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A USER GUIDE FOR TRIVAC VERSION4 A. Hébert

1. LAMBDA lambda i i 1 ndg CEID chid i i 1 ndg j 1 ngrp continued on next page IGE 293 39 Structure inikin data continued from last page NORM fnorm MAX POWER INI power 7 where EDIT iprint NGRP ngrp NDEL ndg BETA beta LAMBDA lambda CHID chid NORM fnorm MAX POWER INI power keyword used to set iprint index integer index used to control the printing in module INIKIN 0 for no print 1 for minimum printing default value larger values of iprint will produce increasing amounts of output keyword used to set the ngrp number By default this information is recovered from the solution object FLUX integer total number of energy groups keyword used to set the ndg number integer total number of the delayed neutron groups keyword used to indicate the reading of beta values from the input file If these values are not provided they should be recorded in the MACROLIB data structure real array containing the delayed neutron fractions for each delayed group keyword used to indicate the reading of lambda values from the input file If these values are not provided they should be recorded in the MACROLIB data structure real array containing the precursors decay constants for each delayed group keyword used to indicate the reading of chid values from the input file If these values are not provided they should be recorded in the MACROLIB data
2. 000E 02 000E 00 000E 00 10 0 2 500E 00 000E 02 000E 00 000E 00 10 0 2 500E 00 000E 02 000E 00 000E 00 10 02 o o OPO Bak Bee E CORR RRR o o ooo ai FP FS BS o 0000 Ab dA A w 5 NS 4 4 4 4 4 4 ASAS DOM A AR GA GA o 0 00 OS 4 0000E 01 8 0000E 02 1 3500E 01 1 3500E 01 2 0 0 0 2E 01 4 0000E 01 8 5000E 02 1 3500E 01 1 3500E 01 2 0 0 0 2E 01 4 00000E 01 1 30000E 01 1 35000E 01 1 35000E 01 2 0 0 0 2E 01 50 IGE 293 DIFF 2 000E 00 3 0000E 01 TOTAL 4 000E 02 1 0000E 02 SCAT 110 0 2 2 0 0 0 4E 01 MIX 5 DIFF 000E 00 3 0000E 01 TOTAL 4 000E 02 5 5000E 02 SCAT 110 0 2 2 0 0 0 4E 01 N TRACK TRIVAT IAEA3D TITLE TEST IAEA 3D EDIT 5 MAXR 405 DUAL 3 1 SYSTEM TRIVAA MACRO TRACK EDIT 5 FLUX FLUD SYSTEM EDIT 2 EDIT OUT FLUX EDIT 2 INTG PLANE NB 1 0000000 0 o 0000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 PLANE NB 2 x 23 45 67 8 0 9 10 11 12 13 14 15 O 16 17 18 19 20 21 0 22 23 24 25 0 0 26 27 28 0 0 29 0 0 0 0 0 0 0 0 0 PLANE NB 3 30 31 32 33 34 35 36 37 0 38 39 40 41 42 43 44 O 45 46 47 48 49 50 O 51 52 53 54 0 0 55 56 57 0 0 58 0 0 0 0 0 o 0 0 0 PLANE NB 4 00000000 0 0000000 o 0000 0 0 0 000 0 0 0 000 0 0 0 0 0 0 0 0 0 IGE 293 52 END 2 4 S30 hexagonal benchmark in 2 D The 30 hexagonal benchmark in 2 D is defined in Ref 14 Its geometry is r
3. ce Structure INACKS i o LL add SaA Structure BIVA TIJ 2 244404 65 008 e AW ee e ee ee Structure bivactsdata e cras 2464 204 ORE a Cee SER were structure PRIVAT ona 2 hi ebb ebb ee de i hoe sis Structure triv t data ooo dla madame aa ee he BEE SS Structure BIVAC AR t e 2 Lu dun Qe A a TERE Structure bivaca data ss run ua a a ee eee ae p BA SR structure TRIVAAS etsad Leg sk Eb ad a ne La eee do bes Structure trivaa data ss amp ale sa da AAA Structure PLUDO ile Ea TE Structure un RR a aaa Structure DELTA e seria sd A na Structure delta data lt o o sac oec 88 a HEH RR eee HER a ee SG R Structure eptilu data ui ee HER EE a De d eee eS Stance CON iria eee ee Lhe ea ee Structure Outsdata nicae nee ee ehh aden eee eh ee eee ed bb els Structure ERROR pausas ns EAR A SEE SO Structure INTKENS sad ai 6 444444 gel a ES E ee ee eS Structure Inikin data e a me eee a structure KINSOL no ea Dhs ou 4 d ee EEE Me ea eee a Structure kinsol data 4 4 aac cs oe 685 e eee eed SVALA E Structure deseval o e 244 0448 Dis ARRE Oe ee ee eae vil IGE 293 1 1 INPUT DATA SPECIFICATIONS 1 1 Syntactic rules for input data specifications The input data to any module is read in free format using the subroutine REDGET The rules for specifying the input data are therefore given in this section The users guide was written using the following conventions e the parameters surround
4. END IGE 293 49 2 3 TAEA 3D benchmark The IAEA 3D benchmark is defined in Ref 18 and its geometry is represented in Fig 13 Here it is solved using a cubic mixed dual method with mesh splitting of the second axial plane A A Plane 1 ai Plane 2 id Mixture index No No 20 cm incoming incoming current 3 current 4 2 1 4 3 3 ih SA A AAN CO O AD OO E Y 7 A A 7 7 Plane 3 Plane 4 No No incoming incoming 3 current 5 current e D A El A Figure 13 Description of the IAEA 3D benchmark LINKED_LIST IAEA3D MACRO TRACK SYSTEM FLUX EDIT MODULE GEO MAC TRIVAT TRIVAA FLUD OUT END IAEA3D GEO CAR3D 9 9 4 EDIT 2 X DIAG X VOID Y SYME Y DIAG Z VOID Zt VOID MESHX 0 0 20 0 40 0 60 0 80 0 100 0 120 0 140 0 160 0 180 0 MESHZ 0 0 20 0 280 0 360 0 380 0 SPLITZ 1 2 1 1 PLANE NB MIX 444 44 4 1 44 44 44 44 4 DDD SS ISIS SAT SAT STATS OF RP ROR b O O 0 GA GA GA IGE 293 MACRO MAC EDIT 2 NGRO 2 NMIX 5 READ INPUT MIX L DIFF TOTAL NUSIGF H FACTOR SCAT MIX 2 DIFF TOTAL NUSIGF H FACTOR SCAT MIX 3 DIFF TOTAL NUSIGF H FACTOR SCAT MIX 4 WF wa KF war PLANE NB 32 2 NNN N NNN W NN ND HR NN N NN bISEHEHPHEHNNN PLANE NB 32 2 WN N DN N N w ND ND N W HR NN NN N hr hr BB NN N WwW PLANE NB 5444 444 54 4 500E 00
5. Hexagonal geometries of type S30 and SA60 5 Hexagonal geometries of type SB60 and S90 6 Hexagonal geometries of type R120 and R180 6 Hexagonal geometry of type SA180 7 Hexagonal geometry of type SB180 7 Hexagonal geometry of type COMPLETE 8 Cylindrical correction in Cartesian geometry 8 Slab geometry with mesh splitting 12 Two dimensional hexagonal geometry 12 Description of the IAEA 2D benchmark 45 Description of the Biblis 2D benchmark rods withdrawn configuration 47 Description of the IAEA 3D benchmark 49 Description of the S30 hexagonal benchmark 52 Description of the LMW benchmark in 2D 53 IGE 293 D I D List of Tables Sten TRIVAGO 25 44 28 4 EI LL kikki LL Sr GEO seu asa LIL a OE Structure geodata 24 0 6656 ER ue EEN bag pala pee MR Structure geo_data2 Structure dese BC soma Les RA MRE AS A BB Structure Ma e e Eu nes d pe Structure desePOS oec ga sim EGR eee SEN We Bae gt ee da Structure MACH lt a Sage GR ERA ee eb ee sert be Structure mac data su 4 4 04 80082 pese a ba DE sr
6. MACROLIB MACRO and used to compute the corresponding system matrices This capa bility is deprecated IGE 293 27 1 9 The FLUD module The FLUD module is used to compute the solution to an eigenvalue problem corresponding to a set of system matrices type L SYSTEM The calling specifications are Table 19 Structure FLUD FLUX FLUD FLUX SYST TRACK MACRO flud_data where FLUX character 12 name of the LCM object type L FLUX containing the solution If FLUX appears on the RHS the solution previously stored in FLUX is used to initialize the new iterative process otherwise a uniform unknown vector is used SYST character 12 name of the LCM object type L SYSTEM containing the system matrices TRACK character 12 name of the LCM object type L_TRACK containing the TRACKING MACRO character 12 name of the optional LCM object type L_MACROLIB containing the cross sections This object is only used to set a link to the MACROLIB name inside the FLUX object By default the name of the MACROLIB is recovered from the link in the SYSTEM object flud_data structure containing the data to module FLUD see Sect 1 9 1 1 9 1 Data input for module FLUD Table 20 Structure flud_data EDIT iprint VAR1 ACCE icll icl2 EXTE maxout epsout THER maxthr epsthr ADI nadi ADJ MONI Imod RAND RELAX relax where EDIT keyword used to set iprint iprint index used to
7. concentric spheres CAR2D two dimensional cartesian geometry TUBEZ polar geometry R Z CAR3D three dimensional cartesian geometry HEX two dimensional hexagonal geometry HEXZ three dimensional hexagonal geometry Ix number of subdivisions along the X axis before mesh splitting IGE 293 4 ly number of subdivisions along the Y axis before mesh splitting Iz number of subdivisions along the Z axis before mesh splitting Ir number of cylinders or spherical shells before mesh splitting lh number of hexagons in an axial plane including the virtual hexagons EDIT keyword used to set iprint iprint index used to control the printing in module GEO 0 for no print 1 for minimum printing default value 2 for printing the geometry state vector descBC structure allowing the boundary conditions surrounding the geometry to be treated descMC structure allowing material mixtures to be associated with a geometry descPOS structure allowing the coordinates of a geometry to be described The inputs corresponding to the descBC structure are the following Table 5 Structure descBC X VOID REFL DIAG TRAN SYME ALBE albedo icode ZERO CYLI ACYL albedo icode X VOID REFL DIAG TRAN SYME ALBE albedo icode ZERO CYLI ACYL albedo icode Y VOID REFL DIAG TRAN SYME CYLI ACYL albedo icode Y VOID REFL DIAG TRAN SYME ALBE albedo
8. for all the fissile iso topes associated with this mixture keyword for input of the multigroup average of the inverse neutron velocity array representing the multigroup average of the inverse neutron velocity lt 1 v gt 2 for the mixture matnum keyword to specify that the power factor for this mixture follows array representing the multigroup power factor for this mixture H9 in MeV em keyword to specify that the macroscopic scattering cross section matrix for this mixture follows IGE 293 nbscat ilastg xsscat 17 array representing the number of secondary groups ig with non vanishing macroscopic scattering cross section towards the primary group jg considered for each anisotropy level associated with this mixture array representing the group index of the most thermal group with non vanishing macro scopic scattering cross section towards the primary group jg considered for each anisotropy level associated with this mixture array representing the multigroup macroscopic scattering cross section 29779 in em from the secondary group ig towards the primary group jg considered for each anisotropy level associated with this mixture The elements are ordered using decreasing secondary group number ig from ilastg to ilastg nbscat 1 and an increasing primary group num ber jg For example the two group isotropic and linearly anisotropic scattering cross sections ngroup 2 naniso 2 given by 151 152 2791 2
9. icode ZERO CYLI ACYL albedo icode Z VOID REFL TRAN SYME ALBE albedo icode ZERO Z VOID REFL TRAN SYME ALBE albedo icode ZERO R VOID REFL ALBE albedo icode ZERO HBC 30 SAGO SB60 90 R120 R180 SA180 SB180 COMPLETE VOID REFL SYME ALBE albedo icode ZERO RADS ANG nrads xrad ir rrad ir ang ir ir 1 nrads ALBE albedo icode ZERO where X negative X side Y negative Y side Z negative Z side X positive X side Yt positive Y side Z positive Z side R side surrounding cylinders or spheres HBC side surrounding a hexagonal geometry VOID the side under consideration has a zero incoming current boundary condition IGE 293 REFL DIAG TRAN SYME ALBE albedo icode ZERO CYLI ACYL 530 SA60 SB60 590 R120 R180 SA180 SB180 COMPLETE the side under consideration has a reflective boundarv condition the side under consideration is external to a diagonal axis of symmetry the side under consideration is connected to the opposite side of the domain This option permits a translation condition to be treated the side under consideration is next to an axial axis of symmetry symmetric with respect to the central axis of the last row of volumes The SYME condition can also be used in hexagonal geometry but only with
