer exportdensitydata e Header records SUBROUTINE exportdensitydata nlimit e Function Applies export of local densities for particles to boundary halos of neighbouring domains
283. te e Header records three cases int fGetOneMomentSite double speed double startpos int fGetOneMomentSite double speed int fpos long tpos int fGetOneMomentSite double speed int fpos int xpos int ypos int zpos e Function Calculates the momentum of one of the fluids at the grid point e Dependencies None 74 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Arguments startpos input double pointer fpos input integer tpos input long integer xpos input integer ypos input integer Zpos input integer speed output double precision array e Comments The calculation is based on pa 5 fi ia The second and third cases are more readable than the first but also slightly slower fGet TotMomentSite e Header records int fGetTotMomentSite double speed double startpos e Function Calculates the momentum of all fluids at the grid point e Dependencies None e Arguments startpos input double pointer speed output double precision array fGet TotMoment Domain e Header records int fGetTotMomentDomain double momentum e Function Calculates the momentum of all fluids in the domain e Dependencies fGetTotMomentSite e Arguments momentum output double precision array e Comments This function is mainly used to verify that the domain momentum along each axis is conserved fGetOneDirecSpeedSite e Header records three cases float fGetOneDirecSpeedSite int dire double startpos float
284. tem e Header records int fInitializeSystem e Function Initializes distribution function for lattice system e Dependencies fGetEquilibriumF fGetEquilibriumFIncom fGetEquilibriumC fGetEquilibriumT e Comments This subroutine as it stands is suitable for initializing most Lattice Boltzmann systems although the user may modify it if it can otherwise be faster more stable or more suitable for a particular calculation fSiteFluidCollisionBGK e Header records int fSiteFluidCollisionBGK double startpos double sitespeed double bodyforce e Function Calculates fluid collisions at a grid point using the Bhatnagar Grook Krook BGK model for compressible fluids 102 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE e Dependencies fGetOneMassSite fReciprocal fGetEquilibriumF e Arguments startpos input double pointer sitespeed input array of doubles bodyforce input double pointer e Comments Collisions for each fluid species are carried out using the BGK single relaxation time 4 e657 gt fi F fSiteFluidCollisionBGK Segregation e Header records int fSiteFluidCollisionBGKSegregation doublex startpos double sitespeed double bodyforce double phaseindex e Function Calculates collisions and phase segregation for the Lishchuk algorithm at a grid point using the Bhatnagar Grook Krook BGK model for compressible fluids e Dependencies fGetAllMassSite fGetTotMassSite fReciprocal fGetEquil
285. th in z direction wdthewz real KIND dp species name namspe character LEN 8 A nspe potential interaction type ktype integer A npot species particle mass amass real KIND dp A nspe species particle charge chge real KIND dp A nspe species frozen status lfrzn integer A nspe interaction parameter storage vvv real KIND dp A mxprm npot Lennard Jones long range potential correction clr real KIND dp A 2 charged frozen particle correction to system stress tensor strcfz real KIND dp AQ charged frozen particle correction to system virial vrlcfz real KIND dp A 3 charged frozen particle correction to system potential energy potcfz real KIND dp integrator thermostat type itype integer dissipative coefficient y collision frequency T gamma real KIND dp A npot random force parameter 0 probability of velocity rescaling TAt sigma real KIND dp A npot Stoyanov Groot Nos Hoover coupling parameter a alphasg real KIND dp thermostat pair list particle pairlsti integer A maxpair thermostat pair list particle j pairlstj integer A maxpair thermostat pair list Maxwell distributed velocity v5 veleq real KIND dp A maxpair number of particle pairs in thermostat pair list npair integer barostat type btype integer barostat target pressure Po prszero real KIND dp barostat parameter a abaro real KIND dp barostat parameter b bbaro real KIND dp x component of piston velocity upx real KIND dp y component of piston velocity upy real
286. the distribution function initially at each grid point and then between them in two separate loops as described by 43 and in section 5 1 This version can be used for either serial or parallel calculations and no boundary layer is necessary this is the default propagation routine for serial calculations fPropagationCombinedSwap e Header records int fPropagationCombinedSwap e Function Moves lattice particles distribution functions to neighbouring grid points using the swap algorithm e Dependencies fSwapPair e Comments This routine is fundamental to Lattice Boltzmann calculations and should not be modified Propagation is carried out by systematic swapping of post collisional values for the distribution function initially at each grid point and then between them in the same loop as described by 43 and in section 5 1 This version can only be used for calculations with non zero boundary layers this is the default propagation routine for parallel calculations 7 2 12 IbpMPI This package is only required for parallel running and does not require detailed knowledge for its use Sev eral subroutines in this package are not described here interested users should consult the code for further information fStartMPI e Header records int fStartMPI int argc char argv e Function Starts Message Passing Interface MPI e Dependencies None fCloseMPI e Header records int fCloseMPI e Function
