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PORE-FLOW User`s Manual (version 1.2)

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Contents

1. PROPERTIES NUM SETS 1 SET I DENSITY 1000 VISCOSITY 3 Copyright by UWM Research Foundation 2010 31 ENDSET 1 END PROPERTIES k MESH_DATA DIMENSIONS NUMBER _ NODES 2223 NUMBER_ELEMENTS 1824 SPACE 3D ELEMENT_TYPE HEXA 8 AXISYMMETRY NO END_DIMENSIONS GEOMETRY INCLUDE C hua tan incompressiveflow1 ELBOW INI END_GEOMETRY END_MESH_DATA Mb K ake ake
2. obe PROPERTIES NUM OF SETSd 3 gt There are 3 sets of properties in this example SET 1 VISCOSITY 1 Property set 1 for the inter tow gap region ENDSET 1 SET 2 VISCOSITY 1 Property set 2 for the tow parallel to z direction POROSITY 5 PERMEABILITY KX 1D 9 KY 1D 9 KZ 5D 9 ROTATION 0 ENDSET 2 SET 3 VISCOSITY 1 Property set 3 for the tow parallel to x direction POROSITY 5 PERMEABILITY KX 5D 9 KY 1D 9 KZ 1D 9 ROTATION 0 ENDSET 3 END_PROPERTIES k k sese se ok MESH_DATA DIMENSIONS NUMBER_NODES 17572 NUMBER_ELEMENTS 15320 SPACE 3D ELEMENT_TYPE HEXA 8 AXISYMMETRY NO END_DIMENSIONS Mesh data is included UNITCELL HEX INCLUDE C hua tan incompressiveflow1 UNITCELL HEX When running the example note the pa
3. ek ok ok ob PORE FLOW 2D dual scale flow problem using fast algorithm PHYSICAL PROBLEM DARCY EQUATION ON BODY FORCES ON GX 0 GY 9 8 GZ 0 END_DARCY FREE_SURFACE ON WICKING OFF DUAL_SCALE ON SINK_MODEL LUMPED END_FREE_SURFACE END_PHYSICAL_PROBLEM PROPERTIES NUM_OF_SETS 1 SET 1 DENSITY 860 VISCOSITY 1875 POROSITY 4742 PERMEABILITY KX 7 303e 10 KY 6 634e 10 KZ 1e 7 ROTATION 0 THICKNESS 1 valid for 2D filling analysis SINK_FUNCTION 1 4 25773 A2 1 02833 A3 1 28814 19593 45 ENDSET 1 END_PROPERTIES
4. k ok NUMERICAL TREATMENT TIME DATA INITIAL_TIME 0 0 FINAL_TIME 5 TIME STEP SIZE 1 THETA 0 5 INTEGRATION POINTS 4 ITERATION PICARD ERROR 5 D 5 OUT OF CORE OFF END NUMERICAL TREATMENT V OUTPUT FILE NAME Duel fast results out FREOUENCY STEP 20 MUMPS_INFORMATION Off END_OUTPUT M k
5. kok MESH_DATA DIMENSIONS For detail about this method see following paper Hua Tan Pillai K M Fast LCM Simulation of Unsaturated Flow in Dual Scale Fiber Mats Using the Imbibition Characteristics of a Fabric Based Unit Cell Polymer Composites Polymer Composites 31 10 1790 1807 2010 Copyright by UWM Research Foundation 2010 45 NUMBER NODES 441 NUMBER ELEMENTS 400 SPACE 2D ELEMENT TYPE OUAD 4 AXISYMMETRY NO END DIMENSIONS GEOMETRY INCLUDE C POREFLOW sourcecode_verl_01 Mold_Geom_2D dat END_GEOMETRY END_MESH_DATA M oo ek ok ob BOUNDARY_CONDITIONS INITIAL_CONDITIONS VX 0 0 VZ 0 END_INITIAL INCLUDE C POREFLOW sourcecode_ver1_01 Mold_BC_2D dat END_BOUNDARY_CONDITIONS M
6. PORE FLOW Title G oo PHYSICAL PROBLEM NAVIER_STOKES_EQUATIONS BRINKMAN_EQUATIONS DARCY_EQUATION HEAT_EQUATION SPECIES_EQUATION FREE SURFACE END PHYSICAL PROBLEM PROPERTIES NUM OF SETS SET DENSITY Copyright by UWM Research Foundation 2010 4 VISCOSITY POROSITY PERMEABILITY CONDUCTIVITY SPECIFIC_HEAT HEAT_GENERATION REACTION_RATE THICKNESS ENDSET END_PROPERTIES MESH_DATA DIMENSIONS GEOMETRY ELEMENTS COORDINATES END_MESH_DATA BOUNDARY_CONDITIONS INITIAL_CONDITIONS DIRICHLET_CONDITIONS NEUMANN_BOUNDARY_CONDITIONS END_BOUNDARY_CONDITIONS NUMERICAL_TREATMENT TIME_DATA INTEGRATION_POINTS ITERATION ERROR OUT_OF_CORE NAVIER_STOKES_BRINKMAN END NUMERICAL TREATMENT OUTPUT FILE NAME FREOUENCY MUMPS INFORMATION END OUTPUT Copyright by UWM Research Foundation 2010 3 Physical problem This block of data can have six sub blocks depends on the problem needed to be solved The structure of these blocks and
7. ok ob MESH DATA DIMENSIONS NUMBER NODES 441 NUMBER ELEMENTS 400 SPACE 2D ELEMENT TYPE OUAD 4 AXISYMMETRY NO END DIMENSIONS GEOMETRY INCLUDE C POREFLOW example Mold_Geom_2D dat END GEOMETRY END MESH DATA M ake ake ok oko BOUNDARY_CONDITIONS INITIAL_CONDITIONS VX 0 VY 0 VZ 0 END_INITIAL INCLUDE C POREFLOW example Mold_BC_2D dat END_BOUNDARY_CONDITIONS NUMERICAL TREATMENT TIME DATA INITIAL 0 0 FINAL TIME 5 TIME STEP SIZE 1 0 5 INTEGRATION POINTS 4 ITERATION PICARD ERROR 5 D 5 OUT OF CORE OFF END NUMERICAL TREATMENT
8. ak oko BOUNDARY_CONDITIONS INITIAL_CONDITIONS VX 0 VY 0 VZ 0 END_INITIAL INCLUDE C hua tan incompressiveflow1 ELBOW INI END_BOUNDARY_CONDITIONS USB ooo ooo NUMERICAL TREATMENT TIME DATA INITIAL 0 0 FINAL 100 TIME STEP SIZE 1 d 1 0 5 INTEGRATION POINTS 8 ITERATION PICNEW ERROR 5 D 5 NAVIER STOKES BRINKMAN BUBBLE FORMULATION OFF PRESSURE INTERPOLATION 1 END NAVIER STOKES END NUMERICAL TREATMENT M ak ake ake OUTPUT FILE_NAME global out FREQUENC
9. Copyright by UWM Research Foundation 2010 46 Front Arrival Time 50 100 150 200 250 300 350 400 450 500 550 0 15 0 1 gt 0 05 0 0 0 05 0 1 0 15 Figure 21 Liquid front movement Tow saturation 01 0 15 0 2 025 03 0 35 0 4 0 45 0 5 055 06 065 0 7 075 08 0 85 0 9 095 015 0 1 0 05 0 0 05 0 1 0 15 Figure 22 Tow saturation as liquid front moves Copyright by UWM Research Foundation 2010 47 10 7 Flow Modeling Diaper Paper POREFLOW can also model wicking and absorption of liquids into porous substrates Diapers are porous substances that absorb and retain liquid at a fast rate The driving force that makes liquid get absorbed by diapers is the capillary pressure Here we considered a simple block representing a thick sheet of paper or a section of diaper of size 20x10x5 mm with a permeability of 2 34e 9 m2 in all directions and a porosity of 0 75 The capillary pressure which acts on the liquid front is taken to be 2000 Pa Here are a series of pictures showing the filling pattern Blue wet region red dry region 009 0 t 5s t 14s t 25s t 42s t 58s t 935 t 107s t 121s Copyright by UWM Research Foundation 2010 48
