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|
*DECK KINSLB
SUBROUTINE KINSLB (IPTRK,IPSYS,IPKIN,LL4,ITY,NUN,NGR,IFL,IPR,IEXP,
1 NBM,NBFIS,NDG,ICL1,ICL2,IMPX,IMPH,TITR,EPS2,MAXINR,EPSINR,MAXX0,
2 PDC,TTF,TTP,DT,OVR,CHI,CHD,SGF,SGD,OMEGA,EVECT,SRC)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Solution of the kinetics multigroup linear systems for the transient
* neutron fluxes in Bivac. Use the inverse power method with a
* two-parameter SVAT acceleration technique.
*
*Copyright:
* Copyright (C) 2010 Ecole Polytechnique de Montreal
* This library 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
*
*Author(s): A. Hebert
*
*Parameters: input
* IPTRK L_TRACK pointer to the tracking information.
* IPSYS L_SYSTEM pointer to system matrices.
* IPKIN L_KINET pointer to the KINET object.
* LL4 order of the system matrices.
* ITY type of solution (1: classical Bivac/diffusion;
* 11: Bivac/SPN).
* NUN number of unknowns in each energy group.
* NGR number of energy groups.
* IFL integration scheme for fluxes: =1 implicit;
* =2 Crank-Nicholson; =3 theta.
* IPR integration scheme for precursors: =1 implicit;
* =2 Crank-Nicholson; =3 theta; =4 exponential.
* IEXP exponential transformation flag (=1 to activate).
* NBM number of material mixtures.
* NBFIS number of fissile isotopes.
* NDG number of delayed-neutron groups.
* ICL1 number of free iterations in one cycle of the inverse power
* method
* ICL2 number of accelerated iterations in one cycle
* IMPX print parameter. =0: no print ; =1: minimum printing ;
* =2: iteration history is printed. =3: solution is printed
* IMPH =0: no action is taken
* =1: the flux is compared to a reference flux stored on lcm
* =2: the convergence histogram is printed
* =3: the convergence histogram is printed with axis and
* titles. The plotting file is completed
* =4: the convergence histogram is printed with axis, acce-
* leration factors and titles. The plotting file is
* completed
* TITR character*72 title
* EPS2 convergence criteria for the flux
* MAXINR maximum number of thermal iterations.
* EPSINR thermal iteration epsilon.
* MAXX0 maximum number of outer iterations
* PDC precursor decay constants.
* TTF value of theta-parameter for fluxes.
* TTP value of theta-parameter for precursors.
* DT current time increment.
* OVR reciprocal neutron velocities/DT.
* CHI steady-state fission spectrum.
* CHD delayed fission spectrum
* SGF nu*fission macroscopic x-sections/keff.
* SGD delayed nu*fission macroscopic x-sections/keff.
* OMEGA exponential transformation parameter.
* SRC fixed source
*
*Parameters: output
* EVECT converged solution
*
*References:
* A. H\'ebert, 'Preconditioning the power method for reactor
* calculations', Nucl. Sci. Eng., 94, 1 (1986).
*
*-----------------------------------------------------------------------
*
USE GANLIB
*----
* SUBROUTINE ARGUMENTS
*----
CHARACTER TITR*72
TYPE(C_PTR) IPTRK,IPSYS,IPKIN
INTEGER LL4,ITY,NUN,NGR,IFL,IPR,IEXP,NBM,NBFIS,NDG,ICL1,ICL2,IMPX,
1 IMPH,MAXINR,MAXX0
REAL EPS2,EPSINR,PDC(NDG),TTF,TTP,DT,OVR(NBM,NGR),
1 CHI(NBM,NBFIS,NGR),CHD(NBM,NBFIS,NGR,NDG),SGF(NBM,NBFIS,NGR),
2 SGD(NBM,NBFIS,NGR,NDG),OMEGA(NBM,NGR),EVECT(NUN,NGR)
DOUBLE PRECISION SRC(NUN,NGR)
*----
* LOCAL VARIABLES
*----
CHARACTER*12 TEXT12
LOGICAL LOGTES,LMPH
DOUBLE PRECISION D2F(2,3),ALP,BET,DTF,DTP,DARG,DK
REAL ERR(250),ALPH(250),BETA(250),TKT,TKB
INTEGER ITITR(18)
REAL, DIMENSION(:,:), ALLOCATABLE :: GRAD1,GRAD2
DOUBLE PRECISION, DIMENSION(:,:), ALLOCATABLE :: GAR1,GAR2,GAR3
REAL, DIMENSION(:), ALLOCATABLE :: WORK1,WORK2,WORK3,WORK4
DATA EPS1,MMAXX/1.0E-4,250/
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(GRAD1(NUN,NGR),GRAD2(NUN,NGR),GAR1(NUN,NGR),
1 GAR2(NUN,NGR),GAR3(NUN,NGR),WORK1(LL4),WORK2(LL4),WORK3(NBM))
*
CALL MTOPEN(IMPX,IPTRK,LL4)
IF(LL4.GT.NUN) CALL XABORT('KINSLB: INVALID NUMBER OF UNKNOWNS.')