287. the number of processing units to be used for simulations The value of maxdim can be increased by the user to allow for non evenly distributed systems by setting a value for densvar in the CONTROL file If using alternative many body DPD interactions to the vapour liquid example provided the routines manybody_force and manybody_potential in manybody_module f90 should be modified by the user as necessary the routine local density should not be altered by the user but the function weight_rho can be changed if an alternative weighting function for calculating local densities is required Additional bond angle and dihedral types can also be added to the subroutines bond_force angle_force and dihedral_force respectively in bond_module f90 but this will also require changes to read_field in config_module f90 to include a four letter code for the bond angle dihedral type that can be read from the FIELD file Appendix B DL MESO Utilities DL_MESO includes a number of utility programs which are not directly needed for Lattice Boltzmann or DPD simulations but are useful both for producing files required as inputs for those calculations and to process output files for visualization These may be found in the LBE utility and DPD utility directories Compilation can either be carried out individually or collectively using makefiles each utility directory includes a makefile to compile all the utilities therein and the working directory WORK includes o
288. the related distribution function 12 8 CHAPTER 2 THE DL_MESO GUI e A block has a vertex at x0 y0 z0 and has size dx dy dz both z0 and dz can be omitted for two dimensional blocks Note that lattice points well within an obstacle are set as blank sites i e they will be ignored in LBE calculations The entire system can be set up as a porous solid by selecting the bounce back type specifying a pore fraction and clicking set pore to randomly select an appropriate number of solid lattice sites Clicking the Create button will write all the lattice space data to a lbin spa file any lattice point defined more than once will hold its latest definition 2 3 Dissipative Particle Dynamics and the DL_MESO GUI To access the DPD facilities in the DL_MESO GUI proceed as follows Click the DPD button to get the DPD panel Click the Define DPD System button and supply the required information The CONTROL file will be created by this step Note that currently no simulation space settings or molecular structure data can be entered using the GUI Click EXIT to finish the settings 2 3 1 Defining the System Figure 2 5 shows the Define DPD System panel with the rows for data entry labelled in red numbering The required data are as follows 1 2 The job header a line of text up to 80 characters long describing the simulation The system volume the pull down list can be used to specify whether this is
289. ticles i j and k can be determined from the bond vectors rj T Tj and Tp Tk Tj Osjx cos ate 11 72 Tig kj The most general form for the bond angle potential is given thus U ijk ij Pkg A Big S rij S 145 S Tak 11 73 2This expression is also used for the virial contribution from the standard DPD pairwise forces i e Equation 9 3 again only applying a single contribution per particle pair 154 CHAPTER 11 DL MESO DPD FEATURES with A 0 as a purely angular function and S r a screening or truncation function The force on particle in dimension a is thus given by 0 F gg Y Out Piss Tki 11 74 o S rij S rrj S rik apa 0551 ro ro fa A ijn S rig S rin Sei Seg 278 ris Tij Tij re A 0ijx S rij S rik Sex Sej PREE PR rej J J 0 A Bigr S rig S 113 See 001 LES rir 11 75 Tik OTik with ab 1 if a b and dq 0 if a b In the absence of screening terms the above formula reduces to o F 57 Adi 11 76 1 0 A 6 sin Dijk olijk ik A ip S E A EE Gn So naa ee 7 Pag ej Tijfkj i Siy ej l The contribution to the virial from the angle is given by WE Fa F Fey Fa 11 78 which is equal to zero for bond angle potentials without screening terms 59 11 6 3 Bond dihedrals Three potential models for bond dihedrals along particles 2 j k and l are provided in DL MESO_DPD a
290. tion such that snapshots at the recorded timesteps and animations can be produced Two versions of the utility are provided traject f90 outputs every particle for all recorded timesteps and trajectselected f90 allows the user to select the number of particles and the number of timesteps to output to the trajectory file Both versions of the utility can be used with both HISTORY and HISTORY files produced by the serial and parallel versions of DL_MESO_DPD respectively their endianness is automatically detected so the utility can be run on a different machine to the one used for DPD calculations If 90 is the command for the available Fortran90 compiler the executable traject exe can be produced by typing e 90 o traject exe traject f90 and either run at the command line or via the GUI in Process DPD Data A command line argument indicating the number of processes and therefore the number of HISTORY or HISTORY files can be included in a similar way to the exportimage utility The alternative version can be compiled in the same way by default the makefiles create executables named trajects exe This version takes the same command line argument as traject f90 After the number of processes is typed in the utility displays the total number of particles the number of unbonded particles in the simulation and the total number of timesteps available before asking for the particle number range and number of timesteps including a starting time
291. tions may be handled in two different ways either 1 locally with each processing unit being allocated a subset of bonds to deal with including bonds across neighbouring units or 2 globally with all units holding all bond data and sharing bonded particle positions each carrying out all bond calculations and appropriately allocating forces to local particles The former method may require larger boundary halo sizes for the bond lengths being simulated but is more efficient for larger numbers of molecules and processing 141 142 CHAPTER 11 DL MESO DPD FEATURES units while the latter method requires the sharing of information between all units but does not require halo information and is guaranteed to find all bonds Bookkeeping arrays bndtbl angtbl and dhdtb1 list all particles involved in bonded interactions according to global index numbers and point to appropriate arrays of parameters to define the potential If the key bonded particle for a bond moves from one processing unit to another the entry in the bookkeeping array is also moved At each time step a list of bonded particles in each domain 1b1c1st is created to relate global index numbers to the local index numbers used by the processing unit in force velocity and coordinate arrays This global local index list is sorted by global index number to allow cross referencing to local index numbers by means of a binary search 11 1 2 Electrostatic interactions For syste