10. ok MESH DATA DIMENSIONS NUMBER NODES 1111 NUMBER ELEMENTS 1000 SPACE 2D ELEMENT TYPE OUAD 4 AXISYMMETRY NO END DIMENSIONS pP R O GEOMETRY INCLUDE C hua tan code validation example swell qu Mesh data is included in swell qu END GEOMETRY When running the example note the path of swell qu END_MESH_DATA BOUNDARY_CONDITIONS POPPER MRA TE er INITIAL_CONDITIONS VX 0 VY 0 VZ 0 INITIAL CONDITIONS does not work in this case END INITIAL m B C data is included in swell ini INCLUDE C hua tan code validation example swell init lt When running the example note A O the path of swell ini END BOUNDARY CONDITIONS
11. NUMERICAL TREATMENT TIME DATA INITIAL 0 0 FINAL TIME 5 TIME STEP SIZE 1 THETA 0 5 INTEGRATION POINTS 4 ITERATION PICARD TIME DATA ITERATION and ERROR 5 D 5 ERROR are not necessary in this case OUT OF CORE OFF END NUMERICAL TREATMENT ok ok OUTPUT FILE_NAME global out FREQUENCY STEP 5 The solution is output every 5 steps MUMPS INFORMATION Off END OUTPUT oko ak Copyright by UWM Research Foundation 2010 26 0 1 Front Arrival Time Pressure 400 5000 380 10000 360 15000 0 08 340 20000 320 25000 300 2n 30000 35000 0 06 260 500 40000 45000 gt 220 50000 200 55000 0 04 gt
12. PHYSICAL PROBLEM DARCY EQUATION ON BODY FORCES ON GX 0 GY 9 8 67 0 4 Consider gravity END DARCY FREE SURFACE ON 4 FREE SURFACE must be turned on since it s a moving boundary problem WICKING ON CAPILLARY PRESSURE 96271 21679 DUAL SCALE OFF END FREE SURFACE Wicking flow and capillary pressure Copyright by UWM Research Foundation 2010 25 END_PHYSICAL_PROBLEM PROPERTIES NUM_OF SETS Since the material is homogenous Only one set of property 1S used in the simulation FeO EN SET 1 DENSITY 1000 VISCOSITY 000911 Permeability is function POROSITY 5 a of filling time PERMEABILITY VARIABLE FILLTIME FUN 0 04508552357 FILLTIME 1 673195381 FILLTIME 5 4 23 62425661 1e 14 0 5 THICKNESS 1 valid for 2D filling analysis ENDSET 1 i T Function expression END PROPERTIES P can be used to give comment in a command line
13. OUTPUT FILE_NAME Mold2D_RESULT dat FREQUENCY STEP 5 MUMPS_INFORMATION Off END_OUTPUT A ok ok Copyright by UWM Research Foundation 2010 38 Pressure 9000 8000 7000 6000 5000 4000 13000 12000 11000 0000 9000 8000 7000 6000 5000 4000 3000 2000 1000 Figure 10 Pressure distribution Front Arival Time 005 01 0 15 0 2 0 25 03 0 35 0 4 0 45 0 5 055 06 0 65 0 7 075 08 0 85 0 3 Figure 11 Liquid front location versus time Copyright by UWM Research Foundation 2010 39 0 2 0 18 0 16 0 14 0 12 E 041 s X 0 08 0 06 0 04 0 02 0 0 2 0 4 0 6 0 8 1 1 2 t s Figure 12 Liquid front location versus time More simulation results for mold filling Geometry Grid and Boundary Conditions Initial pressure P 20000 Impermeable boundary Input Output Impermeable boundary Fig 1
14. CANA V O CANA V 71777 77177 VN V VOZY 777 42 Fig 17 Boundary and Gri Copyright by UWM Research Foundation 2010 upper map is plane lower map is y z plane Fig 18 Distribution of Velocity and Pressure in a porous media 3 D Rectangular Geometry Results Geometry Grid and Boundary Conditions Initial pressure P 20000 Z Fig 19 Boundary and Grid Copyright by UWM Research Foundation 2010 43 Output Output Output Fig 20 Distribution of Velocity and Pressure in a porous media Copyright by UWM Research Foundation 2010 44 10 6 Fast LCM simulation of unsaturated flow duel scale fibermats The problem is a mold of 7 x7 0 1778 0 1778 mold that is filling with a resin or a test liquid The porosity is 0 4742 and the density and viscosity of the liquid are 860 kg m and 0 1875 Pa s 2 respectively The permeabilities of fibermats are 7 303e 10 m and 6 634e 10 along x and y directions and the injection pressure is 20 kPa We want to study flow of resin in such a duel scale mold The domain is discretized using FE mesh as shown in Figure 9 For this problem the Darcy equation and continuity equations are solved to find the pressure distribution using fast LCM mold filling simulation The command file is listed as
15. END_MESH_DATA V BOUNDARY_CONDITIONS INITIAL_CONDITIONS VX 0 VY 0 VZ 0 TEMPERATURE 293 END_INITIAL INCLUDE C hua tan code validation example plateflow2D ini END_BOUNDARY_CONDITIONS NUMERICAL TREATMENT TIME DATA INITIAL 0 0 FINAL 100 TIME STEP SIZE 1D 2 0 5 INTEGRATION POINTS 4 ITERATION NEWTON ERROR 6 D 5 OUT OF CORE OFF NAVIER STOKES BRINKMAN BUBBLE FORMULATION OFF PRESSURE INTERPOLATION 1 END NAVIER STOKES END NUMERICAL TREATMENT OUTPUT FILE_NAME global ou
16. FREE SURFACE CONDITIONS END BOUNDARY CONDITIONS 6 1 Initial conditions The block defines the initial conditions for transient analysis INITIAL CONDITIONS VX V VY V VZ V 70 CURE ao END INITIAL CONDITIONS VX initial velocity in x direction V VY initial velocity in y direction V VZ initial velocity in z direction V For 2D problems do not include this term TEMPERATURE initial temperature If HEAT_EQUATION is turned OFF do not include this term CURE initial degree of cure If SPECIES_EQUATION is turned OFF do not include this term NOTE for pure heat transfer problems the INITIAL_CONDITIONS can be used to give the velocity field 6 2 Dirichlet condition The block defines the Dirichlet boundary conditions Note for NS equations Brinkman equations Dirichlet condition specifies the velocity on the boundary while for Darcy equation Dirichlet condition specifies the pressure value on the boundary DIRICHLET_CONDITIONS in IDvx IDvy IDvz IDT IDcure Vy Vz a NS or Brinkman IDP IDT IDcure Pa T a Darcy equation END_DIRICHLET_CONDITIONS in node number Copyright by UWM Research Foundation 2010 IDvx code for boundary condition of x velocity IDvx is either 0 or 1 0 means x velocity is free 1 means the x velocity is prescribed IDvy code for boundary condition of y velocity The possibilities of IDvy are same as IDvx I