*----
* INVERSE POWER METHOD.
*----
DTF=9999.0D0
DTP=9999.0D0
TEST=0.0
IF(IFL.EQ.1)THEN
DTF=1.0D0
ELSEIF(IFL.EQ.2)THEN
DTF=0.5D0
ELSEIF(IFL.EQ.3)THEN
DTF=DBLE(TTF)
ENDIF
IF(IPR.EQ.2)THEN
DTP=0.5D0
ELSEIF(IPR.EQ.3)THEN
DTP=DBLE(TTP)
ENDIF
DCRIT=MINVAL(DT*PDC(:))
*
ISTART=1
IF(IMPX.GE.1) WRITE (6,600)
IF(IMPX.GE.2) WRITE (6,610)
M=0
10 M=M+1
*
DO 84 IGR=1,NGR
WRITE(TEXT12,'(1HA,2I3.3)') IGR,IGR
CALL MTLDLM(TEXT12,IPTRK,IPSYS,LL4,ITY,EVECT(1,IGR),WORK1)
DO 15 IND=1,LL4
GAR1(IND,IGR)=DTF*WORK1(IND)
15 CONTINUE
IF(IEXP.EQ.0) THEN
DO 16 IBM=1,NBM
WORK3(IBM)=OVR(IBM,IGR)
16 CONTINUE
ELSE
DO 17 IBM=1,NBM
WORK3(IBM)=OVR(IBM,IGR)*(1.0+OMEGA(IBM,IGR)*DT)
17 CONTINUE
ENDIF
CALL KINBLM(IPTRK,NBM,LL4,WORK3,EVECT(1,IGR),WORK1)
DO 20 IND=1,LL4
GAR1(IND,IGR)=GAR1(IND,IGR)+WORK1(IND)
20 CONTINUE
DO 83 JGR=1,NGR
IF(JGR.EQ.IGR) GO TO 40
WRITE(TEXT12,'(1HA,2I3.3)') IGR,JGR
CALL LCMLEN(IPSYS,TEXT12,ILONG,ITYLCM)
IF(ILONG.EQ.0) GO TO 40
CALL MTLDLM(TEXT12,IPTRK,IPSYS,LL4,ITY,EVECT(1,JGR),WORK1)
DO 30 IND=1,LL4
GAR1(IND,IGR)=GAR1(IND,IGR)-DTF*WORK1(IND)
30 CONTINUE
40 DO 82 IFIS=1,NBFIS
DO 50 IBM=1,NBM
WORK3(IBM)=CHI(IBM,IFIS,IGR)*SGF(IBM,IFIS,JGR)
50 CONTINUE
CALL KINBLM(IPTRK,NBM,LL4,WORK3,EVECT(1,JGR),WORK1)
DO 60 IND=1,LL4
GAR1(IND,IGR)=GAR1(IND,IGR)-DTF*WORK1(IND)
60 CONTINUE
DO 81 IDG=1,NDG
DARG=PDC(IDG)*DT
IF(IPR.EQ.1)THEN
DK=1.0D0/(1.0D0+DARG)
ELSEIF(IPR.EQ.4)THEN
DK=(1.0D0-DEXP(-DARG))/DARG
ELSE
DK=1.0D0/(1.0D0+DTP*DARG)
ENDIF
DO 70 IBM=1,NBM
WORK3(IBM)=CHD(IBM,IFIS,IGR,IDG)*SGD(IBM,IFIS,JGR,IDG)
70 CONTINUE
CALL KINBLM(IPTRK,NBM,LL4,WORK3,EVECT(1,JGR),WORK1)
DO 80 IND=1,LL4
GAR1(IND,IGR)=GAR1(IND,IGR)+DTF*DK*WORK1(IND)
80 CONTINUE
81 CONTINUE
82 CONTINUE
83 CONTINUE
84 CONTINUE
*----
* DIRECTION EVALUATION.