292. to happen as maxdim is calculated according to the numbers of particles and processors available taking into account any nfold duplications but the user may wish to use the densvar directive in the CONTROL file to increase this value 235 Message 54 non existent species given in CONFIG file for bead i An undefined species has been found in the definition for the th particle in the CONFIG file Action Check the species definitions in the FIELD file and the th particle in the CONFIG file to ensure that species is defined Message 61 deport coordinate buffers exceeded The amount of particle data received during deport is greater than the current processor can accommodate Action This error message suggests non constant particle densities across the system and poor load balancing The user may wish to use the densvar directive in the CONTROL file to increase the value of maxdim and thus accommodate larger numbers of particles Message 62 deport coordinate buffers exceeded for lees edwards shear The amount of particle data received during deport with Lees Edwards shearing is greater than the current processor can accommodate Action This error message suggests non constant particle densities across the system and poor load balancing The user may wish to use the densvar directive in the CONTROL file to increase the value of maxdim and thus accommodate larger numbers of particles Message 71 import coordinate buffers exceeded
293. trnd global_sum_int e Comments This routine assigns frozen bead walls and other unbonded beads as cubic lattices the latter may be incomplete and species of unbonded beads are randomly assigned according to the numbers specified in the FIELD file No duplication of system using nfold is assumed revive e Header records SUBROUTINE revive key e Function Saves and reads restart configurations e Dependencies export files if reading restart configuration e Arguments key input integer e Comments No duplication of system using nfold is assumed when reading restart files if this is required a CONFIG file should be created and used instead 206 CHAPTER 13 DL MESO DPD PACKAGE REFERENCE read_config e Header records SUBROUTINE read config e Function Reads initial system configuration positions velocities forces from DL POLY style CONFIG file and assigns particles bonds etc to system accounting for system duplication using nfold Dependencies CONFIG file getword getint getdble initialvelocity global_sca_and global_sum_sca_int error Comments The number of particles in the CONFIG file must match up with the number described in the corresponding FIELD file as should any molecule and bond information The periodic boundary key imcon 65 is ignored since all DL_MESO systems are orthorhombic This routine also adds any required frozen bead walls as cubic lattices No checks are made to
294. tydata DPD VV only dragforces_dpdvv DPD VV only importforcedata DPD VV only global_sca_sca_int global_sca_sca_dble global_sum_dble global_sum_int Lowe Peters Stoyanov Arguments stage input integer Comments The Langevin barostat is configured to apply the following piston force rate of change of momentum in dimension a 1 2 e le Pga V Pa _ Po P Ny 2 MV YpPg a Oppa At 2 with the option of keeping the system isotropic by using equal values of Py and Cp o for all dimensions This may be switched off if imposing constant surface tensions at given planar surfaces Rescaling of the simulation volume takes place in the first stage coupled with the integration of particle forces while iteration of the barostat force to achieve convergence of particle velocities to machine precision takes place in the second stage verlet_ _berend e Header records SUBROUTINE verlet_ _berend stage e Function Solves the equations of motion using the Velocity Verlet scheme coupled with the Berendsen barostat 2 Dependencies hardreflect deportdata frozenbead error exportvelocitydata DPD VV only dragforces_dpdvv DPD VV only importforcedata DPD VV only global_sca_sca int global_sum_dble global_sum_int Lowe Peters Stoyanov 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 213 e Arguments stage input integer e Comments The Berendsen barostat rescales particle positions and system sizes i
295. u0 0 2 3 23 where the kinetic viscosity is given by y E 3 ry 3 Similarly the convection diffusion equation governing the evolution of solute transfer and the convection conduction equation governing the evolution of thermal transfer can be obtained 3 5 Mesoscale Interaction The rate of change of momentum is proportional to the force Pua t At pua t Fo At 3 24 The Lattice Boltzmann Equation takes into account the effect of relaxation and it is possible to express Equation 3 24 in a new format 41 Pua t At pua t FaTf 3 25 F with Fa as the component in the a direction can be a long ranged body force or any local interactions In the Shan Chen pseudopotential model for multiple phases and components 55 the force on component a is defined as F p 2 Y gas Y wih Z i s 3 26 b i where gap is the interaction coefficient between elements a and b is related to the density of element a and can take many different forms e g a wa o fi 2 3 27 Po In the Lishchuk continuum based model for single phases and multiple components 35 the force acting between components a and b is expressed as 1 Fab 3900 Kay V Pas 3 28 3 6 SUMMARY OF LATTICE BOLTZMANN EQUATION 27 a b where o5 24 is a phase index between the two components and Ka is the local curvature from the pe p interface model which can be determined from spatial gradients of the phase i
296. uding the boundary lbdm touter total number of grid points in the domain including the boundary Table 4 6 Neighbour information parameter meaning lbnb k rank processor name of neighbour k lbnb k spos start position for sending distribution function message lbnb k rpos start position for receiving distribution function message lbnb k bspos start position for sending boundary condition message lbnb k brpos start position for receiving boundary condition message k 0 right neighbour k 1 left neighbour k 2 upper neighbour k 3 lower neighbour k 4 front neighbour k 5 back neighbour Table 4 7 Simulation information parameter meaning possible values collide collision and forcing type 0 BGK 1 BGK with Guo forcing 2 MRT 3 MRT with Guo like forcing interact mesophase interaction type 0 none 1 Shan Chen 2 Shan Chen with wetting 3 Lishchuk incompress incompressibility of fluids 0 compressible fluids 1 incompressible fluids outtype output file type 0 VTK 1 Legacy VTK 2 Plot3D The notation column in Table 4 8 gives the restrictions applicable on the parameters A indicates an array of data followed by the number of elements in the array For example A lbsy nf means the parameter is actually an array with lbsy nf elements gt 1 means the number must be greater or equal to one while 1 or 0 means the value of the parameter can either be one or zero An asterisk i