17. GPR k kok K K K K K PORE FLOW PERMEABILITY PREDICTION PROBLEM PHYSICAL PROBLEM NAVIER_STOKES_EQUATIONS ON DOMAIN NUM 1 Domain is Stokes equation PRESSURE_ELIMINATION ON PENALTY 1D 8 TRANSIENT OFF A 4 CONVECTION OFF a Convection is turned off so the inertial term is not considered STABLIZATION OFF Convection is turned off hence there is no need to stabilize BODY FORCES OFF oscillatory solution caused by the convection term END NAVIER STOKES EOUATIONS Copyright by UWM Research Foundation 2010 28 BRINKMAN EQUATIONS ON DOMAIN NUM 2 gt Domain 2 is Brinkman equation END_BRINKMAN_EQUATION END_PHYSICAL_PROBLEM M ee k se
18. 60000 ne 65000 70000 120 75000 0 02 100 80000 an 85000 90000 20 0 100 200 300 400 Front Arrival Time a b c Figure 2 a the flow front evolution b the pressure distribution at the end of filling c flow front position vs time Copyright by UWM Research Foundation 2010 27 10 2 Permeability prediction A unit cell model of bi axial fabrics is constructed to predict the permeability The problem is steady state The longitudinal permeability K and transverse permeability K of fiber tow are assumed to be 5e 10 m and le 10 m respectively The liguid viscosity is 1 Pa s The flow in inter tow gap region is modeled using Stokes equations while the flow in the intra tow region is modeled using Brinkman eguation Therefore there are two different computational domain one for Stokes eguation the other one for Brinkman eguation and three sets of properties one for gap region one for tow parallel to z direction one for tow parallel to x direction The FE model of the unit cell is shown in Figure 3 It has 17572 nodes and 15320 hexahedral elements The pressure boundary conditions of 100 Pa and 0 Pa are applied on the opposite surfaces of the unit cell along the flow direction to simulate the z direction flow Symmetric boundary conditions are imposed on the remaining surfaces of the unit cell a b Figure 3 a FE mesh of unit cell b FE mesh of fiber tow region The command file is listed as
19. CONVECTION ON SHELL MODEL OFF STABLIZATION SUPG END HEAT EOUATION Defines the heat transfer eguation END PHYSICAL PROBLEM M EF k k k k ok o PROPERTIES NUM_OF_SETS 1 SET 1 DENSITY 10 Copyright by UWM Research Foundation 2010 34 VISCOSITY 1 CONDUCTIVITY CX 1 CY 1 CZ 1 ROTATION 0 SPECIFIC HEAT 1000 HEAT GENERATION 0 THICKNESS 1d 2 ENDSET 1 END PROPERTIES 8 ok oko MESH_DATA DIMENSIONS NUMBER_NODES 451 NUMBER_ELEMENTS 400 SPACE 2D ELEMENT_TYPE QUAD 4 AXISYMMETRY NO END_DIMENSIONS GEOMETRY INCLUDE C hua tan code validation example plateflow2D qu END_GEOMETRY
20. conditions aenn LEE SER one Oe na 15 6 2 Dirichllet COndIBoD e gt eae 15 6 3 Neurnanmeonditions oae ee oo 16 64 Bree Surface RA F nas 17 Vo Numerical Treatment oc Eo uci edat den OE 18 7 1 Numerical treatment for NS and Brinkman equations 19 RA O srt a nta PI RENE 20 D IPICDIOCESSIE mou Qut Mb Am MSc E ooo OD C Sro sided de 21 10 Numerical examples ste tastes a v 25 10 1 Wicking Flow through swelling 25 10 2 Permeability predist OE PE C C pr te Gen Tn 28 J03 Blow aE CLO uses ra 31 10 4 Heat flow between two parallel plates oae aient trt te Ip ett er P rrr Ritt 34 10 5 Mold filling simulation netter eere nene ved quay sans e eade edo neg teehee 34 10 6 Fast LCM simulation of unsaturated flow in duel scale 45 10 7 Flow Modeling in a Draper Papel ss acit eode x 48 Copyright by UWM Research Foundation 2010 2 1 Introduction PORE FLOW is a comprehensive computational fluid dynamics tool that solves flow infiltration wetting problems encountered in
21. 3 Flow elbow pipe The flow through an elbow pipe is analyzed in this study The problem is three dimensional Navier Stokes flow The liquid density and viscosity are 1000 kg m and 0 3 s respectively The FE model is shown in figure 5 There are 2223 nodes and 1824 hexahedral elements in the model The pressure boundary conditions of 1000 and 0 Pa are applied on the inlet and outlet surfaces respectively The other surfaces are non slip boundary condition Flow inlet A E Figure 5 FE mesh of elbow pipe X Flow outlet command file is listed as k k k k k PORE FLOW ELBOW 3D PROBLEM A I ll lo PHYSICAL PROBLEM NAVIER STOKES EOUATIONS ON PRESSURE ELIMINATION on PENALTY 1D 8 TRANSIENT OFF CONVECTION ON STABLIZATION SUPG SUPG is used to stabilize the numerical solution BODY_FORCES OFF END_NAVIER_STOKES_EQUATIONS END_PHYSICAL_PROBLEM
22. problem is very large the in core memory requirement may exceed the capacity of the computer Turning on OUT OF CORE can use hard drive to store the matrix 7 1 Numerical treatment for NS and Brinkman equations This block determines the parameters just for NS Brinkman equation If NAVIER STOKES EQUATIONS or BRINKMAN EQUATIONS is turned ON the block must be included Otherwise it is not necessary to include the whole block NAVIER STOKES BRINKMAN BUBBLE FORMULATION ON OFF PRESSURE INTERPOLATION n END NAVIER STOKES BUBBLE FORMULATION when tetrahedral elements with 4 nodes are used to solve NS and Brinkman equation BUBBLE FORMULATION should be turned ON For other types of elements it should be turn OFF PRESSURE INTERPOLATION This defines the interpolation used for the pressure An integer must be provided Now it can be only 1 Copyright by UWM Research Foundation 2010 19 8 PORE FLOW uses TECPLOT as post processor OUTPUT FILE_NAME FREQUENCY STEP n MUMPS_INFORMATION ON OFF END_OUTPUT FILE_NAME file name for output file FREQUENCY for transient analysis or filling analysis this parameter determines how often the solution is written into the solution file MUMPS INFORMATION PORE FLOW uses MUMPS to solve the algebraic equation When MUMPS INFORMATION is turn ON the solution information coming from MUMPS will be printed on the screen Otherwise no solution information