10. 12 of the LOM object type L GEOM containing the geometry trivat_data structure containing the data to module TRIVAT see Sect 1 6 1 1 6 1 Data input for module TRIVAT Table 14 Structure trivat_data EDIT iprint TITL TITLE MAXR maxpts PRIM ielem isplh DUAL ielem icol isplh MCFD ielem isplh LUMP ielem 4 SPN n SCAT DIFF iscat VOID nvd ADI nadi VECT iseg PRTV impv where EDIT keyword used to set iprint IGE 293 iprint TITL TITLE MAXR maxpts PRIM DUAL MCFD LUMP ielem icol isplh SPN SCAT DIFF iscat 22 index used to control the printing in module TRIVAT 0 for no print 1 for minimum printing default value Larger values produce increasing amounts of output keyword which allows the run title to be set the title associated with a TRIVAC run This title may contain up to 72 characters The default when TITL is not specified is no title keyword which permits the maximum number of regions to be considered during a TRIVAC run to be specified maximum dimensions of the problem to be considered The default value is set to the number of regions previously computed by the GEO module but this value is insufficient if symmetries or mesh splitting are specified keyword to set a discretization based on the variational collocation method keyword to set a mixed dual finite element discretizatio
11. 21 24 25 27 30 34 38 39 42 44 END 1 epsout 27 28 32 33 42 43 epsthr 27 28 32 33 42 43 ERROR 36 ERROR 36 EXPLICIT 32 33 EXPON 42 EXTE 27 28 32 33 42 43 FIXE 15 16 FLUD 27 FLUD 27 flud_data 27 FLUNAM 44 FLUX 27 29 34 38 39 FLUX 42 FLUXO 30 32 FLUX GPT 32 33 FLUXUNK 44 fnorm 39 FROM TO 32 33 GEO 2 GEO 2 GEO 2 geo datal 2 3 geo data2 2 3 GEOM 18 21 34 GEOMI 2 GEOM2 2 GPT 30 32 33 GPTFLU 32 GPTFLU 32 gptflu_data 32 H FACTOR 15 16 HBC 4 IGE 293 HEX 3 11 HEXZ 3 11 hfact 16 HOMOGE 3 i 9 ic 9 ieli 27 28 92 33 42 icl2 27 28 32 33 42 icode 4 5 icol 18 23 ielem 18 23 IFLU 44 ihom 34 35 ilastg 15 17 imix 9 MPLIC 42 MPLICIT 32 33 impv 21 23 N 34 35 INIKIN 38 NIKIN 24 26 38 inikin data 38 39 INPUT 13 INTERPFLUX 44 INTG 34 iplan 9 iplan1 9 mee HH iprint 3 4 13 18 21 22 24 25 27 30 34 38 39 42 44 iscat 18 19 21 22 iseg 21 23 isplh 18 19 21 23 ispltr 10 11 ispltx 10 11 isplty 10 11 ispltz 10 11 istep 13 14 jmix 9 KINET 38 41 KINSOL 41 KINSOL 24 26 41 kinsol data 41 42 LAMBDA 38 39 lambda 38 39 Ic 9 1h 3 4 11 LINKED_LIST 1 Imod 27 28 Ip 9 Ir 3 4 10 LUMP 21 22 Ix 3 10 59 ly 3 4 10 lz 3 4 10 MAC 13 MAC 5
12. MACRO TRACK SYST MACRO 0 SYST 0 kinsol data where KINET character 12 name of the LCM object type L_KINET in modification mode MACRO character 12 name of the LCM object type L MACROLIB containing the MACROLIB infor mation corresponding to the current time step of a transient TRACK character 12 name of the LCM object type L_TRACK containing the TRACKING informa tion SYST character 12 name of the LCM object type L SYSTEM corresponding to MACROLIB MACRO and TRACKING TRACK MACRO 0 characterx12 name of the LCM object type L_MACROLIB containing the MACROLIB infor mation corresponding to the beginning of step conditions in case a ramp variation of the cross sections in set Beginning of step conditions should not be confused with beginning of transient or initial conditions By default a step variation is set where cross sections are assumed constant and given by MACRO SYST_O character 12 name of the LCM object type L SYSTEM corresponding to MACROLIB MACRO_O and TRACKING TRACK kinsol_data structure containing the data to module KINSOL see Sect 1 15 1 IGE 293 42 1 15 1 Data input for module KINSOL Table 31 Structure kinsol data EDIT iprint DELTA delta SCHEME FLUX IMPLIC CRANK THETA ttflx PREC IMPLIC CRANK EXPON THETA ttprc VAR1 ACCE icll icl2 EXTE maxout epsout THER maxthr epsthr ADI nadi where EDIT keyword used to se
13. TRACKING bivaca_data structure containing the data to module BIVACA see Sect 1 7 1 1 7 1 Data input for module BIVACA Table 16 Structure bivaca_data EDIT iprint UNIT ki where EDIT kevword used to set iprint iprint index used to control the printing in module BIVACA 0 for no print 1 for minimum printing default value Larger values produce increasing amounts of output UNIT A svstem matrix corresponding to cross sections all set to 1 0 is computed This kevword is mandatorv if the svstem matrices in SVST are going to be used bv INIKIN or KINSOL modules see Sects 1 14 and 1 15 IGE 293 25 1 8 The TRIVAA module The TRIVA A module is used to compute the finite element system matrices type L SYSTEM corre sponding to a TRIVAC TRACKING type L TRIVAC and to a set of nuclear properties type L MACROLIB The calling specifications are Table 17 Structure TRIVAA TRIVAA SYST MACRO TRACK DMACRO trivaa data where SYST character 12 name of the LCM object type L SYSTEM containing the system matrices If SYST appears on the RHS the system matrices previously stored in SYST are kept MACRO character 12 name of the LCM object type L MACROLIB containing the macroscopic cross sections and diffusion coefficients TRACK character 12 name of the LCM object type L TRIVAC containing the TRIVAC TRACKING DMACRO character 12 name of the LCM object type L MACROLIB co
14. The GPTFLU module The GPTFLU module is used to compute the solution to a fixed source eigenvalue problem correspond ing to a set of unperturbed system matrices and sources vectors If S is the source term of the explicit generalized adjoint equation this module will solve A o Bo I 1 3 where the direct source vector is orthogonal to the adjoint flux If S is the source term of the implicit generalized adjoint equation this module will solve AT o B Ts 1 4 o where the adjoint source vector Si is orthogonal to the direct flux The calling specifications are Table 23 Structure GPTFLU FLUX_GPT GPTFLU FLUX GPT GPT FLUXO SYST TRACK gptflu data where FLUX GPT character 12 name of the LCM object type L FLUX containing the GPT solution If FLUX GPT appears on the RHS the solution previously stored in FLUX_GPT is used to initialize the new iterative process otherwise a uniform unknown vector is used GPT character 12 name of the LCM object type L_GPT containing the fixed sources FLUXO character 12 name of the LCM object type L FLUX containing the unperturbed flux used to decontaminate the GPT solution SYST character 12 name of the LCM object type L SYSTEM containing the unperturbed system matrices TRACK character 12 name of the LCM object type L_TRACK containing the TRACKING gptflu_data structure containing the data to module GPTFL
15. a AR ob A da ee 25 181 Data input for module TRIVAA s n dun we 25 1 9 The FLUD module s sa m9 6d io da A ARR Ae o ES 27 1 91 Data input for module FLUD e ea ans 27 lo The DELTAS module oak ek a ee RR ee ke 30 110 1 Data input for module DELTA 4 4 dw imma du dd eb ed boas 30 LIL To a SOAS a Se eae A Heo ee 32 Lill Datainput for module G TFEU oa toe wpe ee eee ee es 32 112 Then modales nr AAA SAS She 34 1121 Data input for module OUTS o 4 ne dok ee eh eee Le a be ed 34 1 18 The ERROR module 2 0 00 an ara a eee dda aw ee 36 1 14 The ENTREN modules o ressa ds danni kE RRR AR A ca ES 38 1 14 1 Data input for module INIKIN 38 15 The KINSUL modales sa b gs de ee e ee Rw Rhee ee ER ed 40 1 15 1 Data input for module KINSOL 41 LO Dis VAL module os bina Sr SES 44 LIGA Datadnput for module VALS pipi a S 44 2 EXAMPLES OF INPUT DATA FILES 45 alk TABA 2D benchmark alba bbe a ee oe Rew ee 45 2 Biblis 210 nn eS in E o LELE 46 2 3 LA A us us DU ee Oe Oe bee ae a EE SS di 49 2 4 530 hexagonal benchmark in AD 4 a e Bed 52 2 5 LMW benchmark im QD ss gas A ee a eh 4 ap ee dt 53 ts uu crt oe md de EDAD ON Ee ew ee ew BO a RD D Lada ue 57 I SAL E AAA A RAS ee ee a BS Se 58 IGE 293 vi D I D CU D mm List of Figures The TRIVAC modular approach o nir mesWen id aer aidaa na 2
16. control the printing in module FLUD 0 for no print 1 for minimum printing default value 2 iteration history is printed 3 the solution is printed 4 at each iteration the new solution is compared to a reference solution previously stored in FLUX under name REF 5 the convergence histogram is stored in FLUX IGE 293 VAR1 ACCE icll icl2 EXTE maxout epsout THER maxthr epsthr ADI nadi ADJ MONI Imod RAND 28 keyword used to set the parameters icll and icl2 of the symmetrical variational acceler ation technique SVAT alias keyword for VAR1 number of free outer iterations in a cycle of the SVAT The default value is icll 3 number of accelerated outer iterations in a cycle of the SVAT The default value is icl2 3 A convergence in free iterations is obtained by setting icll 200 or icll maxx0 and icl2 0 keyword to specify that the control parameters for the external iteration are to be modified maximum number of external iterations The fixed default value is maxout 200 convergence criterion for the external iterations The fixed default value is epsout 1 0 x 1074 The outer iterations are stopped when the following criteria is reached max 2 DVD lt epsout x max je where 4 colo i 1 1 is the product of the B matrix times the unknown vector at the k th outer iteration keyword to specify that the control parameters for the thermal iterations are to b
17. dual linear superconvergent finite elements numerically equivalent to PRIM 1 3 Mixed dual quadratic finite elements Quadratic nodal collocation method Mixed dual quadratic superconvergent finite elements numerically equivalent to PRIM 2 3 Mixed dual cubic finite elements Cubic nodal collocation method Mixed dual cubic superconvergent finite elements numerically equivalent to PRIM 3 3 Quartic nodal collocation method IGE 293 21 1 6 The TRIVAT module The TRIVAT module is used to perform a TRIVAC type TRACKING on a 1D 2D 3D geometry l 14 The geometry is analyzed and a LCM object with signature L_TRIVAC is created with the following information e Diagonal and hexagonal symmetries are unfolded and the mesh splitting operations are performed Volumes material mixture and averaged flux recovery indices are computed on the resulting geom etry e A finite element discretization is performed and the corresponding numbering is saved e The unit finite element matrices mass stiffness etc are recovered e Indices related to an ADI preconditioning with or without supervectorization are saved The calling specifications are Table 13 Structure TRIVAT TRACK TRIVAT TRACK GEOM trivat data where TRACK character 12 of the LCM object type L TRIVAC containing the TRACKING information If TRACK appears on the RHS the previous settings will be applied by default GEOM character
18. is created the maximum number of material mixtures a material mixture is characterized by a dis tinct set of macroscopic cross sections keyword used to set ndg This data is used only if the fission spectrum Xp is different from the delayed neutron spectrum x for each precursor group 1 number of delayed neutron groups keyword used to specify the maximum level of anisotropy permitted in the diffusion cross sections This data is given only if MACRI is created the maximum level of anisotropy The default value is naniso 1 keyword used for the input of the physical albedos the maximum number of physical albedos physical albedos real numbers keyword used to create a perturbation directory the index of the perturbation directory keyword used to specify input of the cross section information from default input by REDLEC structure describing the format used for reading the mixture cross sections and diffusion coefficients or perturbation values of the cross sections and diffusion coefficients from the input data file keyword used to specify input of the cross section information from default input by REDLEC in the TRIVAC 2 format The nuclear data will be translated into TRIVAC format and printed on the listing structure describing the format used for reading the mixture cross sections and diffusion coefficients from the input data file in TRIVAC 2 format IGE 293 15 DOLD keyword used to specify perturbed inpu