297. ue from a Maxwellian distribution i e kgT Yi Qij iF 11 4 where Hij ae is the reduced mass between the two particles The velocities of particles and j thus become Ui Uj Kij es s Viz Sie vg ij 11 5 mi Uy U a lt Viz v ij 11 6 o The probability of a particle pair being thermostatted is equal to TAt where I is defined as the collision frequency with a maximum effective value of 27 and the velocity corrections to particle pairs are applied in a random order to prevent biasing The above pairwise correction of velocities is equivalent to applying a thermostatting force equal to a a a da eek ES aa ig Gig 055 big 11 7 and thus a virial correction of FE Tij is applied for each particle pair being thermostatted The viscosity and self diffusion generated by this thermostat for a single species are norr 11 8 75m ce kgT mi BA ED 11 9 m where Tp is the decay time for velocity correlations and inversely proportional to the collision frequency The Schmidt number is therefore proportional to ir and can thus reach values up to O 10 This thermostat is suited to systems with higher viscosities and low diffusitivies while giving the correct system temperature for a wide range of time step sizes within numerical errors due to Velocity Verlet force integration 144 CHAPTER 11 DL MESO DPD FEATURES Its implementation in parallel running uses a
298. uk DL_MESO TERMINATION This Licence Agreement will take effect and the Licence Period will start when the Licensee has agreed to the terms and conditions of this Licence Agreement and downloaded the DL_MESO Software from the DL_MESO Website This Licence Agreement will terminate immediately and automatically if 5 2 1 the Licensee is in breach of this Licence Agreement or 5 2 2 the Licensee becomes insolvent or if an order is made or a resolution is passed for its winding up except voluntarily for the purpose of solvent amalgamation or reconstruction or if an administrator administrative receiver or receiver is appointed over the whole or any part of its assets or if it makes any arrangement with its creditors The Licensee s right to use the DL_MESO Software will cease immediately on the termination of this Licence Agreement and the Licensee will destroy all copies of the DL_MESO Software that it or any of its employees or students then holds Clauses 1 2 2 3 4 5 3 5 4 5 5 and 6 will survive the expiry of the Licence Period and the termination of this Licence Agreement and will continue indefinitely STFC may stop providing any assistance or advice in relation to or any corrections new releases or versions of the DL_MESO and 244 APPENDIX D DL_MESO LICENCE AGREEMENT ACADEMIC PURPOSES may stop updating or publishing the DL_MESO Website at any time 6 GENERAL 6 1 6 2 6 3 6 4 6
299. uld be hard and reflecting 11 7 2 Frozen bead walls frozen This boundary condition is applied by adding layers of frozen beads which do not move during the simulation but still interact with all other particles If appropriate choices for the density of frozen beads in the walls and interactions between frozen and non frozen particles are made non porous boundaries with no slip conditions can be obtained albeit at the cost of density fluctuations near the walls 51 To use this boundary condition a species of frozen beads needs to be specified in the FIELD file along with the interaction types and parameters between this species and all others The directive surface is used in the CONTROL file to specify which boundary surfaces should include frozen beads while the same directive in the FIELD file identifies the frozen bead species the bead density and thickness of the wall regions the number of beads required is automatically determined and the size of the system is adjusted to include the additional wall regions i e the user does not have to include the walls in the system dimensions given in the CONTROL file This boundary condition can only be set up in this manner for new simulations either starting from scratch or using a CONFIG file If creating a CONFIG file from a previous simulation users are advised to use the hard reflecting boundary condition described above to ensure molecules remain within the required non periodic boundarie
300. ult mixing rules for unlike particle parameters Figure 14 1 gives a snapshot of the system at the end of the simulation demonstrating mixing between the three particle types represented by different colours Figure 14 1 Visualization of system at final time step from DPD Mixture Ser test case 14 2 Mixture_Large This simulation example is similar to Mixture_Smal1 but larger it consists of 512 000 particles with 2 species each with a population of 256 000 particles The particle types have identical sizes and masses but different 215 216 CHAPTER 14 DL MESO DPD EXAMPLES energy parameters using the default mixing rules for unlike particle parameters Figure 14 2 gives a snapshot of the system at the end of the simulation demonstrating good mixing between the two particle types Figure 14 2 Visualization of system at final time step from DPD Mixture_ Par test case 14 3 PhaseSeparation This simulation example consists of 3000 particles with 2 species each with a population of 1500 Both particle types have identical sizes masses and like like energy parameters but the unlike energy parameter has been set to a larger value to produce phase separation which can clearly be seen in Figure 14 3 The initial state of this simulation has been provided in a CONFIG file An AVI video file of the first half of the simulation can be found in the Example Simulations page of the DL_MESO website a t 2 t 20 t 50 t 100 Figure 1