*----
DO 120 IGR=1,NGR
DO 90 IND=1,LL4
GRAD1(IND,IGR)=REAL(SRC(IND,IGR)-GAR1(IND,IGR))
90 CONTINUE
DO 110 JGR=1,IGR-1
WRITE(TEXT12,'(1HA,2I3.3)') IGR,JGR
CALL LCMLEN(IPSYS,TEXT12,ILONG,ITYLCM)
IF(ILONG.EQ.0) GO TO 110
CALL MTLDLM(TEXT12,IPTRK,IPSYS,LL4,ITY,GRAD1(1,JGR),WORK1)
DO 100 IND=1,LL4
GRAD1(IND,IGR)=GRAD1(IND,IGR)+REAL(DTF)*WORK1(IND)
100 CONTINUE
110 CONTINUE
CALL KDRCPU(TK2)
TKB=TKB+(TK2-TK1)
*
CALL KDRCPU(TK1)
WRITE(TEXT12,'(1HA,2I3.3)') IGR,IGR
CALL MTLDLS(TEXT12,IPTRK,IPSYS,LL4,ITY,GRAD1(1,IGR))
CALL KDRCPU(TK2)
DO 115 IND=1,LL4
GRAD1(IND,IGR)=GRAD1(IND,IGR)/REAL(DTF)
115 CONTINUE
TKT=TKT+(TK2-TK1)
120 CONTINUE
*----
* PERFORM THERMAL (UP-SCATTERING) ITERATIONS
*----
KTER=0
NADI=5 ! used with SPN approximations
IF(MAXINR.GT.1) THEN
CALL FLDBHR(IPTRK,IPSYS,.FALSE.,LL4,ITY,NUN,NGR,ICL1,ICL2,IMPX,
1 NADI,MAXINR,EPSINR,KTER,TKT,TKB,GRAD1)
ENDIF
*----
* EVALUATION OF THE DISPLACEMENT AND OF THE TWO ACCELERATION PARAMETERS
* ALP AND BET.
*----
DO 204 IGR=1,NGR
WRITE(TEXT12,'(1HA,2I3.3)') IGR,IGR
CALL MTLDLM(TEXT12,IPTRK,IPSYS,LL4,ITY,GRAD1(1,IGR),WORK1)
DO 130 IND=1,LL4
GAR2(IND,IGR)=DTF*WORK1(IND)
130 CONTINUE
IF(IEXP.EQ.0) THEN
DO 135 IBM=1,NBM
WORK3(IBM)=OVR(IBM,IGR)
135 CONTINUE
ELSE
DO 136 IBM=1,NBM
WORK3(IBM)=OVR(IBM,IGR)*(1.0+OMEGA(IBM,IGR)*DT)
136 CONTINUE
ENDIF
CALL KINBLM(IPTRK,NBM,LL4,WORK3,GRAD1(1,IGR),WORK1)
DO 140 IND=1,LL4
GAR2(IND,IGR)=GAR2(IND,IGR)+WORK1(IND)
140 CONTINUE
DO 203 JGR=1,NGR
IF(JGR.EQ.IGR) GO TO 160
WRITE(TEXT12,'(1HA,2I3.3)') IGR,JGR
CALL LCMLEN(IPSYS,TEXT12,ILONG,ITYLCM)
IF(ILONG.EQ.0) GO TO 160
CALL MTLDLM(TEXT12,IPTRK,IPSYS,LL4,ITY,GRAD1(1,JGR),WORK1)
DO 150 IND=1,LL4
GAR2(IND,IGR)=GAR2(IND,IGR)-DTF*WORK1(IND)
150 CONTINUE
160 DO 202 IFIS=1,NBFIS
DO 170 IBM=1,NBM
WORK3(IBM)=CHI(IBM,IFIS,IGR)*SGF(IBM,IFIS,JGR)
170 CONTINUE
CALL KINBLM(IPTRK,NBM,LL4,WORK3,GRAD1(1,JGR),WORK1)
DO 180 IND=1,LL4
GAR2(IND,IGR)=GAR2(IND,IGR)-DTF*WORK1(IND)
180 CONTINUE
DO 201 IDG=1,NDG
DARG=PDC(IDG)*DT
IF(IPR.EQ.1)THEN
DK=1.0D0/(1.0D0+DARG)
ELSEIF(IPR.EQ.4)THEN
DK=(1.0D0-DEXP(-DARG))/DARG
ELSE
DK=1.0D0/(1.0D0+DTP*DARG)
ENDIF
DO 190 IBM=1,NBM
WORK3(IBM)=CHD(IBM,IFIS,IGR,IDG)*SGD(IBM,IFIS,JGR,IDG)
190 CONTINUE
CALL KINBLM(IPTRK,NBM,LL4,WORK3,GRAD1(1,JGR),WORK1)
DO 200 IND=1,LL4
GAR2(IND,IGR)=GAR2(IND,IGR)+DTF*DK*WORK1(IND)
200 CONTINUE
201 CONTINUE
202 CONTINUE
203 CONTINUE
204 CONTINUE
*
270 ALP=1.0D0
BET=0.0D0
D2F(:2,:3)=0.0D0
IF(1+MOD(M-ISTART,ICL1+ICL2).GT.ICL1) THEN
IF(DCRIT.GT.1.0E-6) THEN
* TWO-PARAMETER ACCELERATION. SOLUTION OF A LINEAR SYSTEM.