19. with the last mixture number read either on the GOXS or the input stream NTOTO keyword to specify that the total macroscopic cross sections for this mixture follows TOTAL alias keyword for NTOTO xssigt array representing the multigroup total macroscopic cross section 29 in em associated with this mixture NTOT1 keyword to specify that the P weighted total macroscopic cross sections for this mixture follows xssigl array representing the multigroup Pi weighted total macroscopic cross section 29 in cm 1 associated with this mixture TRANC keyword to specify that the transport correction macroscopic cross sections for this mixture follows IGE 293 xsstra NUSIGF xssigf CHI xschi FIXE xsfixe DIFF diff DIFFX xdiffx DIFFY xdiffy DIFFZ xdiffz NUSIGD xssigd CHDL xschid OVERV overv H FACTOR hfact SCAT 16 array representing the multigroup transport correction macroscopic cross section DZ in cm associated with this mixture keyword to specify that the macroscopic fission cross section multiplied by the average number of neutrons per fission for this mixture follows array representing the multigroup macroscopic fission cross section multiplied by the av erage number of neutrons per fission va in em for all the fissile isotopes associated with this mixture keyword to specify that the fission spectrum for this mixture follows array representing the multig
20. 13 mac data 13 MACLIB 14 MACRI 13 14 MACR2 13 MACRO 24 27 34 38 41 MACROI 36 37 MACRO2 34 36 37 MACRO_O 41 macxs 13 15 matnum 15 16 MAX 39 maxout 27 28 32 33 42 43 maxpts 11 18 19 21 22 MAXR 18 19 21 22 maxthr 27 28 32 33 42 43 MCED 18 19 21 22 MESHX 10 MESHY 10 MESHZ 10 MIX 9 15 34 35 MODULE 1 MONI 27 28 n 18 19 21 23 nadi 21 23 27 28 32 33 42 43 nalbp 13 14 NAMEI 1 NAME2 1 NAMES 1 NAME4 1 NAMES 1 naniso 13 15 17 nbscat 15 17 NDEL 38 39 ndel 13 15 ndg 13 14 38 39 NGRO 13 14 ngroup 13 15 17 NGRP 38 39 ngrp 38 39 NIFI 13 14 nifiss 13 15 NMIX 13 14 nmixt 9 13 15 NORM 39 nrads 4 8 NREG 36 37 nreg 36 37 NTOTO 15 NTOT1 15 NUSIGD 15 16 IGE 293 NUSIGF 15 16 nvd 18 19 21 23 OLD 13 14 OUT 34 OUT 34 out_data 34 OVEL 25 26 OVERV 15 16 overv 15 16 PERT 25 26 PLANE 9 PN 18 19 power 34 39 POWER INI 39 POWR 34 PREC 42 PRIM 18 19 21 22 PRTV 21 23 R 4 R120 4 5 R180 4 5 RADIUS 10 RADS 4 8 RAND 27 28 READ 13 14 REFL 4 5 RELAX 27 29 relax 27 29 rrad 4 8 rrr 10 830 4 5 S90 4 5 SA180 4 5 SA60 4 5 SAME 9 SB180 4 5 SB60 4 5 SCAT 15 16 18 19 21 22 scat 15 SCHEME 42 SEQ ASCII 1 SEQ_BINARY 1 SIDE 10 sidhex 10 SKIP 25 specif 1 SPHERE 3 10 11 SPLITR 10 SPLIT
21. 52 L XI 351 or E 0 0 50cm 0 20em 0 03em 040 em 1 0 05cm O0 00cm 0 00cm 0 04 cm must be entered as SCAT L 0 2 2 2 gt 1 0 03 1 gt 1 0 50 2 2 2 gt 2 0 40 1 gt 2 0 20 L 1 1 1 1 gt 1 0 05 1 2 2 gt 2 0 04 IGE 293 18 1 5 The BIVACT module The BIVACT module is used to perform a BIVAC type TRACKING on a 1D 2D geometry l 14 The geometry is analyzed and a LCM object with signature L BIVAC is created with the following information e Diagonal and hexagonal symmetries are unfolded and the mesh splitting operations are performed Volumes material mixture and averaged flux recovery indices are computed on the resulting geom etry e A finite element discretization is performed and the corresponding numbering is saved e The unit finite element matrices mass stiffness etc are recovered The calling specifications are Table 11 Structure BIVACT TRACK BIVACT TRACK GEOM bivact data where TRACK character 12 name of the LCM object type L_BIVAC containing the TRACKING informa tion If TRACK appears on the RHS the previous settings will be applied by default GEOM character 12 name of the LCM object type L GEOM containing the geometry bivact_data structure containing the data to module BIVACT see Sect 1 5 1 1 5 1 Data input for module BIVACT Table 12 Structure bivact_data EDIT iprint TITL TITLE MAXR maxpts PRIM iele
22. 57370E 02 1 1 150681E 01 1 1 621938Et04 THEN 1 3 971426E 02 1 1 200883E 01 1 2 047011E 04 THEN 1 4 351272E 02 1 1 224600E 01 1 2 245449E 04 MACRO1 SYSTEM1 DELETE MACRO1 SYSTEM1 MACRO1 MACRO2 SYSTEM1 SYSTEM2 MACRO2 SYSTEM2 DELETE MACRO2 SYSTEM2 ENDWHILE ECHO test Imw2D completed 56 IGE 293 57 10 11 12 13 A 15 16 17 18 19 References A H BERT Applied Reactor Physics Presses Internationales Polytechnique ISBN 978 2 553 01436 9 424 p Montr al 2009 A H BERT A Programmer s Guide for the GAN Generalized Driver FORTRAN 77 version Report IGE 158 Ecole Polytechnique de Montr al Institut de G nie Nucl aire December 1994 A HEBERT Application of the Hermite Method for Finite Element Reactor Calculations Nucl Sci Eng 91 34 1985 A HEBERT Variational Principles and Convergence Acceleration Strategies for the Neutron Dif fusion Equation Nucl Sci Eng 91 414 1985 A HEBERT Preconditioning the Power Method for Reactor Calculations Nucl Sci Eng 94 1 1986 A HEBERT Development of the Nodal Collocation Method for Solving the Neutron Diffusion Equation Ann Nucl Energy 14 527 1987 A HEBERT TRIVAC A Modular Diffusion Code for Fuel Management and Design Applications Nucl J of Canada Vol 1 No 4 325 1987 A HEBERT Appl
23. 6 190800E 03 1 035800E 01 H FACTOR 2 506400E 03 4 193500E 02 SCAT 1 1 0 0 2 2 0 0 1 762100E 02 MIX 3 DIFF 1 320000E 00 2 772000E 01 TOTAL 2 576220E 02 7 159600E 02 SCAT 1 1 0 0 2 2 0 0 2 310600E 02 MIX 4 DIFF 1 438900E 00 3 638000E 01 TOTAL 2 746400E 02 9 140800E 02 NUSIGF 7 452700E 03 1 323600E 01 H FACTOR 3 017300E 03 5 358700E 02 SCAT 1 1 0 0 2 2 0 0 1 710100E 02 MIX 5 DIFF 1 438100E 00 3 665000E 01 TOTAL 2 729300E 02 8 482800E 02 NUSIGF 6 190800E 03 1 035800E 01 H FACTOR 2 506400E 03 4 193500E 02 SCAT 1 1 0 0 2 2 0 0 1 729000E 02 MIX 6 IGE 293 DIFF TOTAL NUSIGF H FACTOR SCAT MIX 7 DIFF TOTAL NUSIGF H FACTOR SCAT MIX 8 DIFF TOTAL NUSIGF H FACTOR SCAT TRACK TRIVAT BIBLIS TITLE EDIT 5 MAXR 81 PRIM 2 NON I h NON RNONPR 438500E 00 732400E 02 428500E 03 602600E 03 1 0 0 220 438900E 00 729000E 02 190800E 03 506400E 03 1 0 0 220 439300E 00 732100E 02 428500E 03 602600E 03 BH O W 1 0 0 2 2 0 0 665000E 01 731400E 02 091100E 01 417400E 02 1 719200E 02 679000E 01 802400E 02 035800E 01 193500E 02 1 712500E 02 680000E 01 051000E 02 091100E 01 417400E 02 1 702700E 02 BIBLIS BENCHMARK SYSTEM TRIVAA MACRO TRACK 48 EDIT 5 FLUX FLUD SYSTEM EDIT 2 EDIT OUT FLUX EDIT 2 INTG 12 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 0 30 31 0 0 0 0 o OO OO
24. A P or SP method will therefore behave as diffusion theory number of terms in the scattering sources iscat 1 is used for isotropic scattering in the laboratory system iscat 2 is used for linearly anisotropic scattering in the laboratory system The default value is set to n 1 in P or SP case keyword to set the number of base points in the Gauss Legendre quadrature used to integrate void boundary conditions if icol 3 and n 0 type of quadrature The values permitted are 0 use a n 2 point quadrature consis tent with Pa theory 1 use a n 1 point quadrature consistent with Sn 1 theory 2 use an analytical integration of the void boundary conditions By default nvd 0 IGE 293 20 Various finite element approximations can be obtained by combining different values of ielem and icol e PRIM PRIM 1 2 PRIM PRIM PRIM PRIM PRIM PRIM PRIM PRIM DUAL DUAL DUAL DUAL DUAL DUAL DUAL DUAL DUAL DUAL 1 3 Linear finite elements Mesh corner finite differences Linear superconvergent finite elements Quadratic finite elements Quadratic variational collocation method Quadratic superconvergent finite elements Cubic finite elements Cubic variational collocation method Cubic superconvergent finite elements Quartic variational collocation method Mixed dual linear finite elements Mesh centered finite differences Mixed
25. IX 4 DIFF 2 000E 00 3 0000E 01 TOTAL 4 016E 02 1 0024E 02 SCAT 110 0 2 2 0 0 0 4E 01 TRACK TRIVAT IAEA TITLE TAEA 2D BENCHMARK MAXR 81 PRIM 2 SYSTEM TRIVAA MACRO TRACK FLUX FLUD SYSTEM EDIT 2 EDIT OUT FLUX EDIT 2 INTG 123 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 26 27 28 29 0 0 OOo O O OS END 2 2 Biblis 2D benchmark 46 The rods withdrawn configuration of the Biblis 2D benchmark is defined in Ref 3 and its geometry is represented in Fig 12 Here it is solved using a parabolic variational collocation method without mesh splitting of the elements LINKED_LIST BIBLIS MACRO TRACK SYSTEM FLUX EDIT MODULE GEO MAC TRIVAT TRIVAA FLUD OUT END k BIBLIS GEO CAR2D 9 9 EDIT 2 X DIAG X VOID Y SYME Y DIAG MIX 1 1 e Bor Nr N OPP O HH O 00 EEE UW uy IGE 293 Si A L Mixture index i current 23 1226 cm Figure 12 Description of the Biblis 2D benchmark rods withdrawn configuration 0 MESHX 0 0 23 1226 46 2452 69 3678 92 4904 115 613 138 7356 161 8582 184 9808 208 1034 MACRO MAC EDIT 2 NGRO 2 NMIX 8 READ INPUT MIX 1 DIFF 1 436000E 00 3 635000E 01 TOTAL 2 725820E 02 7 505800E 02 NUSIGF 5 870800E 03 9 606700E 02 H FACTOR 2 376800E 03 3 889400E 02 SCAT 1 1 0 0 2 2 0 0 1 775400E 02 MIX 2 DIFF 1 436600E 00 3 636000E 01 TOTAL 2 729950E 02 7 843600E 02 NUSIGF
26. MAC module In TRIVAC the macroscopic cross sections and diffusion coefficients are read from the input data file using REDLEC The general format of the data for the MAC module in TRIVAC is the following Table 8 Structure MAC MACRI MAC MACRI MACR2 mac data where MACRI character 12 name of the LCM object type L MACROLIB containing the new Macrolib produced by the module A Macrolib contains macroscopic cross sections and diffusion coefficients If MACRI appears on both LHS and RHS it is updated otherwise it is created If MACR1 is created all macroscopic cross sections and diffusion coefficients are first initialized to zero MACR2 character 12 name of the LCM object type L MACROLIB containing a read only Macrolib The information existing in MACR2 is copied into MACR1 but MACR2 is not modified mac data structure containing the data to module MAC see Sect 1 4 1 1 4 1 Data input for module MAC Table 9 Structure mac_data EDIT iprint NGRO ngroup NIFI nifiss DELP ndel ANIS naniso NMIX nmixt DELP ndg ANIS naniso ALBP nalbp albedp ia ia 1 nalbp READ INPUT macxs OLD triv2 DOLD trip2 STEP istep READ INPUT macxs tI where EDIT keyword used to set iprint iprint index used to control the printing in module MAC 0 for no print The macroscopic cross sections will be printed if the parameter iprint is greater than or
27. S30 and SA60 symmetries the side under consideration has an arbitrary albedo to be specified geometrical albedo corresponding to the boundary condition ALBE albedo gt 0 0 index of a physical albedo corresponding to the boundary condition ALBE The numerical values of the physical albedo are supplied by the module MAC the side under consideration has a zero flux boundary condition the side under consideration has a zero incoming current boundary condition with a circular correction applied on the Cartesian boundary This option is only available in the X Y plane for CAR2D and CAR3D geometries defined for TRIVAC full core calculations the side under consideration has an arbitrary albedo with a circular correction applied on the Cartesian boundary This option is only available in the X Y plane for CAR2D and CAR3D geometries defined for TRIVAC full core calculations hexagonal symmetry of one twelfth of an assembly see Fig 2 oco oS SIA DL q TA 5 13 da 8 18 WA 7 Figure 2 Hexagonal geometries of type 530 and SA60 hexagonal symmetry of one sixth of an assembly of type A see Fig 2 hexagonal symmetry of one sixth of an assembly of type B see Fig 3 hexagonal symmetry of one quarter of an assembly see Fig 3 hexagonal symmetry of one third of an assembly rotational symmetry see Fig 4 rotational symmetry of a half assembly see Fig 4 hexagonal symmetry of h