301. um based algorithm is to be used a non zero segregation parameter 8 is required to ensure immiscible fluids separate out from each other Solutes require the following data in the following row numbers 1 The initial concentrations of the solutes throughout the system as used for initialization 10 CHAPTER 2 THE DL_MESO GUI The solute concentrations at the top boundary The solute concentrations at the bottom boundary The solute concentrations at the left boundary The solute concentrations at the right boundary The solute concentrations at the front boundary Greyed out for two dimensional systems The solute concentrations at the back boundary Greyed out for two dimensional systems The relaxation time 7 for each solute representing diffusivities If selected for inclusion the required thermal properties are 1 2 10 11 The initial T temperature for the system The initial dT dt rate of change of temperature related to heat transfers in or out for the entire system The Boussinesq high reference temperature Th for heat convection in the system The Boussinesq low reference temperature T for heat convection in the system The heat relaxation time 7 for the system which represents the thermal diffusivity The temperature and rate of temperature change at the top boundary The temperature and rate of temperature change at the bottom boundary The temperature and
302. ution function and that the fluid modelled using LBE is generally athermal It is possible however to alleviate this problem by defining a temperature at each grid point and either using a thermal lattice scheme with additional link vectors or modelling either the temperature or internal energy on an additional lattice grid 3 3 Derivation of Equilibrium There are two methods by which the local equilibria for the Lattice Boltzmann Equation can be constructed The bottom up method obtains the equilibrium from the Maxwell Boltzmann equilibrium distribution The top down method constructs the equilibrium so that the required macroscopic properties can be reproduced Only the bottom up method is shown here the top down method can be found in 6 The Maxwell Boltzmann single particle equilibrium distribution function is 2 eq _ P E a f Te exp 28 3 4 where 9 kgT m kg is the Boltzmann constant T is temperature m is molar mass D is the space dimension is the thermal velocity and u the macroscopic velocity When l lt v Equation 3 4 can be expanded into 3 3 eq P da 3 5 f Oro A T a T 202 20 ee For a microscopic quantity Y the associated macroscopic quantity Y is calculated by w fu suas 3 6 Let E y 20 where is a rescaled thermal velocity the macroscopic velocity i can be similarly rescaled to v20u Equations 3 5 and 3 6 can thus be combined to give v feyt
303. va hisia The second and third cases are slightly slower than the first but more readable fGetSpeedSite e Header records three cases int fGetSpeedSite double speed double startpos int fGetSpeedSite double speed long tpos int fGetSpeedSite double speed int xpos int ypos int zpos e Function Calculates the macroscopic speed of all compressible fluids at the grid point e Dependencies fReciprocal 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS 73 e Arguments startpos input double pointer tpos input long integer xpos input integer ypos input integer Zpos input integer speed output double precision array e Comments The calculation is based on vg Palit The second and third cases are more readable than the first but also slightly slower fGetSpeedIncomSite e Header records three cases int fGetSpeedIncomSite double speed double startpos int fGetSpeedIncomSite double speed long tpos int fGetSpeedIncomSite double speed int xpos int ypos int zpos e Function Calculates the macroscopic speed of all incompressible fluids at the grid point e Dependencies fReciprocal e Arguments startpos input double pointer tpos input long integer xpos input integer ypos input integer Zpos input integer speed output double precision array e Comments The calculation is based on vg Za The second and third cases are more readable than the first but also slightly slower fGetOneMomentSi
304. values in neighbouring grid points fSiteBlankF e Header records int fSiteBlankF long tpos e Function Sets the fluid particle distribution function at the tpos th grid point to zero e Dependencies None e Arguments tpos input long integer e Comments This routine is used to ensure e g flows inside solid boundaries are negligible fSiteBlankC e Header records int fSiteBlankC long tpos e Function Sets the solute particle distribution function at the tpos th grid point to zero e Dependencies None e Arguments tpos input long integer e Comments This routine is used to ensure e g diffusion inside a bulk solid is negligible compared to that in a liquid fSiteBlankT e Header records int fSiteBlankT long tpos e Function Sets the temperature particle distribution function at the tpos th grid point to zero e Dependencies None e Arguments tpos input long integer e Comments This routine is used to ensure e g negligible heat transfer through an insulator 7 2 DL MESO_LBE SUBROUTINES AND FUNCTIONS 89 fFixedSpeedFluid e Header records int fFixedSpeedFluid long tpos int prop double uwall e Function Calculates the particle distribution function at a fixed speed boundary e Dependencies Many for different lattice schemes e Arguments tpos input long integer prop input long integer uwall output array of doubles e Comments Planar surface calculations are based o
305. vector 1 Cia Ciy 0 0 0 1 1 1 2 1 0 3 1 1 4 0 1 5 1 1 6 1 0 7 1 1 8 0 1 29 30 CHAPTER 4 DL MESO _LBE BASIC DEFINITION 1 1 1 1 1 1 di el 4 2 1 2 1 2 1 2 I 4 1 2 12 1 2 1 2 0 1 1 1 0 1 1 1 0 T 0 1 2 1 0 1 2 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 2 1 0 1 2 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 p P ee 20 3 j jy es wep M2 432 M9 go jz eq as ace Poh om vis jody 0 6 vz Fy VyFy 6 0 Fs ty Fy Y II a F 2 Ur Fy Uy Fy Un Py vy Fy T 1 mh ea a Gia 1 sa 1 54 T TF 1 1 Ax v ron 5 Ari 2 At 31 4 1 LATTICE MODELS D3Q15 Wi aoo 72 Weight factor 1 3 8 10 47 11 14 Speed vector Ci z Ciy Cix 10 11 12 13 14 1 4 1 4 1 4 4 4 4 16 1 1 1 1 1 1 4 1 1 1 1 1 E A 0 heel Ht 0 32 1 7 CHAPTER 4 DL_MESO_LBE BASIC DEFINITION p Cn eea 2p Gett H eo wep FH ja jy j2 qe de dy Jy Gy y Jz Jz qs rie 3ne4 2j2 j2 j pes jody pet dude pet dede ae J 0 2 Ug Ey Vy Fy vzF 2 10 vz Fr vy Fy vF Fo iF Fy 2 3Fy S F FF 2 2u Fr Uy Fy v Fz 2 vy Fy vzF Uy Fy vy Fy Vy uzFy vz Fy Vrt 0