23. 3 Boundary and Grid Copyright by UWM Research Foundation 2010 40 0 15 0 15 Pressure Pressure 18000 18000 16000 16000 14000 14000 0 1 12000 0 1 12000 10000 10000 8000 8000 6000 6000 4000 4000 2000 2000 0 05 0 05 0 0 0 2 0 2 0 15 0 15 Pressure Pressure 18000 18000 16000 16000 14000 14000 0 1 12000 0 1 12000 10000 10000 8000 8000 6000 6000 4000 4000 2000 2000 0 05 0 05 0 0 0 2 0 2 0 15 0 15 Pressure Pressure 18000 18000 16000 16000 14000 14000 0 1 12000 0 1 12000 10000 10000 8000 8000 6000 6000 4000 4000 2000 2000 0 05 0 05 9 0 0 2 9 0 2 Input Rectangular Geometry Results Fig 15 Boundary and Grid Copyright by UWM Research Foundation 2010 Output Fig 14 Distribution of Velocity and Pressure in a porous media 41 2000 6000 10000 14000 18000 Pressure 2000 6000 10000 14000 18000 Pressur 2000 6000 10000 14000 18000 Pressure 2000 6000 10000 14000 18000 Pressure dino yndu 2000 6000 10000 14000 18000 Pressure 2000 6000 10000 14000 18000 Pressure Fig 16 Distributio
24. 57 t 1 673195381 t 23 62425661 The viscosity and density of the liquid are u 0 000911 Pa s and 1000 kg m Porosity o is 0 5 In this case 2D analysis is carried out Quadrilateral elements are used to descritize the computational domain Total numbers of nodes and elements are 1111 and 1000 respectively The mesh model is shown in figure 1 0 1 Outlet edge 0 08 0 06 0 04 0 02 k Inlet edge 0 02 0 0 02 0 04 X Figure 1 FE mesh model command file is listed here M k PORE FLOW 2D swelling media flow problem k k se se k
25. 9 rotation angle of principle direction to x y z coordinates SPECIFIC_HEAT defines the specific heat c Similar to Density specific heat can be defined as either a constant or a function HEAT_GENERATION defines the heat generation Similar to Density heat generation can be defined as either a constant or a function REACTION_RATE defines the reaction rate Similar to Density reaction rate can be defined as either a constant or a function THICKNESS defines the thickness of 2D mesh SINK_FUNCTION This determines parameters for sink function dS ow A Pap dt 1 2 B a Copyright by UWM Research Foundation 2010 12 5 Mesh data This section contains the definition of the computational domain where the problem has to be solved and its discretization MESH_DATA DIMENSIONS GEOMETRY ELEMENTS COORDINATES END_MESH_DATA 5 1 Dimensions This sub block contains the following commands DIMENSIONS NUMBER_NODES ng NUMBER ELEMENTS ne SPACE 2D 3D ELEMENT TYPE TRIA 3 QUAD 4 HEXA 8 TETR 4 AXISYMMETRY YES NO END DIMENSIONS NUMBER NODES total number of nodes in FE mesh NUMBER ELEMENTS total number of elements in FE mesh SPACE defines space dimensions ELEMENT TYPE defines the element type ELEMENT TYPE has the following value depending on the mesh type Value Meaning TRIA 3 Triangular element with 3 nodes QUAD 4 Quadrilateral element with 4 node
26. Dvz code for boundary condition of z velocity The possibilities of IDvz are same as Dvx For 2D problem do not include this term IDP code for boundary condition of pressure for Darcy equation The possibilities of IDP are same as IDvx IDT code for boundary condition of temperature The possibilities of IDT are same as Dvx If HEAT_EQUATION is turned OFF do not include this term IDcure code for boundary condition of cure The possibilities of IDcure are same as IDvx If SPECIES_EQUATION is turned OFF do not include this term x velocity of node in Vy y velocity of node in V z velocity of node in For 2D problem do not include this term Pu pressure of node in T temperature of node in If HEAT EQUATION is turned OFF do not include this term a degree of cure of node in If SPECIES EQUATION is turned OFF do not include this term 6 3 Neumann conditions The block defines the Neumann boundary conditions Note for NS equations Brinkman equations Neumann condition specifies the pressure on the boundary while for Darcy equation Neumann condition specifies flow rate on the boundary NEUMANN CONDITIONS IDP IDFlux Pj Flux for NS or Brinkman in IDF IDFlux Q Flux for Darcy equation END NEUMANN CONDITIONS in node number IDP code for boundary condition of pressure IDP is either 0 or 1 0 means pressure is free 1 means that pressure is prescribed IDF code for bo
27. LOW 2D mold filling flow problem S oko o o o PHYSICAL PROBLEM DARCY_EQUATION ON BODY FORCES ON GX 0 GY 0 GZ 0 END_DARCY FREE_SURFACE ON WICKING OFF DUAL_SCALE OFF END_FREE_SURFACE END PHYSICAL PROBLEM Copyright by UWM Research Foundation 2010 37 M ak ok PROPERTIES NUM_OF_SETS 1 SET 1 DENSITY 860 VISCOSITY 244 POROSITY 5 PERMEABILITY 1 7 KY le 7 KZ 1e 7 ROTATION 0 THICKNESS 1 valid for 2D filling analysis ENDSET 1 END_PROPERTIES sje
28. NEUMANN Or FREE SURFACE CONDITIONS in ID END FREE SURFACE CONDITIONS The details of above characters are explained in sections 6 2 6 3 and 6 4 If the mesh was made in ANSYS then above described node numbers can be obtained through following command 1 Selecting the boundary of the object In a 2D mesh one can use following commands to select a boundary line Select gt gt Entities gt gt Lines gt gt By Num Pick gt gt click on boundary line s gt gt OK 2 Select the nodes connected to previous selected boundary Select gt gt Entities gt gt Nodes gt gt Attached to gt gt Lines all gt gt OK 3 Output the node information List gt gt Nodes gt gt OK Copyright by UWM Research Foundation 2010 23 Following is sample boundary condition for mold filling simulation under constant pressure injection DIRICHLET_CONDITIONS 1 1 20000 42 1 20000 62 1 20000 63 1 20000 77 1 20000 78 1 20000 79 1 20000 80 1 20000 END_DIRICHLET_CONDITIONS FREE_SURFACE_CONDITIONS 10 42 0 62 0 63 0 37 1 38 1 39 1 40 1 41 1 END_FREE_SURFACE_CONDITIONS Copyright by UWM Research Foundation 2010 24 10 Numerical examples 10 1 Wicking Flow through swelling medium The problem is a wicking flow through a swelling medium involving a moving boundary The gravity effect is taken into consideration The permeability is changing with time as follows P 96271 21679 Pa capillary pressure 1E14 0 045085523