28. SIGF 7 503282E 03 1 378004E 01 H FACTOR 3 001310E 03 5 512106E 02 SCAT 1 1 0 0 2 2 0 0 0 171777E 01 OVERV 0 800E 07 4 000E 06 MIX 4 DIFF 1 634220E 00 2 640020E 01 TOTAL 3 025750E 02 4 936351E 02 SCAT 1 1 0 0 2 2 0 0 0 275969E 01 OVERV 0 800E 07 4 000E 06 MIX 5 DIFF 1 423910E 00 3 563060E 01 TOTAL 2 795756E 02 8 766216E 02 NUSIGF 6 477691E 03 1 127328E 01 H FACTOR 2 591070E 03 4 509310E 02 SCAT 1 1 0 0 2 2 0 0 0 175555E 01 OVERV 0 800E 07 4 000E 06 MIX 6 IGE 293 DIFF 1 423910E 00 3 563060E 01 TOTAL 2 850756E 02 9 146217E 02 NUSIGF 6 477691E 03 1 127328E 01 H FACTOR 2 591070E 03 4 509310E 02 SCAT 1 1 0 0 2 2 0 0 0 175555E 01 OVERV 0 800E 07 4 000E 06 TRACK TRIVAT LMW TITLE LMW 2 D BENCHMARK EDIT MAXR 144 MCFD 2 SYSTEM1 TRIVAA MACRO1 TRACK EDIT 1 UNIT FLUX FLUD SYSTEM1 TRACK EDIT EXTE 5 0E 7 assertS FLUX K EFFECTIVE 1 1 014803 gaia Crank Nicholson space time kinetics poe EVALUATE TIME 0 0 KINET INIKIN MACRO1 TRACK SYSTEM1 FLUX EDIT 1 NDEL 6 BETA 0 000247 0 0013845 0 001222 0 0026455 0 000832 0 000169 LAMBDA 0 0127 0 0317 0 115 0 311 1 40 3 87 CHID 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 NORM POWER INI 1 0E4 EVALUATE sigti 2 850756E 02 EVALUATE sigt2 9 146217E 02 WHILE TIME 26 7 lt DO EVALUATE sigti sigti 5 5E 4 0 1 26 7 EVALUATE sigt2 sigt2 3 8E 3 0 1 26 7 MACRO2 MAC MACRO EDIT 0 READ INPUT MIX 6 TOTAL lt lt sig
29. TECHNICAL REPORT IGE 293 A USER GUIDE FOR TRIVAC VERSION4 A HEBERT Institut de g nie nucl aire D partement de g nie m canique Ecole Polytechnique de Montr al September 11 2014 IGE 293 ii Copyright Notice for TRIVAC The development of TRIVAC is financially supported directly or indirectly by various organizations including cole Polytechnique de Montr al Hydro Qu bec and the Hydro Qu bec chair in nuclear engi neering the Natural Science and Engineering Research Council of Canada NSERC Atomic Energy of Canada limited AECL and the CANDU Owners Group COG The code TRIVAC and its users guide are and will remain the property of cole Polytechnique de Montr al Trivac is free software you can redistribute it and or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation either version 2 1 of the License or at your option any later version Permission is granted to the public to copy TRIVAC without charge cole Polytechnique de Montr al makes no warranty express or implied and assumes no liability or responsibility for the use of TRIVAC IGE 293 ili Acknowledgments The computer code TRIVAC results from a concerted effort made at cole Polytechnique de Montr al The main authors of this report would therefore like to express their thanks to cole Polytechnique de Montr al for its support along the years as well as to the graduate students and
30. TRIVAC modules will be given in the following sections IGE 293 2 The input data always begin with the declaration of each LCM object XSM file sequential binary or ASCII file that will be required by the following modules This is followed by the declaration of the modules actually used in the input data deck The following data describe a sequence of module calls in the format of the GAN generalized driver As indicated in Fig 1 the modules communicate with each other throught LCM objects or XSM files whose specifications are given in section 2 The TRIVAC user generally have the choice to declare its data structures as LINKED_LIST to reduce CPU time resources or as XSM_FILE to reduce CPU memory resources The input data always end with a call to the END module TRIVAT E NCR B IVACT BIVACA FLUD L_MACROLIB TRIVAA L_MACROLIB Figure 1 The TRIVAC modular approach 1 3 The GEO module The GEO module is used to create or modify a geometry The geometry definition module in TRIVAC permits all the characteristics coordinates material mixture type indices and boundary conditions of a simple or complex geometry to be specified The method used to specify the geometry is indepen dent of the discretization module to be used subsequently Each geometry is represented by a name characte
31. U 1 11 1 Data input for module GPTFLU Table 24 Structure gptflu_data EDIT iprint IX VAR1 ACCE icll icl2 EXTE maxout epsout THER maxthr epsthr ADI nadi EXPLICIT IMPLICIT FROM TO ALL isrel isre2 l El IGE 293 where EDIT iprint VAR1 ACCE icll icl2 EXTE maxout epsout THER maxthr epsthr ADI nadi EXPLICIT IMPLICIT FROM TO ALL Usrel Usrel 33 keyword used to set iprint index used to control the printing in module GPTFLU 0 for no print 1 for minimum printing default value 2 iteration history is printed 3 the solution is printed 4 at each iteration the new solution is compared to a reference solution previously stored in FLUX_GPT under the name REF 5 the convergence histogram is stored in FLUX_GPT keyword used to set the parameters icll and icl2 of the variational acceleration technique alias keyword for VAR1 number of free outer iterations in a cycle of the SVAT The default value is icll 3 number of accelerated outer iterations in a cycle of the SVAT The default value is icl2 3 A convergence in free iterations is obtained by setting icll 200 or icll maxx0 and icl2 0 keyword to specify that the control parameters for the external iteration are to be modified maximum number of external iterations The fixed default value is maxout 200 convergence criterion for the external iterat
32. X ihom i i 1 nreg where EDIT keyword used to set iprint iprint index used to control the printing in module OUT O for no print 1 for minimum printing default value DIRE use the direct flux to perform homogenization default value ADJO use the adjoint flux to perform homogenization POWR keyword used to set power power value of the power used to normalize the flux By default the flux is not normalized INTG keyword used to compute the reaction rates IGE 293 35 IN keyword for computing the reaction rates on the geometry mesh see Sect 1 3 1 before mesh splitting MIX keyword for computing the reaction rates on the mixture mesh previously used to define the geometry see Sect 1 3 1 before mesh splitting ihom index of the homogenized region corresponding to the each region of the geometry see Sect 1 3 1 before mesh splitting IGE 293 36 1 13 The ERROR module The ERROR module is used to compare reaction rates contained into two extended MACROLIBS and to print statistics regarding the comparison The QUANDRY type power densities are first compared These power densities are defined by the following relation LV g pauandry _ 2 Vi NP where P is the total power and V is the volume of the region 7 The maximum and averaged errors are respectively defined by quandry quandry IP h Emax max pquandry i and quandrv quandry o1 y ps ps Voore pauandrys
33. X 10 SPLITY 10 SPLITZ 10 SPN 18 19 21 22 60 STEP 13 14 SYME 4 5 SYST 24 27 32 38 41 SYSTO 30 SYST 0 41 THER 27 28 32 33 42 43 THETA 42 theta 42 TITL 18 19 21 22 TITLE 18 19 21 22 TOTAL 15 TRACK 18 21 24 25 27 28 30 32 34 38 41 43 TRACKING 44 TRAN 4 5 8 TRANC 15 trip2 13 15 triv2 13 14 TRIVAA 25 TRIVAA 25 trivaa_data 25 TRIVAC 1 TRIVAT 21 TRIVAT 21 trivat_data 21 TRKNAM 44 ttfix 42 ttprc 42 TUBE 3 10 11 TUBEZ 3 10 11 UNIT 24 26 UPTO 9 VAL 44 VAL 44 VAR1 27 28 32 33 42 VECT 21 23 VOID 4 9 18 19 21 23 X 4 8 10 X 4 8 10 xdiffx 15 16 xdiffy 15 16 xdiffz 15 16 xhfact 15 xrad 4 8 xschi 15 16 xschid 15 16 xsfixe 15 16 XSM_FILE 1 xsscat 17 xssigl 15 xssigd 15 16 xssigf 15 16 IGE 293 61 xssigt 15 xsstra 15 16 xxx 10 Yt 4 8 10 Y 4 8 10 yyy 10 Z 4 8 10 Z 4 8 10 ZERO 4 5 zzz 10
34. alf a type A assembly see Fig 5 hexagonal symmetry of half a type B assembly see Fig 6 complete hexagonal assembly see Fig 7 IGE 293 Figure 3 Hexagonal geometries of type SB60 and S90 Figure 4 Hexagonal geometries of type R120 and R180 IGE 293 Figure 5 Hexagonal geometry of type SA180 Figure 6 Hexagonal geometry of type SB180 IGE 293 8 Figure 7 Hexagonal geometry of type COMPLETE RADS This keyword is used to specify the cylindrical correction applied in the X Y plane for CAR2D and CAR3D geometries 7 ANG This keyword allows the angle see Fig 8 of the cylindrical notch to be set By default no notch is present nrads Number of different corrections along the cylinder main axis i e the Z axis xrad ir Coordinate of the Z axis from which the correction is applied rrad ir Radius of the real cylindrical boundary ang ir Angle of the cylindrical notch This data is given if and only if the keyword ANG is present ang ir 5 by default i e the correction is applied at every angle A Figure 8 Cylindrical correction in Cartesian geometry The only combinations of diagonal symmetry permitted are X DIAG Y DIAG and X DIAG Y DIAG In these cases the geo
35. alues must be given in order from Z to Z rrr Radii in the cases of cylindrical TUBE or TUBEZ spherical SPHERE It is important to note that we must have rrr 1 0 0 sidhex length of a side of a hexagon SPLITX keyword for mesh splitting of the geometry along the X axis SPLITY keyword for mesh splitting of the geometry along the Y axis SPLITZ keyword for mesh splitting of the geometry along the Z axis SPLITR keyword for mesh splitting of the geometry in the radial direction IGE 293 ispltx isplty ispltz ispltr 11 number of sub volumes that will be defined for each row of the volume along the X axis If the geometry presents a diagonal symmetry this input will also be used for the splitting along the Y axis By default ispltx 1 number of sub volumes that will be defined for each row of the volume along the Y axis If the geometry presents a diagonal symmetry this input will also be used for the splitting along the X axis By default isplty 1 number of sub volumes that will be defined for each row of the volume along the Z axis By default ispltz i 1 the value of ispltr gives the number of sub volumes that will be defined for each tube or each spherical shell A negative value permits a splitting into equal sub volumes a positive value permits a splitting into equal sub radius spacings By default ispltr 1 The user of the options described above should take care not to exceed the limits imposed by the
36. amount of dynamically allocated memory available For a pure geometry let us define the variables l p lyp lzp and Irp as lap lyp lzp Irp la 5 isplta i 1 ly isplty 2 i 1 lz 5 ispltz i i 1 lr gt ispltr i i 1 thus the limits that must be respected are the following e xp gt maxpts for a CAR1D geometry e Ih gt maxpts for a HEX geometry e lrp gt maxpts for the TUBE and SPHERE geometries e lzpxlyp gt maxpts for the CAR2D geometry without diagonal symmetry e lap x lyp 1 2 gt maxpts for the CAR2D geometry with diagonal symmetry e Irp lzp gt maxpts for the TUBEZ geometry e lzpxlypxlzp gt maxpts for the CAR3D geometry without diagonal symmetry e lap x lyp 1 x lzp 2 gt maxpts for the CAR3D geometry with diagonal symmetry e lhxlzp gt maxpts for the HEXZ geometry 1 3 2 Examples of geometries We will now give a few examples which will permit users to better understand the procedure used to define the geometries in TRIVAC IGE 293 12 1 Slab geometry see Fig 9 GEOMETRY1 GEO CAR D 6 X VOID X ALBE 1 2 MESHX 0 0 0 1 0 3 0 5 0 6 0 8 1 0 SPLITX 222121 MIX 123456 Figure 9 Slab geometry with mesh splitting 2 Two dimensional hexagonal geometry see Fig 10 GEOMETRY4 GED HEX 12 HBC 830 ALBE 1 6 SIDE 1 3 MIX 111222333456 A se Figure 10 Two dimensional hexagonal geometry IGE 293 13 1 4 The
