\section{EXAMPLES OF INPUT DATA FILES} \subsection{IAEA-2D benchmark} The IAEA-2D benchmark is defined in Refs.~\citen{bivac,anl} and its geometry is represented in Fig.~\fig(iaea2d). Here, it is solved using a parabolic variational collocation method without mesh splitting of the elements: \begin{figure}[htbp] \begin{center} \epsfxsize=8.0cm \centerline{ \epsffile{iaea2d.eps}} \parbox{14cm}{\caption{Description of the IAEA-2D benchmark.}\label{fig:iaea2d}} \end{center} \end{figure} \begin{verbatim} LINKED_LIST IAEA MACRO TRACK SYSTEM FLUX EDIT ; MODULE GEO: MAC: TRIVAT: TRIVAA: FLUD: OUT: END: ; * IAEA := GEO: :: CAR2D 9 9 EDIT 2 X- DIAG X+ VOID Y- SYME Y+ DIAG MIX 3 2 2 2 3 2 2 1 4 2 2 2 2 2 2 1 4 2 2 2 2 1 1 4 2 2 2 1 4 4 3 1 1 4 0 1 4 4 0 4 0 0 0 0 0 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 1 1 0.0 2 2 0.0 0.2E-01 MIX 2 DIFF 1.500E+00 4.0000E-01 TOTAL 3.012E-02 8.5032E-02 NUSIGF 0.000E+00 1.3500E-01 H-FACTOR 0.000E+00 1.3500E-01 SCAT 1 1 0.0 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 MIX 4 DIFF 2.000E+00 3.0000E-01 TOTAL 4.016E-02 1.0024E-02 SCAT 1 1 0.0 2 2 0.0 0.4E-01 ; TRACK := TRIVAT: IAEA :: TITLE 'IAEA-2D BENCHMARK' MAXR 81 PRIM 2 ; SYSTEM := TRIVAA: MACRO TRACK :: ; FLUX := FLUD: SYSTEM :: EDIT 2 ; EDIT := OUT: FLUX :: EDIT 2 INTG 1 2 3 4 5 6 7 8 0 9 10 11 12 13 14 15 0 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 ; END: ; \end{verbatim} \subsection{Biblis-2D benchmark} The rods-withdrawn configuration of the Biblis-2D benchmark is defined in Ref.~\citen{bivac} and its geometry is represented in Fig.~\fig(biblis). Here, it is solved using a parabolic variational collocation method without mesh splitting of the elements: \begin{figure}[htbp] \begin{center} \epsfxsize=8.0cm \centerline{ \epsffile{biblis.eps}} \parbox{14cm}{\caption{Description of the Biblis-2D benchmark, rods-withdrawn configuration.}\label{fig:biblis}} \end{center} \end{figure} \begin{verbatim} LINKED_LIST BIBLIS MACRO TRACK SYSTEM FLUX EDIT ; MODULE GEO: MAC: TRIVAT: TRIVAA: FLUD: OUT: END: ; * BIBLIS := GEO: :: CAR2D 9 9 EDIT 2 X- DIAG X+ VOID Y- SYME Y+ DIAG MIX 1 8 2 6 1 7 1 4 3 1 8 2 8 1 1 4 3 1 8 2 7 1 4 3 2 8 1 8 4 3 2 5 4 3 3 4 4 3 0 3 3 0 0 0 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 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 DIFF 1.438500E+00 3.665000E-01 TOTAL 2.732400E-02 8.731400E-02 NUSIGF 6.428500E-03 1.091100E-01 H-FACTOR 2.602600E-03 4.417400E-02 SCAT 1 1 0.0 2 2 0.0 1.719200E-02 MIX 7 DIFF 1.438900E+00 3.679000E-01 TOTAL 2.729000E-02 8.802400E-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 1.712500E-02 MIX 8 DIFF 1.439300E+00 3.680000E-01 TOTAL 2.732100E-02 9.051000E-02 NUSIGF 6.428500E-03 1.091100E-01 H-FACTOR 2.602600E-03 4.417400E-02 SCAT 1 1 0.0 2 2 0.0 1.702700E-02 ; TRACK := TRIVAT: BIBLIS :: TITLE 'BIBLIS BENCHMARK' EDIT 5 MAXR 81 PRIM 2 ; SYSTEM := TRIVAA: MACRO TRACK :: EDIT 5 ; FLUX := FLUD: SYSTEM :: EDIT 2 ; EDIT := OUT: FLUX :: EDIT 2 INTG 1 2 3 4 5 6 7 8 0 9 10 11 12 13 14 15 0 16 17 18 19 20 21 0 22 23 24 25 26 0 27 28 29 0 0 30 31 0 0 0 0 0 0 0 0 ; END: ; \end{verbatim} \eject \subsection{IAEA-3D benchmark} The IAEA-3D benchmark is defined in Ref.~\citen{anl} and its geometry is represented in Fig.