29. OROSITY PERMEABILITY CONDUCTIVITY SPECIFIC_HEAT HEAT_GENERATION REACTION_RATE THICKNESS SINK_FUNCTION ENDSET n END_PROPERTIES NUM OF SETS defines the total number of property sets For example if there are two different permeabilities in a porous medium then n 2 SET determines n sets of properties DENSITY defines the density p If density is a constant then a float type number pis followed by DENSITY e g DENSITY 1000 0 Density can be defined as a function of variables for example DENSITY VARIABLE TIME FILLTIME TEMP CURE X Y Z FUN expression of the function VISCOSITY defines the viscosity u Similar to Density viscosity can be defined as either a constant or a function POROSITY defines the porosity 0 Similar to Density porosity can be defined as either a constant or a function PERMEABILITY defines the permeability tensor If permeability tensor is a constant KX k x component of permeability tensor KY k y component of permeability tensor KZ k z component of permeability tensor ROTATION 9 rotation angle of principle direction to x y Z coordinates If permeability is homogenous it can be defined as a function similar to density Copyright by UWM Research Foundation 2010 11 CONDUCTIVITY defines the thermal conductivity tensor If conductivity tensor is constant CX k x component of conductivity tensor CY k y component of conductivity tensor CZ k z component of conductivity tensor ROTATION
30. RESEARCH FOUNDATION PORE FLOW User s Manual version 1 2 Hua Tan Reza Masoodi and Krishna M Pillai January 2011 Laboratory for Flow and Transport Studies in Porous Media University of Wisconsin Milwaukee Laboratory for Flow and Transport Studies in Porous Media 99 at Copyright by UWM Research Foundation 2010 TABLE OF CONTENTS 14 reos 3 Ld PBeatures dnd Benefits ep eei te reti 3 2 Overview or FORETEOWOGMATITE Neos ean eve 95277555858 4 2 1 General ir aka ea satu pa Ee EEE ULL EAS Ee EL UG EES 4 212 SUUCHHES ot command ooo dere Het a e i ET EIU DS 4 3 Physical problem tet Oh eaa I P EU Om EN US PER 6 3 1 6 3 22 BERKA guations TUN E 7 3 3 Irsa m ii 8 d Heat eqUAtlON a o eed e E eiit br Oe 8 3 5 SPECIES egualioli oo As Da RE Ma MM c M ME LM AE M 9 26 Bree sutace problem os ne tere da ee Pre Pr Ive e EI Pr l en 10 T Physical propere eto 11 5 1 es 13 5 2 fen RR AE ARE VEEN R 13 6 Boundary COHIPODS Sor eo I A E ooo 15 6 1 Initial
31. S EQUATION has two options ON The heat equation is solved OFF The heat equation is not solved Copyright by UWM Research Foundation 2010 9 3 6 Free surface flow problem PORE FLOW uses control volume method to track the flow front The block of commands describing the free surface flow problem to be solved is the following FREE_SURFACE ON OFF WICKING ON CAPILLARY_PRESSURE p OFF DUAL_SCALE ON OFF END_FREE_SURFACE The header of the block FREE SURFACE has two options ON The free surface is considered OFF The free surface is not considered WICKING This command determines the wicking flow ON the wicking flow is considered CAPILLARY PRESSURE must be provided pa should be a negative number OFF it s not wicking flow DUAL_SCALE The command determines if dual scale flow is considered ON dual scale flow OFF single scale flow SINK_MODEL This command determines the algorithm for solving flow through the dual scale fibrous media When DUAL_SCALE is turned ON This card must be provided MULTISCALE the algorithm needs two meshes one is global mesh and the other one is unit cell mesh LUMPED the algorithm needs only one mesh The parameters for sink function must be defined under PHYSICAL PROPERTIES Copyright by UWM Research Foundation 2010 10 4 Physical properties This block of commands provides the physical properties used in simulation PROPERTIES NUM_OF_SETS n SET n DENSITY VISCOSITY P
32. Y STEP 8 END_OUTPUT Sp k ake ake ake Copyright by UWM Research Foundation 2010 32 Flow inlet Velocity Pressure Pressure 1 8 1 6 1000 1 4 900 12 800 1 700 0 8 600 06 500 0 4 400 Z 0 2 300 200 Flow outlet a b c Figure 6 a pressure distribution of the elbow b velocity distribution and vector on the middle plane of the elbow c pressure distribution on the middle plane Copyright by UWM Research Foundation 2010 33 10 4 Heat flow between two parallel plates The problem is a cold liquid of 20 C flowing between two infinitely large plates with a higher constant temperature of 75 C The liquid density viscosity conductivity and specific heat are 10 kg m 1 Pas 1 W m K and 1000 J kg K respectively The inlet flow velocity is 1 m s Since the domain is symmetrical only half of the domain is discretized using FE mesh as shown in figure 7 For this problem the NS equations are first solved to obtain the ve
33. as woven stitched mats by first solving at the microscale Copyright by UWM Research Foundation 2010 3 1 Overview of PORE FLOW data file 21 General remarks The main purpose of this document is to explain how to create the command file for PORE FLOW The command file consists of several command blocks A template for all of blocks is presented in the corresponding section The command file has the following properties gt Lines starting with the symbol are skipped Symbols and are skipped Symbol 1 or can be used to give a comment a command line Only the first EIGHT alphabetic characters of commands are read It is not case sensitive Blanks are not considered V V V V ON v The commands written between brackets are optional 2 2 Structure of the command file The command file consists of several groups blocks of commands of them have a starting word that identifies the group and must finish with the same word following the word END There are also several sub groups of commands that must be provided following the same syntax The order of the commands within the groups is irrelevant The complete list of blocks and sub blocks of command file is listed as following G oo sk