37. ation of the reactor should be used to compute its harmonics If symmetries are set in the geometry some harmonics may be skipped If the reactor is symmetric a uniform initial estimate of the harmonics may cause some harmonics to be skipped the keyword RAND should therefore be used the Imod first bi orthonormalized harmonics of the solution are computed using the SVAT accelerated preconditioned power method with a Hotelling deflation procedure keyword used to initialize the harmonics calculations option MONI with a random estimate rather than a uniform estimate This option has no effect if FLUX appears on the RHS IGE 293 RELAX relax 29 keyword used to set the relaxation parameter This keyword must be specified each time a relaxation is required relaxation parameter selected in the interval 0 lt relax lt 1 0 and used to update the flux information in the FLUX object The updated value is taken equal to 1 0 relax times the previous value given in the RHS FLUX object plus relax times the value computed within current FLUD call The default value is relax 1 0 IGE 293 30 1 10 The DELTA module The DELTA module is used to compute the source components of a fixed source eigenvalue problem corresponding to a set of unperturbed and perturbation system matrices type L SYSTEM In the direct case the fixed source is computed as S 6A X 6B 6 6 B Y 1 1 where the direct so
38. blems Finally several implicit numerical schemes are available for the solving of space time neutron kinetics problems The execution of TRIVAC is controlled by the generalized GAN driver It is modular and can be interfaced easily with other production codes IGE 293 v Contents Copyright Notice for TRIVAC si A ee ii Acknowledgmems NUS eae EE ER eee e bye eed a OY 111 COmMent ss bop hae ea rr e a a RR A e a r a Rede v List of Figures sms eg t Grona e e d anh amp de bi n was vi List GE Tables acc a E RMR RE ee a eee Re ROSS vii 1 INPUT DATA SPECIFICATIONS sou ee Le RE a a G E 1 11 Syntactic rules for input data specifications 1 1 2 The lobalinpui MUS i LU SED Ea ee a B a eee 1 1 3 The GEG module isa ss sa db rr bb da ee 2 Lol Data input for module GEO 2 ke ii binasa 3 1 3 2 Examples of geometries 11 14 The NAG WOTE so he a RRM RE RE QE DR Ne dos 13 1 4 1 Data input for module MAG s o e 4 4 5 e a E ee gas 13 142 Description of the nuclear data 15 1 5 The BIVAGT modale xo eau ee La E 18 1 5 1 Data input for module BIVACT o 2 24 4 44 hu a aoe mu aa 18 1 6 Th TREVAT module gt cotos md PAG ee mu hu diet bb ed 21 1 6 1 Data input for module TRIVATS cocos 44e 40 6484 mon 21 1 7 The BIVAGA modale cumes parir DO LS Le dpt DR US pe dont Me 24 ll Data input for module BIVACAS aa a 24 1 8 Whe TREVAS BO
39. bute mixture numbers to each volume inside a single 2D plane This option is valid only for 3D geometries Cartesian or hexagonal plane number for which material mixture are input keyword to attribute the same material mixture numbers of the iplan1 plane to the iplan plane In hexagonal geometry it can indicate that the mixture numbers of the current crown of the iplanth plane will be identical to those of the same crown of the iplanith plane plane number used as reference to input the current plane or crown s number of volumes in a plane In Cartesian geometry lp lx ly and in hexagonal geometry lp lh keyword to attribute mixture numbers to each hexagon of a single crown This option is only valid for COMPLETE hexagonal geometry definition Each use of the keyword CROWN increases the crown number by 1 So it is not required to give its number but crowns must be defined from the center to the peripherical regions of a plane number of hexagons in the current crown For the ith crown of a compelete hexagonal plane lc i 1 6 The first crown is composed of only one hexagon keyword to specify that the Ic material mixture number of the current crown have the same value jmix keyword to attribute material mixture numbers of the current crown up to the ic one number of the last crown in UPTO option Its value must be greater than equal to the current crown number IGE 293 10 Here we will assume that lreg is the
40. e modified maximum number of thermal iterations The fixed default value is maxthr 0 correspond ing to no thermal iterations convergence criterion for the thermal iterations The fixed default value is epsthr 1 0 x 107 keyword used to set nadi in cases where Trivac is used number of alternating direction implicit ADI inner iterations per outer iteration The default value is nadi 1 If this value causes a failure of the acceleration process it is recommended that a larger value be tried The optimal choice is generally the minimum value of nadi which allows a convergence in less than 75 outer iterations nadi 1 or nadi 2 is generally the best choice for production type calculations The greater nadi is the smaller the asymptotic convergence constant ACC becomes Taking an arbitrary large value e g nadi 20 leads to numerical results identical to those of the inverse power method where the system matrices are accurately inverted at each outer iteration at a prohibitive CPU cost In this case the ACC is almost equal to the dominance ratio of the iterative matrix The default value is recovered in the state vector of the TRACKING object TRACK keyword used to obtain the solution to both the direct and adjoint eigenvalue problems The adjoint solution is required if we subsequently want to perform a perturbation calculation keyword used to obtain the first harmonics of the solution and to set Imod A full core represent
41. ed by single square brackets denote an optional input the parameters surrounded by double square brackets denote an optional input which may be repeated as many times as desired the parameters in braces separated by vertical bars denote a choice of input where one and only one is mandatory the parameters in bold face and in brackets denote an input structure the parameters in italics and in brackets with an index data i i 1 n denote a set of n inputs the words using the typewriter font are character constants keywordS used as keywords e the words in italics are user defined variables they should be lower case and are of type integer starting with to n and real starting with a to hor o to 2 or of type character in uppercase CHARACTER 1 2 The global input structure TRIVAC is built around the GAN generalized driver Input data must therefore follow the calling specifications given below Table 1 Structure TRIVAC LINKED_LIST NAMEI XSM_FILE NAME2 SEQ_BINARY NAMES SEQ_ASCII NAME4 MODULE NAMES specif where NAME1 Character 12 name of a LCM object NAME2 Character 12 name of an XSM file NAME3 Character 12 name of a sequential binary file NAME4 Character 12 name of a sequential ASCII file NAMES Character 12 name of a module specif Input specifications for a single module Specifications for
42. epresented in Fig 14 Here it is solved using a mesh centered finite difference method without mesh splitting of the hexagonal elements gt 13 044 cm Figure 14 Description of the 30 hexagonal benchmark LINKED_LIST HEX MACRO TRACK SYSTEM FLUX EDIT MODULE GEO MAC TRIVAT TRIVAA FLUD OUT END HEX GEO HEX 6 EDIT 2 HBC 530 ZERO SIDE 13 044 MIX 1 2 2 2 3 3 MACRO MAC EDIT 2 NGRO 2 NMIX 3 READ INPUT MIX 1 DIFF 1 5E 00 4 00E 01 TOTAL 3 0E 02 1 30E 01 NUSIGF 0 0E 00 1 35E 01 H FACTOR 0 0E 00 1 35E 01 SCAT 110 0220 0 0 2E 01 MIX 2 DIFF 1 5E 00 4 00E 01 TOTAL 3 0E 02 8 50E 02 NUSIGF 0 0E 00 1 35E 01 H FACTOR 0 0E 00 1 35E 01 SCAT 110 0220 0 0 2E 01 MIX 3 DIFF 2 0E 00 3 0E 01 TOTAL 4 0E 02 1 0E 02 SCAT 110 0220 0 0 4E 01 IGE 293 TRACK TRIVAT HEX TITLE 830 HEXAGONAL BENCHMARK IN 2 D EDIT 5 MAXR 50 MCFD IELEM 1 ISPLH 1 SYSTEM TRIVAA MACRO TRACK EDIT 5 FLUX FLUD SYSTEM EDIT 2 EDIT OUT FLUX EDIT 2 INTG IN END 2 5 LMW benchmark in 2 D The LMW benchmark in 2 D is a space time kinetics problem introduced by Greenman 9 and used by Monierl Its geometry is represented in Fig 15 Here it is solved using a parabolic nodal collocation method with 2x2 mesh splitting of each element A reactivity transient is induced by the rapid withdrawal of the control rod in material mixture 6 The control rod is removed in 26 7 s causing a ne
43. equal to 2 The transfer cross sections will be printed if this parameter is greater than or equal to 3 IGE 293 NGRO ngroup NIFI nifiss DELP ndel ANIS naniso NMIX nmixt DELP ndg ANIS naniso ALBP nalbp albedp STEP istep READ macxs OLD triv2 14 keyword used to define the number of energy groups This data is given if and only if MACRI is created the number of energy groups used for the calculations in TRIVAC keyword used to specify the maximum number of fissile spectrum associated with each mixture Each fission spectrum generally represents a fissile isotope This information is required only if MACLIB is created and the cross sections are taken directly from the input data stream the maximum number of fissile isotopes per mixture The default value is nifiss 1 keyword used to specify the number of delayed neutron groups the number of delayed neutron groups The default value is ndel 0 keyword used to specify the maximum level of anisotropy permitted in the scattering cross sections This information is required only if MACLIB is created and the cross sections are taken directly from the input data stream number of Legendre orders for the representation of the scattering cross sections The default value is naniso 1 corresponding to the use of isotropic scattering cross sections keyword used to define the number of material mixtures This data is given if and only if MACRI
44. es of iprint will produce increasing amounts of output DIM keyword to specify the number dim dim number of dimension of the geometry dxyz mesh interval along each direction which is used to define the grid where the flux is interpolated IGE 293 45 2 EXAMPLES OF INPUT DATA FILES 2 1 IAEA 2D benchmark The IAEA 2D benchmark is defined in Refs 3 18 and its geometry is represented in Fig 11 Here it is solved using a parabolic variational collocation method without mesh splitting of the elements Mixture index lt _ 20 cm No incoming current Figure 11 Description of the IAEA 2D benchmark LINKED_LIST IAEA MACRO TRACK SYSTEM FLUX EDIT MODULE GEO MAC TRIVAT TRIVAA FLUD OUT END k IAEA GEO CAR2D 9 9 EDIT 2 X DIAG X VOID Y SYME Y DIAG MIX 32223 242 2 YN NN w NNN NS PPE PE N N COOP RP BP RP RP RB o 000 OF A A MESHX 0 0 20 0 40 0 60 0 80 0 100 0 120 0 140 0 160 0 180 0 MACRO MAC EDIT 2 NGRO 2 NMIX 4 READ INPUT MIX 1 DIFF 1 500E 00 4 0000E 01 TOTAL 3 012E 02 8 0032E 02 NUSIGF 0 000E 00 1 3500E 01 H FACTOR 0 000E 00 1 3500E 01 SCAT 110 0 2 2 0 0 0 2E 01 MIX 2 DIFF 1 500E 00 4 0000E 01 IGE 293 TOTAL 3 012E 02 8 5032E 02 NUSIGF 0 000E 00 1 3500E 01 H FACTOR 0 000E 00 1 3500E 01 SCAT 110 0 2 2 0 0 0 2E 01 MIX 3 DIFF 1 500E 00 4 00000E 01 TOTAL 3 012E 02 1 30032E 01 NUSIGF 0 000E 00 1 35000E 01 H FACTOR 0 000E 00 1 35000E 01 SCAT 1 1 0 0 2 2 0 0 0 2E 01 M