~\fig(iaea3d). Here, it is solved using a cubic mixed-dual method with mesh splitting of the second axial plane: \begin{figure}[htbp] \begin{center} \epsfxsize=15cm \centerline{ \epsffile{iaea3d.eps}} \parbox{14cm}{\caption{Description of the IAEA-3D benchmark.}\label{fig:iaea3d}} \end{center} \end{figure} \begin{verbatim} 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 Z+ 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 1 *) MIX 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 4 4 4 0 4 0 0 0 0 0 (* PLANE NB 2 *) 3 2 2 2 3 2 2 1 4 2 2 2 2 2 2 1 4 2 2 2 2 1 1 4 2 2 2 1 4 4 3 1 1 4 0 1 4 4 0 4 0 0 0 0 0 (* PLANE NB 3 *) 3 2 2 2 3 2 2 1 4 2 2 2 2 2 2 1 4 3 2 2 2 1 1 4 2 2 2 1 4 4 3 1 1 4 0 1 4 4 0 4 0 0 0 0 0 (* PLANE NB 4 *) 5 4 4 4 5 4 4 4 4 4 4 4 4 4 4 4 4 5 4 4 4 4 4 4 4 4 4 4 4 4 5 4 4 4 0 4 4 4 0 4 0 0 0 0 0 ; MACRO := MAC: :: EDIT 2 NGRO 2 NMIX 5 READ INPUT MIX 1 DIFF 1.500E+00 4.0000E-01 TOTAL 3.000E-02 8.0000E-02 NUSIGF 0.000E+00 1.3500E-01 H-FACTOR 0.000E+00 1.3500E-01 SCAT 1 1 0.0 2 2 0.0 0.2E-01 MIX 2 DIFF 1.500E+00 4.0000E-01 TOTAL 3.000E-02 8.5000E-02 NUSIGF 0.000E+00 1.3500E-01 H-FACTOR 0.000E+00 1.3500E-01 SCAT 1 1 0.0 2 2 0.0 0.2E-01 MIX 3 DIFF 1.500E+00 4.00000E-01 TOTAL 3.000E-02 1.30000E-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 MIX 4 DIFF 2.000E+00 3.0000E-01 TOTAL 4.000E-02 1.0000E-02 SCAT 1 1 0.0 2 2 0.0 0.4E-01 MIX 5 DIFF 2.000E+00 3.0000E-01 TOTAL 4.000E-02 5.5000E-02 SCAT 1 1 0.0 2 2 0.0 0.4E-01 ; 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 *) 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (* PLANE NB 2 *) 1 2 3 4 5 6 7 8 0 9 10 11 12 13 14 15 0 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 0 45 46 47 48 49 50 0 51 52 53 54 0 0 55 56 57 0 0 58 0 0 0 0 0 0 0 0 0 (* PLANE NB 4 *) 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ; END: ; \end{verbatim} \subsection{S30 hexagonal benchmark in 2-D} The S30 hexagonal benchmark in 2-D is defined in Ref.~\citen{benaboud}. Its geometry is represented in Fig.~\fig(hexS30). Here, it is solved using a mesh centered finite difference method without mesh splitting of the hexagonal elements: \begin{figure}[htbp] \begin{center} \epsfxsize=6cm \centerline{ \epsffile{hexS30.eps}} \parbox{14cm}{\caption{Description of the S30 hexagonal benchmark.}\label{fig:hexS30}} \end{center} \end{figure} \begin{verbatim} LINKED_LIST HEX MACRO TRACK SYSTEM FLUX EDIT ; MODULE GEO: MAC: TRIVAT: TRIVAA: FLUD: OUT: END: ; * HEX := GEO: :: HEX 6 EDIT 2 HBC S30 ZERO SIDE 13.044 SPLITH 0 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 1 1 0.0 2 2 0.0 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 1 1 0.0 2 2 0.0 0.2E-01 MIX 3 DIFF 2.0E+00 3.0E-01 TOTAL 4.0E-02 1.0E-02 SCAT 1 1 0.0 2 2 0.0 0.4E-01 ; TRACK := TRIVAT: HEX :: TITLE 'S30 HEXAGONAL BENCHMARK IN 2-D.' EDIT 5 MAXR 50 MCFD (* IELEM= *) 1 ; SYSTEM := TRIVAA: MACRO TRACK :: EDIT 5 ; FLUX := FLUD: SYSTEM :: EDIT 2 ; EDIT := OUT: FLUX :: EDIT 2 INTG IN ; END: ; \end{verbatim} \subsection{LMW benchmark in 2-D} The LMW benchmark in 2-D is a space-time kinetics problem introduced by Greenman\cite{greenman} and used by Monier\cite{monier}. Its geometry is represented in Fig.