306. ware or any assistance or advice that STFC may give in connection with the DL_MESO Software The Licensee will indemnify STFC against any and all claims arising as a result of the Licensee having made any of the DL_MESO Software or any Derived Work available to any third party Before using any of the DL_MESO Software the Licensee will check that the DL_MESO Software does not contain any Harmful Element STFC does not warrant that the DL_MESO Software will run without interruption or be error free or be free from any Harmful Element STFC is not obliged to provide any support or error correction service assistance or advice in relation to the DL_MESO Software but the Licensee may access any error corrections and online assistance that STFC chooses to make 242 3 3 3 4 3 6 3 7 3 8 APPENDIX D DL_MESO LICENCE AGREEMENT ACADEMIC PURPOSES available on the DL_MESO Website from time to time If STFC does provide that sort of service assistance or advice subject to clause 3 7 STFC will not be liable for any loss or damage suffered by the Licensee as a result STFC will not be liable to the Licensee to the extent that any loss or damage is caused by the Licensee s failure to implement or the Licensee s delay in implementing any correction or advice in relation to the DL_MESO Software that STFC has made available on the DL_MESO Website or by the Licensee s failure to acquire a licence of and to implement any new r
307. well as plots of y component velocity density of the fluid particles and temperature defined only by x and z components of velocity in this case The snapshot demonstrates a slight porosity of the frozen particle wall due to soft DPD interactions which could be alleviated by a higher frozen particle density 48 while the emergent velocity profile is similar to that expected for Poiseuille flow The temperature and density profiles are mainly flat across the entire spacing between the walls apart from significant density fluctuations close to the walls a Visualization of system at t 2 000 5 T T T T T T T T i e e Density s s Temperature a PAT ES ATT y w rrr Time averaged vertical velocity lt v gt o gt a a a N Pt e a Time averaged particle density lt p gt or temperature lt T gt o gr A pg i ope i 1 l i i i RY E 1 l i y l i l y 3 6 8 10 12 0 2 4 6 8 10 12 0 2 4 Horizontal position x Horizontal position x b Time averaged y component of velocity c Time averaged fluid density and temperature Figure 14 8 Visualization and plots from DPD PoiseuilleFlow test case broken lines denote positions of no slip boundaries due to frozen particle walls 14 9 ShearFlow This simulation example consists of 3000 unbonded particles in a box of 10 x 10 x 10 DPD length units with Lees Edwards shearing boundaries orthogonal to the y axis
308. wen Shan and Hudong Chen Simulation of nonideal gases and liquid gas phase transitions by the lattice Boltzmann equation Physical Review E Statistical Physics Plasmas Fluids and related interdisciplinary topics 49 4 2941 2948 April 1994 W Smith Molecular dynamics on hypercube parallel computers Computer Physics Communications 62 2 3 229 248 March 1991 W Smith A replicated data molecular dynamics strategy for the parallel Ewald sum Computer Physics Communications 67 3 392 406 January 1992 W Smith Calculating the pressure CCP3 Information Quarterly 39 14 20 October 1993 W Smith T R Forester and I T Todorov The DL_POLY Classic user manual STFC STFC Daresbury Laboratory Daresbury Warrington Cheshire WA4 4AD United Kingdom version 1 0 edition December 2010 T J Spencer I Halliday and C M Care Lattice Boltzmann equation method for multiple immiscible continuum fluids Physical Review E 82 6 066701 December 2010 Simeon D Stoyanov and Robert D Groot From molecular dynamics to hydrodynamics A novel Galilean invariant thermostat Journal of Chemical Physics 122 11 114112 2005 Sauro Succi The Lattice Boltzmann Equation for Fluid Dynamics and Beyond Clarendon Press Oxford 2001 Michael R Swift W R Osborn and J M Yeomans Lattice Boltzmann simulation of nonideal fluids Physical Review Letters 75 5 830 833 July 1995 I T Todorov and W Smith The DL_POLY_4 user manual ST
309. where c is the speed of sound for the lattice Re the Reynolds number for the flow t the time step p the density U the x component of velocity V the y component of velocity W the z component of velocity and the space boundary condition property The 1 0 between the lattice speed of sound and flow Reynolds number represents the freestream angle of attack The density of the fluid may be replaced with its concentration or scalar temperature If all properties are output each property is given a uniquely named file based on the number of fluid or solute e g lbout0O0dens q for the density of fluid 0 and its property 1bout dens q lbout frac q lbout conc q and lbouttemp q Chapter 7 DL MESO LBE Package Reference 7 1 Overview DL_MESO LBE consists of nine packages e 1bpMODEL Contains subroutines to assign lbw 1bv and 1bopv for D2Q9 D3Q15 D3Q19 and D3Q27 lattice models e IbpBASIC Contains general purpose subroutines which can be used elsewhere e g a random number generator producing values between 1 and 1 e 1bpGET Contains subroutines to calculate macroscopic quantities e g macroscopic density speed and momentum e lbpI0 Contain subroutines to read parameters and write numerical results for plotting and visualization 1bpI0 Contains subroutines to read input files calculate and write summaries 1bpI0Plot3D Contains subroutines to write calculation output files in Plot3D format lbpIOLegacyV
310. x_dble aaa e Function Finds global maximum value of double precision number aaa e Dependencies None e Arguments aaa input output array of real KIND dp global_sca_max_int e Header records SUBROUTINE global_scamax_int iii e Function Finds global maximum value of integer iii e Dependencies None e Arguments iii input output array of integers 13 2 DL MESO _DPD SUBROUTINES AND FUNCTIONS 175 global_sca_min_dble e Header records SUBROUTINE global_sca_min_dble aaa e Function Finds global minimum value of double precision number aaa e Dependencies None e Arguments aaa input output array of real KIND dp global_sca_min_int e Header records SUBROUTINE global_scamin_int iii e Function Finds global minimum value of integer iii e Dependencies None e Arguments iii input output array of integers msg_receive_blocked e Header records SUBROUTINE msg_receive_blocked msgtag buf length e Function In a blocking call receives data in the form of a double precision array buf O e Dependencies None e Arguments buf output array of real KIND dp msgtag input integer length input integer e Comments For a double precision scalar the alternative SUBROUTINE msg_receive_sca_blocked msgtag buf length is available msg_receive_unblocked e Header records INTEGER FUNCTION msg_receive_unblocked msgtag buf length e Function In a non blocking call re