45. exact number of cells or elementary cases to be considered For example if we had used the DIAG option with a geometry of type CAR3D Ix ly we would have lreg Ix 1 lyxlz 2 The folowing dimensional constraints must also be respected e nmerge number of merged cells with nmerge gt lreg e ngen number of generation cells with ngen gt nmerge The inputs corresponding to the descPOS structure are the following Table 7 Structure descPOS MESHX xxx i i 1 lx 1 MESHY yyy i i 1 ly 1 MESHZ zzz i i 1 12 1 RADIUS rrr i i 1 lr 1 SIDE sidhex SPLITX ispltx i i 1 1x SPLITY isplty i i 1 ly SPLITZ ispltz i i 1 12 SPLITR ispltr i i 1 1r where MESHX keyword for the mesh of the geometry along the X axis MESHY keyword for the mesh of the geometry along the Y axis MESHZ keyword for the mesh of the geometry along the Z axis RADIUS keyword for the mesh of the geometry in the radial direction SIDE keyword for the length of a side of a hexagon XXX abscissa corresponding to the limits of the regions making up the geometry These values must be given in order from X to X If the geometry presents a diagonal symmetry this data will also be used for the ordinate yyy ordinate corresponding to the limits of the regions making up the geometry These values must be given in order from Y to Y ZZZ height corresponding to the limits of the regions making up the geometry These v
46. gative ramp variation in total cross section E zero flux XN 019Z SSS Figure 15 Description of the LMW benchmark in 2 D TEST CASE LMW 2D k k REF G Greenman A Quasi Static Flux Synthesis Temporal Integration Scheme for an Analytic Nodal Method Nuclear Engineer s Thesis Massachusetts Institute of Technology Department of Nuclear Engineering May 1980 k x x Define STRUCTURES and MODULES used x LINKED LIST LMW TRACK MACRO1 SYSTEM1 MACRO2 SVSTEM2 FLUX KINET MODULE GEO MAC TRIVAT TRIVAA FLUD INIKIN KINSOL GREP DELETE END IGE 293 REAL fnorm sigti sigt2 REAL TIME 0 0 PROCEDURE assertS asserts2 LMW GEO CAR2D 6 6 X REFL X ZERO Y REFL Y ZERO MIX111234 111134 115134 611334 333344 444440 MESHX 0 0 10 30 50 70 90 110 MESHY 0 0 10 30 50 70 90 110 SPLITX 222222 SPLITY 2 22222 MACRO1 MAC EDIT O NGRO 2 NMIX 6 READ INPUT MIX 1 DIFF 1 423910E 00 3 563060E 01 TOTAL 2 795756E 02 8 766216E 02 NUSIGF 6 477691E 03 1 127328E 01 H FACTOR 2 591070E 03 4 509310E 02 SCAT 1 1 0 0 2 2 0 0 0 175555E 01 OVERV 0 800E 07 4 000E 06 MIX 2 DIFF 1 423910E 00 3 563060E 01 TOTAL 2 850756E 02 9 146219E 02 NUSIGF 6 477691E 03 1 127328E 01 H FACTOR 2 591070E 03 4 509310E 02 SCAT 1 1 0 0 2 2 0 0 0 175555E 01 OVERV 0 800E 07 4 000E 06 MIX 3 DIFF 1 425610E 00 3 505740E 01 TOTAL 2 817031E 02 9 925634E 02 NU
47. gles 3 for splitting each hexagon into 24 triangles etc The values permitted with the PRIM option are 1 full hexagons and 2 for splitting each hexagon into 6 triangles The values permitted with the Thomas Raviart Schneider method are 1 3 lozenges per hexagon gt 1 for performing a mesh splitting in 3x isplh losanges per hexagon keyword to set a simplified spherical harmonics SP expansion of the flux This option is available with 1D 2D and 3D Cartesian geometries and with 2D and 3D hexagonal geometries order of the P or SP expansion odd number Set to zero for diffusion theory default value keyword to limit the anisotropy of scattering sources keyword to force using 1 3D9 as 34 cross sections A Pi or SP method will therefore behave as diffusion theory number of terms in the scattering sources iscat 1 is used for isotropic scattering in the laboratory system iscat 2 is used for linearly anisotropic scattering in the laboratory system The default value is set to n 1 in P or SP case IGE 293 VOID nvd ADI nadi VECT iseg PRTV impv 23 keyword to set the number of base points in the Gauss Legendre quadrature used to inte grate void boundary conditions if icol 3 and n 0 type of quadrature The values permitted are 0 use a n 2 point quadrature consistent with Pa theory 1 use a n 1 point quadrature consistent with 5 41 theory 2 use an analytical integration of
48. ication of a Dual Variational Formulation to Finite Element Reactor Calcula tions Ann nucl Energy 20 823 1993 A HEBERT The Search for Superconvergence in Spherical Harmonics Approximations Nucl Sci Eng 154 134 2006 A HEBERT Mixed dual implementations of the of the simplified P method Ann nucl Energy 37 498 2010 J H WILKINSON The Algebraic Eigenvalue Problem Clarendon Press Oxford 1965 R ROY Private communication A MONIER Application of the Collocation Technique to the Spatial Discretization of the Gener alized Quasistatic Method for Nuclear Reactors Ph D Thesis Ecole Polytechnique de Montr al Institut de G nie Energ tique December 1991 A BENABOUD R solution de V quation de la diffusion neutronique pour une g om trie hexag onale Ph D Thesis Ecole Polytechnique de Montr al Institut de G nie Energ tique December 1992 A HEBERT A Raviart Thomas Schneider solution of the diffusion equation in hexagonal geom etry Ann nucl Energy 35 363 2008 W H PRESS S A TEUKOLSKY W T VETTERLING and B P FLANNERY Numerical Recipes in FORTRAN Second Edition Chapter 16 Cambridge University Press 1992 J J LAUTARD LOUBIERE and C FEDON MAGNAUD CRONOS a Computational Modu lar System for Neutronic Core Calculations Proc International Atomic Energy Agency Specialists Mtg on Advanced Calculational Methods for Po
49. ions The fixed default value is epsout 1 0 x 1074 The outer iterations are stopped when the following criteria is reached max ire re lt epsout x max re KA 2 where FA cofre i 1 I is the product of the B matrix times the unknown vector at the k th outer iteration keyword to specify that the control parameters for the thermal iterations are to be modified maximum number of thermal iterations The fixed default value is maxthr 0 correspond ing to no thermal iterations convergence criterion for the thermal iterations The fixed default value is epsthr 1 0 x 1072 keyword used to set nadi in cases where Trivac is used number of alternating direction implicit ADI inner iterations per outer iteration The default value is nadi 1 If this value causes a failure of the acceleration process it is recommended that a larger value be tried The optimal choice is generally the minimum value of nadi which allows a convergence in less than 75 outer iterations nadi 1 or nadi 2 is generally the best choice for production type calculations The greater nadi is the smaller the asymptotic convergence constant ACC becomes Taking an arbitrary large value e g nadi 20 leads to numerical results identical to those obtained by inverting the system matrices at each outer iteration at a prohibitive CPU cost In this case the ACC is almost equal to the dominance ratio of the iterative matrix keyword used to obtain
50. lvnomials Bv default ielem 1 tvpe of quadrature used to integrate the mass matrices The values permitted are 1 an alvtical integration 2 Gauss Lobatto quadrature or 3 Gauss Legendre quadrature Bv default icol 2 The analvtical integration corresponds to classical finite elements the Gauss Lobatto quadrature corresponds to a variational or nodal tvpe collocation and the Gauss Legendre quadrature corresponds to superconvergent finite elements type of hexagonal mesh splitting This data is given only if the geometry is 2D hexagonal The values permitted are 1 full hexagons 2 for splitting each hexagon into 6 triangles 3 for splitting each hexagon into 24 triangles 5 for splitting each hexagon into 96 triangles 9 for splitting each hexagon into 384 triangles and 17 for splitting each hexagon into 1536 triangles The values permitted with the Thomas Raviart Schneider method are 1 3 lozanges per hexagon gt 1 for performing a mesh splitting in 3xisplh losanges per hexagon keyword to set a spherical harmonics P expansion of the flux keyword to set a simplified spherical harmonics SP expansion of the flux P 10l This option is currently available with 1D and 2D Cartesian geometries and with 2D hexagonal geometries order of the P or SP expansion odd number Set to zero for diffusion theory default value keyword to limit the anisotropy of scattering sources keyword to force using 1 3D9 as DY cross sections
51. m icol isplh DUAL ielem icol isplh MCFD isplh PN SPN n SCAT DIFF iscat VOID nvd where EDIT keyword used to set iprint iprint index used to control the printing in module BIVACT 0 for no print 1 for minimum printing default value Larger values produce increasing amounts of output IGE 293 TILL TITLE MAXR maxpts PRIM DUAL MCFD ielem icol isplh PN SPN SCAT DIFF iscat VOID nvd 19 kevword which allows the run title to be set the title associated with a TRIVAC run This title mav contain up to 72 characters The default when TITL is not specified is no title kevword which permits the maximum number of regions to be considered during a TRIVAC run to be specified maximum dimensions of the problem to be considered The default value is set to the number of regions previouslv computed bv the GEO module but this value is insufficient if symmetries or mesh splitting are specified kevword to set a primal finite element classical discretization kevword to set a mixed dual finite element discretization If the geometrv is hexagonal a Thomas Raviart Schneider method is used l kevword to set a mesh centered finite difference discretization in hexagonal geometrv order of the finite element representation The values permitted are 1 linear polvno mials 2 parabolic polvnomials 3 cubic polvnomials or 4 quartic po
52. metry must be a square The only combinations of translational symmetry permitted are X TRAN X TRAN Y TRAN Y TRAN and Z TRAN Z TRAN IGE 293 The input corresponding to the descMC structure are the following M I where MIX imix PLANE iplan SAME iplan1 Ip CROWN Ic ALL UPTO ic Table 6 Structure descMC X imix i i 1 lreg PLANE iplan imix i i 1 Jp SAME iplan1 CROWN imix i i 1 lc ALL jmix SAME iplan1 UPTO ic ALL mix SAME iplan1 keyword to attribute an material mixture number to each volume inside the axes of sym metry When a volume is located inside the axes of symmetry but outside the calculation region it must be declared virtual for example the corners of a nuclear reactor The material mixture number should be specified for each volume before mesh splitting type of material mixture associated with a region It is important that imix lt nmixt where nmixt is defined in the module If imix 0 the corresponding volume is replaced by a VOID boundary condition In this case the volume is considered to be virtual and the flux is not calculated In the case of a diagonal symmetry the type indicator must not be specified for the volumes outside the axis of symmetry These values must be specified in the following order from X to X from Y to Y from Z to Z and finally radially from the inside out keyword to attri
53. n If the geometry is hexagonal a Thomas Raviart Schneider method is used kevword to set a discretization based on the nodal collocation method The mesh centered finite difference approximation is the default option and is generallv set using MCFD 1 The MCFD approximations are numericallv equivalent to the DUAL approximations with icol 2 however the MCFD approximations are less expensive kevword to set a discretization based on the nodal collocation method with serendipitv approximation The serendipitv approximation is different from the MCFD option in cases with ielem gt 2 This option is not available for hexagonal geometries order of the finite element representation The values permitted are 1 linear polvnomials 2 parabolic polvnomials 3 cubic polvnomials or 4 quartic polvnomials Bv default ielem 1 type of quadrature used to integrate the mass matrices The values permitted are 1 analytical integration 2 Gauss Lobatto quadrature or 3 Gauss Legendre quadrature By default icol 2 The analytical integration corresponds to classical finite elements the Gauss Lobatto quadrature corresponds to a variational or nodal type collocation and the Gauss Legendre quadrature corresponds to superconvergent finite elements type of hexagonal mesh splitting This data is given only if the geometry is 2D or 3D hexagonal The values permitted with the MCFD option are 1 full hexagons 2 for splitting each hexagon into 6 trian