DO 285 IGR=1,NGR
DO 280 I=1,LL4
D2F(1,1)=D2F(1,1)+GAR2(I,IGR)**2
D2F(1,2)=D2F(1,2)+GAR2(I,IGR)*GAR3(I,IGR)
D2F(2,2)=D2F(2,2)+GAR3(I,IGR)**2
D2F(1,3)=D2F(1,3)-(GAR1(I,IGR)-SRC(I,IGR))*GAR2(I,IGR)
D2F(2,3)=D2F(2,3)-(GAR1(I,IGR)-SRC(I,IGR))*GAR3(I,IGR)
280 CONTINUE
285 CONTINUE
D2F(2,1)=D2F(1,2)
CALL ALSBD(2,1,D2F,IER,2)
IF(IER.NE.0) THEN
DCRIT=1.0E-6
GO TO 270
ENDIF
ALP=D2F(1,3)
BET=D2F(2,3)/ALP
IF((ALP.LT.1.0D0).AND.(ALP.GT.0.0D0)) THEN
ALP=1.0D0
BET=0.0D0
ELSE IF(ALP.LE.0.0D0) THEN
ISTART=M+1
ALP=1.0D0
BET=0.0D0
ENDIF
ELSE
* ONE-PARAMETER ACCELERATION.
DO 295 IGR=1,NGR
DO 290 I=1,LL4
D2F(1,1)=D2F(1,1)+GAR2(I,IGR)**2
D2F(1,3)=D2F(1,3)-(GAR1(I,IGR)-SRC(I,IGR))*GAR2(I,IGR)
290 CONTINUE
295 CONTINUE
IF(D2F(1,1).NE.0.0D0) THEN
ALP=D2F(1,3)/D2F(1,1)
ELSE
ISTART=M+1
ENDIF
ENDIF
DO 305 IGR=1,NGR
DO 300 I=1,LL4
GRAD1(I,IGR)=REAL(ALP)*(GRAD1(I,IGR)+REAL(BET)*GRAD2(I,IGR))
GAR2(I,IGR)=ALP*(GAR2(I,IGR)+BET*GAR3(I,IGR))
300 CONTINUE
305 CONTINUE
ENDIF
*
LOGTES=(M.LT.ICL1).OR.(MOD(M-ISTART,ICL1+ICL2).EQ.ICL1-1)
IF(LOGTES) THEN
ALLOCATE(WORK4(LL4))
DELT=0.0
DO 350 IGR=1,NGR
WORK1(:LL4)=0.0
WORK2(:LL4)=0.0
DO 320 JGR=1,NGR
WRITE(TEXT12,'(1HB,2I3.3)') IGR,JGR
CALL LCMLEN(IPSYS,TEXT12,ILONG,ITYLCM)
IF(ILONG.EQ.0) GO TO 320
CALL MTLDLM(TEXT12,IPTRK,IPSYS,LL4,ITY,EVECT(1,JGR),WORK4)
DO 310 I=1,LL4
WORK1(I)=WORK1(I)+WORK4(I)
310 CONTINUE
CALL MTLDLM(TEXT12,IPTRK,IPSYS,LL4,ITY,GRAD1(1,JGR),WORK4)
DO 315 I=1,LL4
WORK2(I)=WORK2(I)+WORK4(I)
315 CONTINUE
320 CONTINUE
DELN=0.0
DELD=0.0
DO 340 I=1,LL4
EVECT(I,IGR)=EVECT(I,IGR)+GRAD1(I,IGR)
GAR1(I,IGR)=GAR1(I,IGR)+GAR2(I,IGR)
GRAD2(I,IGR)=GRAD1(I,IGR)
GAR3(I,IGR)=GAR2(I,IGR)
DELN=MAX(DELN,ABS(WORK2(I)))
DELD=MAX(DELD,ABS(WORK1(I)))
340 CONTINUE
IF(DELD.NE.0.0) DELT=MAX(DELT,DELN/DELD)
350 CONTINUE
DEALLOCATE(WORK4)
IF(IMPX.GE.2) WRITE (6,620) M,ALP,BET,DELT
* COMPUTE THE CONVERGENCE HISTOGRAM.