34. clear fluid problem DOMAIN NUM n must be provided n is an integer assigned to the finite elements which lie in the porous domain Copyright by UWM Research Foundation 2010 7 PRESSURE_ELIMINATION This command determines if penalty method is used in solution of NS equations or not ON Penalty method is used and PENALTY lt must be provide must be a very small number e g le 8 OFF Penalty method is not used BODY_FORCES the command defines body force ON body force is considered GX x component of g GY y component of g GZ z component of g OFF no body force is considered 3 3 Darcy equation The block of commands describing the Darcy equation to be solved is the following DARCY_EQUATION ON OFF BODY FORCES ON g GY g GZ g OFF END_DARCY_EQUATION The header of the block DARCY EOUATION has two options ON The Darcy equation is solved OFF The Darcy equation is not solved BODY_FORCES the command defines body force ON body force is considered GX x component of g GY y component of g GZ z component of g OFF no body force is considered 3 4 Heat equation The block of commands describing the heat equation to be solved is the following HEAT_EQUATION ON OFF TRANSIENT ON OFF CONVECTION ON OFF SHELL MODEL ON WALL TEMPERATURE Tj OFF STABLIZATION SUPG FCT OFF END_HEAT_EQUATION Copyright by UWM Research Foundation 2010 8 The header of the block HEAT EOUATION has two
35. etermines if the transient effect is considered or not ON Transient term in NS equations is taken into account OFF No transient term considered CONVECTION This command determines if the inertia term is considered or not ON Inertia term in NS equations is taken into account OFF No Inertia term considered It s in fact Stokes equation STABLIZATION This command determines stabilized technique When the convection is strong element Reynolds number may be too large to cause solution oscillation The stabilized technique can stabilize the solution without refining the mesh When CONVECTION is turned it is suggested that the stabilized technique be used SUPG Streamline Upwinding Petrov Galerkin method OFF No stabilized technique is used BODY_FORCES the command defines body force ON body force is considered GX x component of g GY y component of g GZ z component of g OFF no body force is considered 3 2 Brinkman equations All the parameters for Brinkman equations are defined in the following block BRINKMAN EQUATIONS ON OFF DOMAIN NUM n PRESSURE ELIMINATION ON PENALTYze OFF BODY FORCES ON GX gx GY gy GZ 9 OFF END BRINKMAN EQUATION The header of the block BRINKMAN EQUATIONS has two options ON The Brinkman equations are solved OFF The Brinkman equations are not solved DOMAIN is an optional parameter When Brinkman equations combined with NS equations are solved simultaneously for porous
36. industrial porous media The finite element control volume method is implemented in the code to simulate flow behind a moving boundary The algorithm is efficient and robust for solving the moving boundary problems in complex domain geometries The geometry may be 2D or 3D and the mesh may be structured or unstructured to give maximum flexibility to the user The porous medium flow in the code is governed by either Darcy s law or Brinkman equation depending on the user s choice PORE FLOW also can solve the fluid flow problems governed by Stokes or Navier Stokes equations The heat flow as well as certain types of reactive flows can also be simulated by the code 1 1 Features and Benefits gt Easy implementation Can be used with current software ANSYS preprocessing and Tecplot post processing Extensive validation Modeling tools have been extensively validated using controlled mold filling experiments Less modeling error 30 better agreement compared to current alternatives Cheaper Minimizes cost through optimization of mold design lower design costs lower prototyping costs and lessens need for reworking of molds More accurate Better prediction of pressure and temperature in molds Better prediction Flux corrected transport for filling simulation removes localized wiggle often seen in solutions and better predictions for permeability More versatile More precise estimation with different mat types such
37. is printed Copyright by UWM Research Foundation 2010 20 9 Preprocessing In order to run this software one needs three following files 1 Command file 2 Mesh file 3 Boundary condition file The command file was discussed in the previous sections We discuss how to make the mesh and boundary condition files in this section 9 1 Mesh file Mesh file has two parts the first part is in the following format ELEMENTS element number Domain ID Property ID local node 1 local node 8 END_ELEMENTS The first three columns are the element domain ID and property ID The next columns are nodes associated with the element in the first column Therefore we have 4 nodes for 2D and 8 nodes for 3D simulation The second part of mesh file is coordinate which gives the coordinate information for nodes Here is the format COORDINATES node number x coordinate y coordinate z coordinate END_COORDINATES In case of working in 2D then one of these columns is zero or there are just two columns In case there is one column the other column is considered to be zero If the mesh was made in ANSYS then above data can be achieved through following command Preprocessor gt gt Archive Model gt gt Write gt gt Data to Archive gt gt pick GEOM then in Archive file give a name for output file Copyright by UWM Research Foundation 2010 21 We need to delete some rows or columns from GEOM file For