~\fig(lmw). Here, it is solved using a parabolic nodal collocation method with $2\times 2$ 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 negative ramp variation in total cross section. \begin{figure}[htbp] \begin{center} \epsfxsize=7cm \centerline{ \epsffile{lmw.eps}} \parbox{14cm}{\caption{Description of the LMW benchmark in 2-D.}\label{fig:lmw}} \end{center} \end{figure} \goodbreak \begin{verbatim} *---- * TEST CASE LMW 2D * * 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). * *---- * Define STRUCTURES and MODULES used *---- LINKED_LIST LMW TRACK MACRO1 SYSTEM1 MACRO2 SYSTEM2 FLUX KINET ; MODULE GEO: MAC: TRIVAT: TRIVAA: FLUD: INIKIN: KINSOL: GREP: DELETE: END: ; REAL fnorm sigt1 sigt2 ; REAL TIME := 0.0 ; PROCEDURE assertS assertS2 ; * LMW := GEO: :: CAR2D 6 6 X- REFL X+ ZERO Y- REFL Y+ ZERO MIX 1 1 1 2 3 4 1 1 1 1 3 4 1 1 5 1 3 4 6 1 1 3 3 4 3 3 3 3 4 4 4 4 4 4 4 0 MESHX 0.0 10. 30. 50. 70. 90. 110. MESHY 0.0 10. 30. 50. 70. 90. 110. SPLITX 2 2 2 2 2 2 SPLITY 2 2 2 2 2 2 ; MACRO1 := MAC: :: EDIT 0 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 NUSIGF 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 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 1 MAXR 144 MCFD 2 ; SYSTEM1 := TRIVAA: MACRO1 TRACK :: EDIT 1 UNIT ; FLUX := FLUD: SYSTEM1 TRACK :: EDIT 1 EXTE 5.0E-7 ; assertS FLUX :: 'K-EFFECTIVE' 1 1.014803 ; *---- * Crank-Nicholson space-time kinetics *---- 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 sigt1 := 2.850756E-02 ; EVALUATE sigt2 := 9.146217E-02 ; WHILE TIME 26.7 <= DO EVALUATE sigt1 := sigt1 5.5E-4 0.1 26.7 / * - ; EVALUATE sigt2 := sigt2 3.8E-3 0.1 26.7 / * - ; MACRO2 := MAC: MACRO1 :: EDIT 0 READ INPUT MIX 6 TOTAL <> <> ; SYSTEM2 := TRIVAA: MACRO2 TRACK :: EDIT 1 UNIT ; KINET := KINSOL: KINET MACRO2 TRACK SYSTEM2 MACRO1 SYSTEM1 :: EDIT 5 DELTA 0.1 SCHEME FLUX CRANK PREC CRANK EXTE 1.0E-6 ; GREP: KINET :: GETVAL 'TOTAL-TIME' 1 >>TIME<< ; ECHO "TIME=" TIME "S" "sigt=" sigt1 sigt2 ; IF TIME 1.0 - ABS 1.0E-3 < THEN assertS2 KINET :: 'CTRL-FLUX' 1 1.986270E+02 ; assertS2 KINET :: 'CTRL-PREC' 1 1.095509E-01 ; assertS2 KINET :: 'E-POW' 1 1.008753E+04 ; ELSEIF TIME 5.0 - ABS 1.0E-3 < 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 < THEN assertS2 KINET :: 'CTRL-FLUX' 1 2.305455E+02 ; assertS2 KINET :: 'CTRL-PREC' 1 1.104699E-01 ; assertS2 KINET :: 'E-POW' 1 1.176902E+04 ; ELSEIF TIME 15.0 - ABS 1.0E-3 < THEN assertS2 KINET :: 'CTRL-FLUX' 1 2.641221E+02 ; assertS2 KINET :: 'CTRL-PREC' 1 1.121002E-01 ; assertS2 KINET :: 'E-POW' 1 1.352433E+04 ; ELSEIF TIME 20.0 - ABS 1.0E-3 < THEN assertS2 KINET :: 'CTRL-FLUX' 1 3.157370E+02 ; assertS2 KINET :: 'CTRL-PREC' 1 1.150681E-01 ; assertS2 KINET :: 'E-POW' 1 1.621938E+04 ; ELSEIF TIME 25.0 - ABS 1.0E-3 < THEN assertS2 KINET :: 'CTRL-FLUX' 1 3.971426E+02 ; assertS2 KINET :: 'CTRL-PREC' 1 1.200883E-01 ; assertS2 KINET :: 'E-POW' 1 2.047011E+04 ; ELSEIF TIME 26.7 - ABS 1.0E-3 < THEN assertS2 KINET :: 'CTRL-FLUX' 1 4.351272E+02 ; assertS2 KINET :: 'CTRL-PREC' 1 1.224600E-01 ; assertS2 KINET :: 'E-POW' 1 2.245449E+04 ; ENDIF ; MACRO1 SYSTEM1 := DELETE: MACRO1 SYSTEM1 ; MACRO1 := MACRO2 ; SYSTEM1 := SYSTEM2 ; MACRO2 SYSTEM2 := DELETE: MACRO2 SYSTEM2 ; ENDWHILE ; ECHO "test lmw2D completed" ; \end{verbatim}