54. ntaining derivatives or pertur bations of the macroscopic cross sections and diffusion coefficients If DMACRO is given only the derivatives or perturbations of the system matrices are computed trivaa_data structure containing the data to module TRIVAA see Sect 1 8 1 1 8 1 Data input for module TRIVAA Table 18 Structure trivaa_data EDIT iprint SKIP DERI PERT UNIT OVEL ki where EDIT kevword used to set iprint iprint index used to control the printing in module TRIVAA 0 for no print 1 for minimum printing default value Larger values produce increasing amounts of output SKIP kevword used to skip the system matrix assembly but to perform the L D LT factor ization Use the system matrices already present in SYST DERI The information recovered from DMACRO is used as derivatives of nuclear properties with respect to a state variable Derivatives of svstem matrices with respect to the same state variable are computed IGE 293 26 PERT The information recovered from DMACRO is used as the perturbation of the nuclear properties Perturbations of the system matrices are computed UNIT A system matrix corresponding to cross sections all set to 1 0 is computed This keyword is mandatory if the system matrices in SYST are going to be used by INIKIN or KINSOL modules see Sects 1 14 and 1 15 OVEL The reciprocal neutron velocities for each material mixture are recovered from the input
55. olution for precursors is written 1 Seer th A stn 1 Y Ae 1 Os Ore A XB cor tam m L 1 9 1 ONV Dir V g r tn 1 Erol dols tam G DI Bocal atte DGE Ft er y E Or Of ar 1 e7 Atn e xd Felr ta 1 1 10 where the ed fission reaction rates are defined as SB n r tn 1 11 The ete corresponding to the implicit theta solution is presented in Chapter 5 of Ref 1 and is written 1 e Sa r tn a 17 17 Op AeAtn del Vag Ain Eno 1 0p Ae At Xt g 7 celr tn 1 Porta DM 0 l onfv Dy r V s r tn 1 Sig r by Ps tal 1 rat Phl r stn 1 Fx rita kay E fi or or Fr Pato tt 1 12 IGE 293 41 The flux equation at end of step is now presented The equation corresponding to the analytic solution for precursors is written Tar bal stn Or V Da r Vlr tn Or Hrg r del tn n g n G Str tn Or Y senior n r tn E Enr Fr ta OD AE y ar 107 Atn Flt tn 1 13 The equation corresponding to the implicit theta solution is presented in Chapter 5 of Ref 1 and is written 1 Vag Atn q f tn Ot V Da r V g r tn Of Erg 1 g r tr G S r tn Or gt Egealr nlr tn RET h g SS e 1 Or Xg r F r tn 01 xir IFOAM At For tn 1 14 p n The calling specifications are Table 30 Structure KINSOL KINET KINSOL KINET
56. r 12 and is saved in a LCM object or an XSM file under its given name It is always possible to modify a given existing geometry or copy it into a neighbouring LCM object under a new name The calling specifications are Table 2 Structure GEO GEOMI GED geo datal GEOMI GEO GEOMI GEOM2 geo_data2 where GEOMI character 12 name of the LCM object type L GEOM that will contain the geometry GEOM2 character 12 name of a LCM object type L_GEOM containing the existing geometry The type and all the characteristics of GEOM2 will be copied onto GEOMI IGE 293 3 geo datal structure describing the characteristics of a new geometry see Sect 1 3 1 geo_data2 structure describing the change to the characteristics of an existing geometry see Sect 1 3 1 1 3 1 Data input for module GEO Structures geo datal and geo data2 serve to define the principle components of a geometry dimensions materials boundary conditions Table 3 Structure geo datal HOMOGE CAR1D Ix TUBE Ir SPHERE Ir CAR2D Ix ly TUBEZ Ir Iz CAR3D Ix ly Iz HEX Ih HEXZ Ih Iz EDIT iprint descBC descMC descPOS 2 Table 4 Structure geo_data2 EDIT iprint descBC descMC descPOS where HOMOGE infinite homogeneous geometry CAR1D one dimensional plane geometry infinite slabs TUBE cylindrical geometry infinite tubes or cylinders SPHERE spherical geometry
57. r the asvmptotic convergence constant ACC becomes Taking an arbitrarv large value e g nadi 20 leads to numerical results identical to those obtained by inverting the svstem matrices at each outer iteration at a prohibitive CPU cost In this case the ACC is almost equal to the dominance ratio of the iterative matrix The default value is recovered in the state vector of the TRACKING object TRACK IGE 293 44 1 16 The VAL module The VAL module supplies an interpolation of the flux in diffusion calculations for Cartesian geometries The calling specifications are Table 32 Structure VAL IFLU VAL TRKNAM FLUNAM descval where IFLU character 12 name of the INTERPFLUX data structure L FVIEW signature where the interpolated flux distribution will be stored TRKNAM character 12 name of the read only TRACKING data structure L TRACK signature containing the tracking FLUNAM character 12 name of the read only FLUXUNK data structure L FLUX signature con taining a transport solution descval structure containing the input data to this module to compute interpolated flux see Section 1 16 1 1 16 1 Data input for module VAL Table 33 Structure descval EDIT iprint DIM dim dxyz i i 1 dim 7 where EDIT keyword used to modify the print level iprint iprint integer index used to control the printing in module VAL 0 for no print 1 for min imum printing default value larger valu
58. research associates which have contributed to the development of TRIVAC along the years Finally the TRIVAC team would never have survived without the financial support of the Natural Science and Engineering Research Council of Canada NSERC Hydro Qu bec and Atomic Energy of Canada Limited AECL IGE 293 iv SUMMARY TRIVAC is a computer code intended to compute the neutron flux in a fractional or in a full core representation of a nuclear reactor Interested readers can obtain fundamental informations about full core calculations in Chapter 5 of Ref 1 The multigroup and multidimensional form of the diffusion equation or simplified P equation is first discretized to produce a consistent matrix system This ma trix system is subsequently solved using iterative techniques inverse or preconditioned power method with ADI preconditioning and sparse matrix algebra techniques triangular factorization The actual implementation of TRIVAC allows the discretization of 1 D geometries slab and cylindrical 2 D ge ometries Cartesian cylindrical and hexagonal and 3 D geometries Cartesian and hexagonal Many discretization techniques are available including mesh corner or mesh centered finite difference methods collocation techniques of various order and finite element methods based on a primal or dual functional formulation TRIVAC also permits the equations of the generalized perturbation theory GPT to be solved as fixed source eigenvalue pro
59. roup fission spectrum x9 for all the fissile isotopes associated with this mixture keyword to specify that the fixed neutron source density for this mixture follows array representing the multigroup fixed neutron source density for this mixture S9 in Slams stem keyword to specify that the isotropic diffusion coefficient for this mixture follows array representing the multigroup isotropic diffusion coefficient for this mixture D9 in cm keyword for input of the X directed diffusion coefficient array representing the multigroup X directed diffusion coefficient DZ in cm for the mix ture matnum keyword for input of the Y directed diffusion coefficient array representing the multigroup Y directed diffusion coefficient Df in cm for the mix ture matnum keyword for input of the Z directed diffusion coefficient array representing the multigroup Z directed diffusion coefficient DS in cm for the mix ture matnum keyword to specify that the delayed macroscopic fission cross section multiplied by the average number of neutrons per fission for this mixture follows array representing the delayed multigroup macroscopic fission cross section multiplied by the average number of neutrons per fission agian in em for all the fissile isotopes associated with this mixture keyword to specify that the delayed fission spectrum for this mixture follows array representing the delayed multigroup fission spectrum x9 del
60. structure real array representing the delayed multigroup fission spectrum keyword used to normalize the initial flux By default the flux is not normalized real normalization factor keyword used to set the flux normalization factor to 1 fmax where fmax is the maximum flux in the core keyword used to set the flux normalization factor to a given value of the initial power real initial power IGE 293 40 1 15 The KINSOL module The KINSOL module is used to solve the space time neutron kinetics equations at current time step of transient Several implicit numerical schemes are available for this purpose Consider first the differential equation for precursor concentrations Oce r t a Aece r t Voss on r t 1 Na 1 6 h 1 Consider a solution between times n 1 and tn tn 1 Atn First an analytic solution can be obtained by assuming a ramp variation of the fission reaction rates over time step Atn This solution is written Fo r ty 1 atin a re x AR 1 ere Ain e7 Ain Fy r ba 1 Ig Ad 1 et Atm L toa mi 1 7 where the delaved fission reaction rates are defined as Y VS 1 Tr phl r ta AV uma dnl r t A 1 8 An implicit Pan solution is presented in nia 5 of Ref 1 This solution is written ce r tn Re E FE ce r tn 1 ma PR 1 Se Fe r tn Op re Atn re 1 Op Ae Atn where Op is the theta factor for precursors The fixed source corresponding to the analytic s
61. t where pee is computed using the reference powers stored in MACRO1 and Veore is the total volume of the regions where the power density is not equal to zero The normalized remo val rates TA each re ion i and energv group are next computed usin the 1 9 8 By 8 g 8 following formula Leg Lig Daig Pi g Vi 1 norm __ T E TNT i 9 E y Tig g ig where X g is the total macroscopic cross section Xwi g is the within group scattering cross section and Ps is the neutron flux The maximum and averaged errors are respectively defined by 1 9 Tnorm 1 9 norm normx IT o Tig Emax y max 5 _L i and norm norm Tire Tig norm Lig 1 sr where T is computed using the reference values stored in MACRO1 and N is the total number of regions in the MACROLIB The calling specifications are Table 27 Structure ERROR ERROR MACROI MACRO NREG nreg where IGE 293 MACRO1 MACRO2 NREG nreg 37 character 12 name of the LCM object type L MACROLIB containing the extended MACROLIB used to compute the reference reaction rates character 12 name of the LCM object type L MACROLIB containing the extended MACROLIB used to compute the approximate reaction rates keyword used to set the nreg number integer number set to the number of regions used in statistics By default all available regions are used IGE 293 38 1 14 The INIKIN module The INIKIN mod