311. xdim corrective force z component on charged frozen particle fcfx real KIND dp A maxdim corrective force y component on charged frozen particle fcfy real KIND dp A maxdim corrective force z component on charged frozen particle fcfz real KIND dp A maxdim velocity z component of particle VXX real KIND dp A maxdim velocity y component of particle vyy real KIND dp A maxdim velocity z component of particle vzz real KIND dp A maxdim Cartesian coordinate x for particle XXX real KIND dp A maxdim Cartesian coordinate y for particle yyy real KIND dp A maxdim Cartesian coordinate z for particle zzz real KIND dp A maxdim particle global identity number lab integer A maxdim particle species number ltp integer A maxdim particle molecule type number ltm integer A maxdim particle link cell population number lct integer A maxdim particle link cell number link integer A maxdim particle local domain cell identity number loc integer A maxdim particle domain cell number lmp integer A maxdim particle molecule type number ltm integer A maxdim species name for particle atmnam character 8 A maxdim molecule name for particle molnam character 8 A maxdim particle mass weight real KIND dp A maxdim potential energy accumulator pe real KIND dp virial accumulator vir real KIND dp stress tensor accumulator stress real KIND dp A9 kinetic energy accumulator tke real KIND dp bond potential energy accumulator be real KIND dp angle potential energ
312. ximum specified length for the potential or cannot be calculated due to lack of available information for both particles The bond s identified as overly long or lost is are printed either in the OUTPUT file or in the standard output e g screen Action If calculating bonds locally increasing the size of boundary halos may reduce the likelihood of bonds being broken alternatively global bond calculations can ensure all data is available at the cost of replication over all processors Adjusting the parameters for the bond potential may also help ensure bonds do not get too long Message 201 too many interacting pairs The number of interacting pairs for non DPD thermostats Lowe Andersen Peters Stoyanov Groot exceeds the maximum number calculated from the number of particles in the system maxpair Action The user may wish to use the densvar directive in the CONTROL file to increase the values of maxdim and maxpair thus accommodating larger numbers of interacting pairs Messages 1001 1096 allocation deallocation errors Allocation or deallocation of arrays for DPD calculations including reading of input data transfer buffers for communications between processors global arrays of particle velocities for Lowe Andersen Peters Stoyanov 237 Groot thermostats etc has failed This may be due to a lack of addressable memory required for the DPD calculations These messages identify which allocation deallocation has failed
313. xpansions of simulation volume set permittivity constant for system I to f set required system pressure to f target pressure for constant pressure ensem bles print system data every n timesteps see cutoff restart job from end point of previous run i e continue current simulation using export files restart job from previous run without rescaling to system temperature i e begin a new simulation from older run without temperature reset restart job from previous run after rescaling to system temperature i e begin a new simulation from older run with temperature reset rescale system temperature every n steps during equilibration apply Slater type exponential charge smearing with coefficient 6 set to f set rolling average stack to n timesteps accumulate statistics data and write to CORREL file every n timesteps run simulation for n timesteps set required surface repulsive range Zc to f length units default f re set hard adsorbing walls orthogonal to i axis x y z if specified multiple walls can be specified if separated with spaces or commas 12 1 INPUT FILES surface frozen i surface shear i temperature f trajectory i j 159 set frozen bead walls orthogonal to i axis x y z if specified multiple walls can be specified if separated with spaces or commas Note that this can only be used for brand new simulations this directive is ignored if a simulation is restarted set moving Lees Edwards
314. y the parsing utilities Define system CONTROL The CONTROL file contains the control variables for running a DPD simulation and is read by the subroutine read_control in config_module Such files can can be obtained either via use of the DL_MESO GUI or by editing existing files of that name such as those in the DEMO DPD directory These consist primarily of directives character strings that appear as the first entry of a data record and invoke a particular operation or provide numerical parameters Extra options may be added by the inclusion of keywords to qualify a particular directive Directives can be included in any order except for the simulation name up to 80 characters long on the first line of the file and the finish directive which marks the end of the file A list of the directives available follows with bold type specifying the minimum number of letters required by DL_MESO_DPD Some directives may include optional words or parameters as indicated by brackets directive boundary halo f close time f cutoff f densvar f electrostatic cutoff f ensemble nvt mdvv ensemble nvt dpdvv ensemble nvt lowe ensemble nvt peters ensemble nvt stoyanov a meaning set size of boundary halo overriding default values determined from interaction cutoff maximum bond lengths and short range electrostatics as f length units set job closure time to f seconds set maximum interaction cutoff radius re to f length units allow for