38. locity field then the heat transfer equation is solved to obtain the temperature field Wall Temperature 75 20 7 Hawai eu Ce EL pf IL I 2217 Symmetry Figure 7 FE mesh The command file is listed as oko o kk I A PORE FLOW 2D heat transfer problem PHYSICAL PROBLEM NAVIER_STOKES_EQUATIONS ON PRESSURE_ELIMINATION ON PENALTY 1D 8 TRANSIENT OFF CONVECTION ON Defines the NS eguation STABLIZATION SUPG BODY FORCES OFF END NAVIER STOKES EOUATIONS HEAT EOUATION ON TRANSIENT OFF
39. n of Velocity and Pressure in a porous media 3 D Square Geometry Results pressure P 20000 itia In Geometry Grid and Boundary Conditions gt 71771 SOD ANY CLIX YAAK KKK 71717176117 SINAN ANNA 1711111178 7771711119 WAY O CODD 0000 0 0 08 778 aN x 5 a 71111111111 AMO AMAN NNNM M S 1111199919 714 o MN MRA rr VVN A ARAD RRR QUO 0200 17111111111 ARBOR RARO KANNUR RAO RRA 441 ARON VVN ARIANA NNN NANOS CORSO QOO ASSAM QOO AAA NAAN OOO KAKA AAA RRA SPUN NN SN OOOO OOOO NNN V VVN YER ROO OOOO O00 O0 CAN V 7717 A un 1911197177 19 91 9777 ROA 79111977777 ea CROOK 5 97777 S PRO VODY 5 00004 0 CANNA V 777 16111111771 A 0000000 CANADY V 0000946 CANA V A 4 CANAUX V
40. options ON The heat equation is solved OFF The heat equation is not solved TRANSIENT This command determines if the transient effect is considered or not ON Transient term is taken into account OFF No transient term considered CONVECTION This command determines if the convective heat transfer is considered or not ON heat convection is taken into account OFF No convective term considered It s in fact pure heat conduction equation SHELL_MODEL determines if the thin wall model used in 3D heat transfer problem ON thin wall model is considered In this case only heat conduction in thickness direction is considered along with heat transfer in plane WALL_TEMPERATURE represent wall temperature Twan OFF no thin wall model is used STABLIZATION This command determines stabilized techniques When the heat convection is strong element Peclet number may be too large to cause solution oscillation so called convection dominated convection diffusion equation The stabilized techniques can stabilize the solution without refining the mesh When CONVECTION is turned it is suggested that the stabilized technique be used SUPG Streamline Upwinding Petrov Galerkin method FCT Flux Corrected Transport method OFF No stabilized technique is used 3 5 Species equation The block of commands describing the species equation to be solved is the following SPECIES EQUATION ON OFF END SPECIES EQUATION The header of the block SPECIE
41. ry in this case Copyright by UWM Research Foundation 2010 29 NAVIER_STOKES_BRINKMAN BUBBLE_FORMULATION OFF ON PRESSURE_INTERPOLATION 1 END_NAVIER_STOKES END_NUMERICAL_TREATMENT ake ake ak ok OUTPUT FILE_NAME global out Since it is a steady state problem FREQUENCY STEP 8 FREQUENCY does not work in this MUMPS INFORMATION OFF END_OUTPUT Mb kok ok ok Pressure Y x sb 2 Copyright by UWM Research Foundation 2010 b Figure 4 a pressure distribution across the unit cell b z velocity and velocity vector Velocity z 0 18 0 17 0 16 0 15 0 14 0 13 30 10
42. s HEXA 8 Hexahedral element with 8 nodes TETR 4 Tetrahedral element with 4 nodes AXISYMMETRY YES gt axi symmetrical problem NO This option is necessary for 2D problems Note for axi symmetrical problem y direction is always viewed as axis of symmetry 5 0 Geometry This block of commands defines the FE mesh Copyright by UWM Research Foundation 2010 13 ELEMENTS ie IDdomain IDset node node n END ELEMENTS COORDINATES in LOCX LOCY LOCZ END COORDINATES END GEOMETRY ELEMENTS defines the connectivity of each element element number IDdomain domain number corresponding to DOMAIN in Section 3 1 and 3 2 IDset property set number corresponding to SET n in Section 4 node node n list of nodes belonging to element ie COORDINATES defines the coordinates of nodes in node number LOCX x coordinate of node in LOCY y coordinate of node in LOCZ z coordinate of node in NOTE To make the command file compact and neat the sub blocks of ELEMENTS and COORDINATES can be included in another file The path and file name need to be provided in GEOMETRY e g GEOMETRY INCLUDE C XXX XX END_GEOMETRY Copyright by UWM Research Foundation 2010 14 6 Boundary conditions This block contains the definition of the boundary conditions for the problem to be solved BOUNDARY_CONDITIONS INITIAL_CONDITIONS DIRICHLET_CONDITIONS NEUMANN_CONDITIONS
43. t FREQUENCY STEP 5 MUMPS_INFORMATION OFF END_OUTPUT Copyright by UWM Research Foundation 2010 35 0 2 Velocity x 0 10 20 30 40 50 60 70 80 9 1 1 1 1 2 1 3 1 4 Temperature 25 30 35 40 45 50 55 60 65 70 a b Figure 8 a velocity distribution b temperature distribution Copyright by UWM Research Foundation 2010 36 10 5 Mold filling simulation The problem is a mold of 7 x7 0 1778x0 1778m mold that is filling with a resin or a test liquid The porosity is 0 5 and the density and viscosity of liquid are 860 kg m and 0 244 Pa s respectively The permeability of fibermats is 1e 7 m and the injection pressure is 20 kPa We want to study the flow of resin in such a simple 2 d mold The domain is discretized using FE mesh as shown in Figure 9 For this problem the Darcy equation and continuity equations are solved to find the pressure distribution Then the liquid front location and velocity will be found using Darcy s law flow flow Figure 9 FE mesh The command file is listed as k k PORE F