IF((IMPH.GE.1).AND.(M.LE.250)) THEN
LMPH=IMPH.GE.1
CALL FLDXCO(IPKIN,LL4,NUN,EVECT(1,NGR),LMPH,ERR(M))
ALPH(M)=REAL(ALP)
BETA(M)=REAL(BET)
ENDIF
IF(DELT.LT.EPS2) GO TO 370
ELSE
DO 365 IGR=1,NGR
DO 360 I=1,LL4
EVECT(I,IGR)=EVECT(I,IGR)+GRAD1(I,IGR)
GAR1(I,IGR)=GAR1(I,IGR)+GAR2(I,IGR)
GRAD2(I,IGR)=GRAD1(I,IGR)
GAR3(I,IGR)=GAR2(I,IGR)
360 CONTINUE
365 CONTINUE
IF(IMPX.GE.2) WRITE (6,620) M,ALP,BET
* COMPUTE THE CONVERGENCE HISTOGRAM.
IF((IMPH.GE.1).AND.(M.LE.250)) THEN
LMPH=IMPH.GE.1
CALL FLDXCO(IPKIN,LL4,NUN,EVECT(1,NGR),LMPH,ERR(M))
ALPH(M)=REAL(ALP)
BETA(M)=REAL(BET)
ENDIF
ENDIF
IF(M.EQ.1) TEST=DELT
IF((M.GT.30).AND.(DELT.GT.TEST)) CALL XABORT('KINSLB: CONVERGENC'
1 //'E FAILURE.')
IF(M.GE.MIN(MAXX0,MMAXX)) THEN
WRITE (6,710)
GO TO 370
ENDIF
GO TO 10
*----
* SOLUTION EDITION.
*----
370 IF(IMPX.EQ.1) WRITE (6,640) M
IF(IMPX.GE.3) THEN
DO 380 IGR=1,NGR
WRITE (6,690) IGR,(EVECT(I,IGR),I=1,LL4)
380 CONTINUE
ENDIF
IF(IMPH.GE.2) THEN
IGRAPH=0
390 IGRAPH=IGRAPH+1
WRITE (TEXT12,'(5HHISTO,I3)') IGRAPH
CALL LCMLEN (IPKIN,TEXT12,ILENG,ITYLCM)
IF(ILENG.EQ.0) THEN
MDIM=MIN(250,M)
READ (TITR,'(18A4)') ITITR
CALL LCMSIX (IPKIN,TEXT12,1)
CALL LCMPUT (IPKIN,'HTITLE',18,3,ITITR)
CALL LCMPUT (IPKIN,'ALPHA',MDIM,2,ALPH)
CALL LCMPUT (IPKIN,'BETA',MDIM,2,BETA)
CALL LCMPUT (IPKIN,'ERROR',MDIM,2,ERR)
CALL LCMPUT (IPKIN,'IMPH',1,1,IMPH)
CALL LCMSIX (IPKIN,' ',2)
ELSE
GO TO 390
ENDIF
ENDIF
*----
* SCRATCH STORAGE DEALLOCATION
*----
DEALLOCATE(GRAD1,GRAD2,GAR1,GAR2,GAR3,WORK1,WORK2,WORK3)
RETURN
*
600 FORMAT(1H1/50H KINSLB: ITERATIVE PROCEDURE BASED ON INVERSE POWE,
1 8HR METHOD/9X,30HSPACE-TIME KINETICS EQUATIONS.)
610 FORMAT(/11X,5HALPHA,3X,4HBETA,6X,8HACCURACY,12(1H.))
620 FORMAT(1X,I3,4X,2F8.3,1PE13.2)
640 FORMAT(/23H KINSLB: CONVERGENCE IN,I4,12H ITERATIONS.)
690 FORMAT(//52H KINSLB: SPACE-TIME KINETICS SOLUTION CORRESPONDING ,
1 12HTO THE GROUP,I4//(5X,1P,8E14.5))
710 FORMAT(/53H KINSLB: ***WARNING*** THE MAXIMUM NUMBER OF OUTER IT,
1 20HERATIONS IS REACHED.)
END
|