315. y accumulator ae real KIND dp dihedral potential energy accumulator de real KIND dp electrostatic potential energy accumulator ee real KIND dp bond length accumulator bdlng real KIND dp bond length maximum value bdlmax real KIND dp bond length minimum value bdlmin real KIND dp bond angle accumulator bdang real KIND dp bond dihedral accumulator bddhd real KIND dp average system potential energy avepe real KIND dp average system virial avevir real KIND dp average system kinetic energy avetke real KIND dp average system total energy avete real KIND dp average system pressure aveprs real KIND dp average system volume avevlm real KIND dp average system temperature avettp real KIND dp average system bond potential energy avebe real KIND dp average system angle potential energy aveae real KIND dp average system dihedral potential energy avede real KIND dp average system electrostatic potential energy aveee real KIND dp system potential energy fluctuation flcpe real KIND dp system virial fluctuation flevir real KIND dp system kinetic energy fluctuation flcke real KIND dp system total energy fluctuation flcte real KIND dp system pressure fluctuation flcprs real KIND dp system volume fluctuation flcvlm real KIND dp system temperature fluctuation flcttp real KIND dp system bond potential energy fluctuation flcbe real KIND dp system angle potential energy fluctuation flcae real KIND dp system dihedral pot
316. y molecule generate cpp to create molecules for the DPD simulation and write them 16 CHAPTER 2 THE DL_MESO GUI DL_MESO LBE DPD SPH Manual Help Exit Dissipative Particle Dynamics DUDES Peles LH la set species 1 set interactions 2 operating system gt v create molecules 3 Prior compilation of molecule generate utility required external force none v set parameters 4 text editor dimesoEditor w edit FIELD file 5 Figure 2 7 Set DPD Interactions to the FIELD file The utility should be compiled beforehand to give the executable molecule exe refer to Appendix B for more details 4 It is possible to define an external force field on all particles in the system using the pull down box to define the type Constant gravitational fields and linear shear boundaries can be defined Clicking on the button set parameters opens a pop up window to define the parameters for the external force field and write them to the FIELD file 5 A text editor including the built in dlmesoEditor may be selected using the pull down box to view and edit the FIELD file An alternative editor can be used by selecting other and typing its name in the text box before clicking on the edit FIELD file button After the data for particle species interactions molecules and external fields are entered and written to the FIELD file clicking SAVE will complete the file which can still be viewed
317. ystem e Header records int fDefineSystem const char filename lbin sys e Function Reads calculation parameters lattice scheme types of collisions and forcing mesophase algorithms num bers of fluids solutes temperature scalars phase field order parameters grid size from input system file lbin sys 76 CHAPTER 7 DL MESO _LBE PACKAGE REFERENCE Dependencies lbin sys data file Arguments filename input array of characters Comments The default file name is 1bin sys to use different file names the argument for this routine can be changed by the user fPrintSystemInfo Header records int fPrintSystemInfo Function Prints system information lattice model dimensions boundary width numbers of fluids solutes and temperature scalars collision model forcing type and mesophase interactions Dependencies None fPrintEndEquilibration Header records int fPrintEndEquilibration Function Prints message indicating end of static equilibration process Dependencies None Comments This message is not printed if no equilibration steps are specified in the lbin sys file fPrint DomainMass Header records int fPrintDomainMass Function Calculates and prints total and individual fluid masses in domain Dependencies double fGetTotMassDomain double fGetOneMassDomain Comments This routine only produces the masses for the entire system if running in serial to obtain system
318. ystem corrections e Dependencies error global_sca_and zero e Header records SUBROUTINE zero e Function Sets step counters initial time parameters system parameters accumulators for statistical properties and long range potential corrections to zero initializes random number generators e Dependencies duni mtrnd 13 2 13 field module This module requires the modules constants variables bond_module manybody_module ewald_module surface_module numeric_container and domain_module to be loaded beforehand Different versions of each subroutine are available in this module for different integrators and or thermostats e DPD thermostat with standard molecular dynamics Velocity Verlet integration MD VV 67 mdvv DPD thermostat with DPD Velocity Verlet integration DPD VV 3 dpdvv Lowe Andersen thermostat 36 lowe e Peters thermostat 47 peters Stoyanov Groot thermostat 62 stoyanov forces_ e Header records SUBROUTINE forces_ nlimit e Function Calculates all forces between particles particularly pairwise forces within cut off radius 210 CHAPTER 13 e Dependencies mtrnd duni gaussmp manybody_force manybody_potential ewald_real ewald_reciprocal bondforcesglobal bondforceslocal hardreflect Arguments nlimit input integer Comments DL_MESO_DPD PACKAGE REFERENCE DPD random forces are calculated using a uniform random number generator 16 by default the Mersenne
319. ystem of free particles interacting directly through soft forces e The system is coupled to a heat bath via stochastic forces which act on the particles in a pairwise manner e The particles also experience a damping or drag force which also acts in a pairwise manner e Thermodynamic equilibrium is maintained through the balance of the stochastic and drag forces i e the method satisfies the fluctuation dissipation theorem e At equilibrium or steady state the properties of the system are calculated as averages over the individual particles as in Molecular Dynamics 9 2 Outline of Method In DPD the system is modelled as a system of free particles which are spherical and interact over a range that is of the same order as their diameters The particles can be thought of as assemblies or aggregates of molecules such as solvent molecules or polymers or more simply as carriers of momentum lThe outline of the DPD method supplied here is based on 16 127 128 CHAPTER 9 DISSIPATIVE PARTICLE DYNAMICS BASIC THEORY The equations governing the time evolution in a DPD simulation resemble those of ordinary MD di F d E Si cih 2 T v 9 2 in which r v and F are the position velocity and force of the ith particle which has mass m The force on the particle is a sum of pair forces N R PC AD BR A Y ES FD FR 9 3 IA in which ES represents the force exerted on particle due to the presence

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