62. t iprint index iprint integer index used to control the printing in module KINSOL 0 for no print 1 for minimum printing default value larger values of iprint will produce increasing amounts of output DELTA keyword used to set the delta value delta current time increment At of transient SCHEME keyword used to indicate the temporal numerical schemes FLUX keyword used to select the temporal scheme for the fluxes equations PREC keyword used to select the temporal scheme for the precursors equations IMPLIC keyword used to indicate the full implicit temporal scheme CRANK keyword used to indicate the Crank Nicholson temporal scheme EXPON keyword used to indicate the analytical integration scheme for precursors equations THETA keyword used to indicate the general temporal scheme according to the theta method ttflx value of theta parameter Of for the flux equations This value should be greater than 0 5 and less than 1 0 ttprc value of theta parameter for the precursors equations This value should be greater than 0 5 and less than 1 0 VAR1 keyword used to set the parameters icll and icl2 of the symmetrical variational acceler ation technique SVAT ACCE alias keyword for VAR1 icll number of free outer iterations in a cycle of the SVAT The default value is icll 3 icl2 number of accelerated outer iterations in a cycle of the SVAT The default value is icl2 3 A convergence in free iterations is obtained by se
63. t of the cross section information from default input by REDLEC in the TRIVAC 2 format The perturbed nuclear data will be translated into TRIVAC format and printed on the listing trip2 structure describing the format used for reading the mixture values of the perturbed cross sections and diffusion coefficients from the input data file in TRIVAC 2 format 1 4 2 Description of the nuclear data Table 10 Structure macxs MIX matnum NTOTO TOTAL xssigt jg jg 1 ngroup NTOT1 xssigl jg jg 1 ngroup TRANC xsstra jg jg 1 ngroup NUSIGF xssigf jfjg jg 1 ngroup jf 1 nifiss CHI xschi jf jg jg 1 ngroup jf 1 nifiss FIXE xsfixe jg jg 1 ngroup DIFF diff jg jg 1 ngroup DIFFX xdiffx jg jg 1 ngroup DIFFY xdiffy jg jg 1 ngroup DIFFZ xdiffz jg jg 1 ngroup NUSIGD xssigd jf idel jg jg 1 ngroup idel 1 ndel jf 1 nifiss CHDL xschid jf idel jg jg 1 ngroup idel 1 ndel jf 1 nifiss OVERV overv jg jg 1 ngroup H FACTOR xhfact jg jg 1 ngroup SCAT nbscat jl jg ilastg jljg scat jljgig ig 1 nbscat jl jg jg 1 ngroup jl 1 naniso where MIX keyword to specify that the macroscopic cross sections associated with a new mixture are to be read matnum identifier for the next mixture to be read The maximum value permitted for this identifier is nmixt When matnum is absent the mixtures are numbered consecutively starting with 1 or
64. the solution of an direct fixed source eigenvalue problem keyword used to obtain the solution of an adjoint fixed source eigenvalue problem If neither EXPLICIT nor IMPLICIT are provided the default value will be chosen as a function of Nvar and Nest 1 keyword used to specify the numbers of the sources for which a generalized adjoint will be calculated keyword used to recover all sources available in GPT number of the first source number of the last source IGE 293 34 1 12 The OUT module The OUT module is used to compute the reaction rates and to store them in an extended MACROLIB type L_MACROLIB corresponding to a solution type L FLUX of the matrix system The calling specifi cations are Table 25 Structure OUT MACROS OUT FLUX TRACK MACRO GEOM out data where MACRO2 character 12 name of the LCM object type L MACROLIB containing the extended MACROLIB FLUX character 12 name of the LCM object type L_FLUX containing a solution TRACK character 12 name of the LCM object type L TRACK containing a TRACKING MACRO character 12 name of the LCM object type L MACROLIB containing the reference MACROLIB GEOM character 12 name of the LCM object type L_GEOM containing the reference GEOMETRY out data structure containing the data to module OUT 1 12 1 Data input for module OUT Table 26 Structure out_data EDIT iprint DIRE ADJO POWR power INTG IN MI
65. the void boundary conditions By default nvd 0 keyword to set the number of ADI iterations at the inner iterative level number of ADI iterations default nadi 2 keyword to set an ADI preconditionning with supervectorization By default TRIVAC uses an ADI preconditionning without supervectorization width of a vectorial register iseg is generally a multiple of 64 By default iseg 64 keyword used to set impv index used to control the printing in supervectorization subroutines 0 for no print 1 for minimum printing default value Larger values produce increasing amounts of output Various finite element approximations can be obtained by combining different values of ielem and isplh see Sect 1 5 IGE 293 24 1 7 The BIVACA module The BIVACA module is used to compute the finite element system matrices type L SYSTEM corre sponding to a BIVAC TRACKING type L_BIVAC and to a set of nuclear properties type L MACROLIB The calling specifications are Table 15 Structure BIVACA BIVACA SYST MACRO TRACK bivaca_data where SYST character 12 name of the LCM object type L SYSTEM containing the system matrices If SYST appears on the RHS the system matrices previously stored in SYST are kept MACRO character 12 name of the LCM object type L MACROLIB containing the macroscopic cross sections and diffusion coefficients TRACK character 12 name of the LCM object type L_BIVAC containing the BIVAC
66. ti gt gt lt lt sigt2 gt gt SYSTEM2 TRIVAA MACRO2 TRACK EDIT 1 UNIT KINET KINSOL KINET MACRO2 TRACK SYSTEM2 MACRO1 SVSTEMI EDIT 5 DELTA 0 1 SCHEME FLUX CRANK PREC CRANK EXTE 1 0E 6 GREP KINET GETVAL TOTAL TIME 1 gt gt TIME lt lt ECHO TIME TIME S sigt sigti sigt2 IF TIME 1 0 ABS 1 0E 3 lt THEN assertS2 KINET CTRL FLUX 1 1 986270E 02 assertS2 KINET CTRL PREC 1 1 095509E 01 assertS2 KINET E POW 1 1 008753Et04 ELSEIF TIME 5 0 ABS 1 0E 3 lt THEN assertS2 KINET CTRL FLUX 1 2 090369E 02 assertS2 KINET CTRL PREC 1 1 097266E 01 assertS2 KINET E POW 1 1 063990E 04 ELSEIF TIME 10 0 ABS 1 0E 3 lt THEN assertS2 KINET CTRL FLUX 1 2 305455E 02 assertS2 KINET CTRL PREC 1 1 104699E 01 55 IGE 293 assertS2 KINET E POW ELSEIF TIME 15 0 ABS 1 0E 3 lt assertS2 KINET CTRL FLUX assertS2 KINET CTRL PREC assertS2 KINET E POW ELSEIF TIME 20 0 ABS 1 0E 3 lt assertS2 KINET CTRL FLUX assertS2 KINET CTRL PREC assertS2 KINET E POW ELSEIF TIME 25 0 ABS 1 0E 3 lt assertS2 KINET CTRL FLUX assertS2 KINET CTRL PREC assertS2 KINET E POW ELSEIF TIME 26 7 ABS 1 0E 3 lt assertS2 KINET CTRL FLUX assertS2 KINET CTRL PREC assertS2 KINET E POW ENDIF 1 1 176902E 04 THEN 1 2 641221E 02 1 1 121002E 01 1 1 352433E 04 THEN 1 3 1
67. tting icll 200 or icll maxx0 and icl2 0 IGE 293 EXTE maxout epsout THER maxthr epsthr ADI nadi 43 keyword to specify that the control parameters for the external iteration are to be modified maximum number of external iterations The fixed default value is maxout 200 convergence criterion for the external iterations The fixed default value is epsout 1 0 x 107 The outer iterations are stopped when the following criteria is reached max jo DU lt epsout x max o where Q F core i 1 1 is the product of the B matrix times the unknown vector at the k th outer iteration keyword to specify that the control parameters for the thermal iterations are to be modified maximum number of thermal iterations The fixed default value is maxthr 0 correspond ing to no thermal iterations convergence criterion for the thermal iterations The fixed default value is epsthr 1 0 x 1077 kevword used to set nadi in cases where Trivac is used number of alternating direction implicit ADI inner iterations per outer iteration The default value is nadi 1 If this value causes a failure of the acceleration process it is recommended that a larger value be tried The optimal choice is generallv the minimum value of nadi which allows a convergence in less than 75 outer iterations nadi 1 or nadi 2 is generallv the best choice for production tvpe calculations The greater nadi is the smalle
68. ule is used to recover the steady state solution and to initialize the kinetics param eters The delayed neutron information can be provided directly from the input file or recovered from the MACROLIB data structure The initial presursor concentrations are obtained as a function of the strady state solution If r to is the initial flux in energy group g divided by keg the corresponding initial conditions of the precursors are obtained as r to Ly 0 on r to L 1 Na 1 5 where v de r is v times the delayed macroscopic fission cross section in energy group h for precursor group The calling specifications are Table 28 Structure INIKIN KINET INIKIN MACRO TRACK SYST FLUX inikin_data where KINET character 12 name of the LCM object type L_KINET to be created by the module MACRO character 12 name of the LCM object type L MACROLIB containing the MACROLIB infor mation TRACK character 12 name of the LCM object type L_TRACK containing the TRACKING informa tion SYST character 12 name of the LCM object type L SYSTEM corresponding to MACROLIB MACRO and TRACKING TRACK FLUX character 12 name of the LCM object type L FLUX containing the initial steady state solution inikin_data structure containing the data to module INIKIN see Sect 1 14 1 1 14 1 Data input for module INIKIN Table 29 Structure inikin_data EDIT iprint NGRP ngrp NDEL ndg BETA beta i i 1 ndg
69. urce vector is orthogonal to the unperturbed adjoint flux In the adjoint case the fixed source is computed as S 5A 6B amp A BI 1 2 where the adjoint source vector S is orthogonal to the unperturbed direct flux and where dA is the perturbation of the eigenvalue as computed from the Rayleigh ratio The calling specifications are Table 21 Structure DELTA GPT DELTA GPT FLUXO SYSTO DSYST TRACK delta data where GPT character 12 name of the LCM object type L GPT containing the fixed source If GPT appears on the RHS this information is used to initialize the state vector FLUXO character 12 name of the LCM object type L FLUX containing the unperturbed flux SYSTO character 12 name of the LCM object type L SVSTEM containing the unperturbed system matrices DSYST character 12 name of the LCM object type L SYSTEM containing a perturbation to the system matrices TRACK character 12 name of the LCM object type L TRACK containing the TRACKING delta data structure containing the data to module DELTA see Sect 1 10 1 1 10 1 Data input for module DELTA Table 22 Structure delta_data EDIT iprint ADJ 7 where IGE 293 EDIT iprint ADJ kevword used to set iprint index used to control the printing in module DELTA kevword used to set the source on an adjoint fixed source eigenvalue problem 31 IGE 293 32 1 11
70. wer Reactors Cadarache France September 1990 Argonne Code Center Benchmark Problem Book ANL 7416 Supp 2 ID11 A2 Argonne National Laboratory 1977 G GREENMAN A Quasi Static Flux Synthesis Temporal Integration Scheme for an Analytic Nodal Method Nuclear Engineer s Thesis Massachusetts Institute of Technology Department of Nuclear Engineering May 1980 IGE 293 Index tencia 02 98 isre2 32 lreg 10 2 13 18 21 24 25 27 30 32 34 36 38 41 44 2 13 18 21 24 25 27 30 32 34 38 41 44 voll ACCE 27 28 32 33 42 ACYL 4 5 ADI 21 23 27 28 32 83 42 43 ADJ 27 28 90 31 ADJO 34 ALBE 4 5 albedo 4 5 albedp 13 14 ALBP 13 14 ALL 9 32 33 ANG 4 8 ang 4 8 ANIS 13 14 BETA 38 39 beta 38 39 BIVACA 24 BIVACA 24 bivaca data 24 BIVACT 18 BIVACT 18 bivact data 18 CAR1D 3 11 CAR2D 3 5 8 11 CAR3D 3 5 8 10 11 CHDL 15 16 CHI 15 16 CHID 38 39 chid 38 39 COMPLETE 4 5 9 CRANK 42 CROWN 9 CYLI 4 5 DELP 13 14 DELTA 42 delta 42 DELTA 30 DELTA 30 delta_data 30 DERI 25 descBC 3 4 descMC 3 4 9 descPOS 3 4 10 descval 44 58 DIAG 4 5 8 10 DIFF 15 16 18 19 21 22 diff 15 16 DIFFX 15 16 DIFFY 15 16 DIFFZ 15 16 DIM 44 dim 44 DIRE 34 DMACRO 25 26 DOLD 13 15 DSYST 30 DUAL 18 19 21 22 dxyz 44 EDIT 3 4 13 18

A USER GUIDE FOR TRIVAC VERSION4 A. Hébert

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A USER GUIDE FOR TRIVAC VERSION4 A. H&eacute;bert

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A USER GUIDE FOR TRIVAC VERSION4 A. Hébert