44. th of END_GEOMETRY UNITCELL HEX END_MESH_DATA k k BOUNDARY_CONDITIONS INITIAL_CONDITIONS VX 0 VY 0 VZ 0 It s not work in this case END_INITIAL INCLUDE C hua tan incompressiveflow INUNITCELL INI BC data is included in UNITCELL INI When running the example note the path of UNITCELL INI END BOUNDARY CONDITIONS oko o kk NUMERICAL TREATMENT TIME DATA INITIAL 0 0 FINAL 100 TIME STEP SIZE 1 d 1 0 5 INTEGRATION P OINTS 8 Eight integration points used ITERATION NEWTON Us ERROR are not necessa
45. their sub blocks are PHYSICAL_PROBLEM NAVIER STOKES EQUATIONS BRINKMAN_EQUATIONS DARCY_EQUATION HEAT_EQUATION SPECIES_EQUATION FREE SURFACE END PHYSICAL PROBLEM 3 1 Navier Stokes equations All the parameters for NS equations are defined in the following block NAVIER STOKES EQUATIONS ON OFF DOMAIN NUM n PRESSURE ELIMINATION ON PENALTY OFF TRANSIENT ON OFF CONVECTION ON OFF STABLIZATION SUPG OFF BODY FORCES ON gx GY gy GZ g OFF END NAVIER STOKES EQUATIONS The header of the block NAVIER STOKES EQUATIONS has two options ON The NS equations are solved OFF The NS equations are not solved DOMAIN is an optional parameter When NS equations combined with Brinkman equations are solved simultaneously for porous clear fluid problem DOMAIN NUM n must be provided n is an integer assigned to the finite elements which lie in the clear fluid domain PRESSURE ELIMINATION This command determines if penalty method is used solution of NS equations or not ON Penalty method is used and PENALTY c must be provide must be a very small number e g 1e 8 OFF Penalty method is not used In penalty method the pressure DOFs do not appear in the final discrete algebraic equations The continuity equation is incorporated into the momentum equations through a penalty term Details can be found in FIDAP theory manual Copyright by UWM Research Foundation 2010 6 TRANSIENT This command d
46. this purpose UltraEdit is a powerful editing software Following is a sample 2D mesh file ELEMENTS element number Domain ID Property ID local node 1 local node 4 111 1 3 81 80 211 3 4 100 81 211 4 5 119 100 411 5 6 138 119 5 11 6 7 157 138 611 7 8 176 157 7141 8 9 195 176 8 11 9 10 214 195 911 10 11 233 214 10 1 1 11 12 252 233 393 1 1 308 327 49 50 394 1 1 327 346 48 49 395 1 1 346 365 47 48 396 1 1 365 384 46 47 397 1 1 384 403 45 46 398 1 1 403 422 44 45 399 1 1 422 441 43 44 400 1 1 441 41 22 43 END_ELEMENTS COORDINATES node number x coordinate y coordinate z coordinate 0 00000000 0 177800000 8 890000000E 03 1 778000000E 02 2 667000000E 02 3 556000000E 02 4 445000000E 02 5 334000000E 02 6 223000000E 02 10 7 112000000E 02 NO VODU 435 0 168910000 0 115570000 436 0 168910000 0 124460000 Copyright by UWM Research Foundation 2010 22 437 0 168910000 0 133350000 438 0 168910000 0 142240000 439 0 168910000 0 151130000 440 0 168910000 0 160020000 441 0 168910000 0 168910000 END COORDINATES 9 2 Boundary condition file Boundary condition has two or three of following parts DIRICHLET CONDITIONS in IDvx IDvy IDvz IDT IDcure Vy Vz a NS or Brinkman IDP IDT IDcure Pa a Darcy equation END DIRICHLET CONDITIONS Or NUMANN CONDITIONS in IDP IDFlux Pa Flux for NS or Brinkman in IDF IDFlux Q Flux for Darcy equation END
47. undary condition of flow rate IDF is either 0 or 1 0 means pressure is free 1 means that flow rate is prescribed Copyright by UWM Research Foundation 2010 16 pressure applied on node in Q flow rate applied on node in Flux heat flow applied on node in If HEAT_EQUATION is turned OFF do not include this term 6 4 Free Surface Conditions This block defines the inlet and outlet boundaries The block is necessary only when FREE SURFACE is turned FREE_SURFACE_CONDITIONS in ID END_FREE_SURFACE_CONDITIONS in node number ID code for inlet or outlet ID is either 0 or 1 0 means node in belongs to inlet 1 means node in belongs to outlet NOTE To make the command file compact and neat the sub blocks of DIRICHLET_CONDITIONS NEUMANN CONDITIONS and FREE SURFACE CONDITIONS can be included in a file The path and file name need to be provided in BOUNDARY_CONDITIONS e g BOUNDARY_CONDITIONS INITIAL_CONDITIONS VX 0 VY 0 VZ 0 END_INITIAL_CONDITIONS INCLUDE CVAN XX END_BOUNDARY_CONDITIONS Copyright by UWM Research Foundation 2010 17 7 Numerical Treatment The block determines the parameters in numerical solution NUMERICAL_TREATMENT TIME DATA INTEGRATION POINTS ITERATION ERROR OUT OF CORE NAVIER STOKES BRINKMAN BUBBLE FORMULATION PRESSURE INTERPOLATION END NAVIER STOKES END NUMERICAL TREATMENT TIME DATA determines the time integration algorithm for transient analysis
48. which has following keywords INITIAL TIME initial time FINAL TIME end of time TIME STEP SIZE time increment in each step an adjustable parameter varying between 0 and 1 can be 0 forward 0 5 Crank Nicolson 1 backward Note all the keywords including TIME DATA should be in the same line for example TIME DATA INITIAL TIME 0 0 FINAL 100 TIME STEP SIZE 1 e 1 0 5 INTEGRATION POINTS the number of integral points for each element It is an integer number which is determined by the element type of Section 5 1 Element type Integration points TRIA 3 4 QUAD 4 4or9 HEXA 8 8 or 27 TETR 4 1 4 5 10 or 11 ITERATION iteration method It can be following value PICARD fixed point iteration method NEWTON Newton iteration method Copyright by UWM Research Foundation 2010 18 PICNEW n the combination of Picard and Newton method Here n means the number of iteration using Picard method In this method the first n steps use Picard method followed by Newton method When PICNEW is used n must be provided ERROR criterion for iteration method When the difference between the solutions of successive iterations is less than the number the convergence is reached For example lu u u 1 Ee where u is solution subscript i is iteration number is error of iteration OUT OF CORE ON or OFF When the

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