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|
!
!-----------------------------------------------------------------------
!
!Purpose:
! Compute the neutron flux and interface currents using the current
! iteration method for the multicell surfacic approximation.
!
!Copyright:
! Copyright (C) 2025 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
! IPAS total number of regions.
! NMCEL total number of cells in the domain.
! NMERGE total number of merged cells for which specific values
! of the neutron flux and reactions rates are required.
! Many cells with different position in the domain can
! be merged before the neutron flux calculation if they
! own the same generating cell (NMERGE.le.NMCEL).
! NGEN total number of generating cells. A generating cell is
! defined by its material and dimensions, irrespective of
! its position in the domain (NGEN.le.NMERGE).
! IJAT total number of distinct out-currents.
! NPIJ size of cellwise scattering-reduced collision probability matrices.
! NPIS size of cellwise scattering-reduced escape probability matrices.
! NPSS size of cellwise scattering-reduced transmission probability matrices.
! EPSJ stopping criterion for flux-current iterations.
! NUNKNO total number of unknowns in vectors SUNKNO and FUNKNO.
! NMIX nmber of out-currents (dimension of arrays MIX and DVX).
! NIFR nmber of in-currents (dimension of arrays IFR and ALB).
! SUNKNO input source vector.
! IMPX print flag (equal to 0 for no print).
! NMC_NODE offset of the first volume in each generating cell.
! NMC_SURF offset of the first boundary surface in each generating cell.
! IFR index-number of in-currents.
! ALB transmission/albedo associated with each in-current.
! INUM index-number of the merged cell associated to each cell.
! MIX index-number of out-currents.
! DVX weight associated with each out-current.
! Note: IFR, ALB, MIX and DVX contains information to rebuild
! the geometrical 'A' matrix.
! IGEN index-number of the generating cell associated with each
! merged cell.
! IMAC global merge index assigned to each node in the surfacic
! geometry.
! PIJW cellwise scattering-reduced collision probability matrices.
! PISW cellwise scattering-reduced escape probability matrices.
! PSJW cellwise scattering-reduced collision probability matrices
! for incoming neutrons.
! PSSW cellwise scattering-reduced transmission probability matrices.
!
!Parameters: input/output
! FUNKNO unknown vector.
!
!-----------------------------------------------------------------------
!
SUBROUTINE MUSJJ2(IPAS,NMCEL,NMERGE,NGEN,IJAT,NPIJ,NPIS,NPSS,EPSJ,NUNKNO, &
& NMIX,NIFR,FUNKNO,SUNKNO,IMPX,NMC_NODE,NMC_SURF,IFR,ALB,INUM,MIX,DVX, &
& IGEN,IMAC,PIJW,PISW,PSJW,PSSW)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
!----
! SUBROUTINE ARGUMENTS
!----
INTEGER IPAS,NMCEL,NMERGE,NGEN,IJAT,NPIJ,NPIS,NUNKNO,NMIX,NIFR,IMPX, &
& NMC_NODE(NGEN+1),NMC_SURF(NGEN+1),IFR(NIFR),INUM(NMCEL),MIX(NMIX), &
& IGEN(NMERGE),IMAC(IPAS)
REAL EPSJ,FUNKNO(NUNKNO),SUNKNO(NUNKNO),ALB(NIFR),DVX(NMIX),PIJW(NPIJ), &
& PISW(NPIS),PSJW(NPIS),PSSW(NPSS)
!----
! LOCAL VARIABLES
!----
REAL PIJ,PIS
LOGICAL LOGTES
PARAMETER (MAXIT=400,LACCFC=2,ICL1=3,ICL2=3)
!----
! ALLOCATABLE ARRAYS
!----
INTEGER, DIMENSION(:), POINTER :: INDNMC
DOUBLE PRECISION, DIMENSION(:), POINTER :: CIT0
DOUBLE PRECISION, DIMENSION(:,:), POINTER :: CITR,AITR
DOUBLE PRECISION, DIMENSION(:), POINTER :: WCURR
!----
! SCRATCH STORAGE ALLOCATION
!----
ALLOCATE(INDNMC(NMERGE))
ALLOCATE(CITR(3,IJAT),CIT0(IJAT),AITR(2,IJAT))
ALLOCATE(WCURR(IJAT))
!
KNMC=0
DO JKK=1,NMERGE
JKG=IGEN(JKK)
J2=NMC_NODE(JKG+1)-NMC_NODE(JKG)
INDNMC(JKK)=KNMC
KNMC=KNMC+J2
ENDDO
!
DO I=1,IJAT
WCURR(I)=1.0D0
CIT0(I)=0.0D0
CITR(1,I)=FUNKNO(IPAS+I)
ENDDO
!----
! COMPUTE PSJW * Q(*) CONTRIBUTION
!----
DO IKK=1,NMERGE
IKG=IGEN(IKK)
I2=NMC_NODE(IKG+1)-NMC_NODE(IKG)
I3=NMC_SURF(IKG+1)-NMC_SURF(IKG)
IT=0
DO IK=1,IKK-1
IT=IT+(NMC_SURF(IGEN(IK)+1)-NMC_SURF(IGEN(IK)))
ENDDO
IPSJ=0
DO IK=1,IKG-1
IPSJ=IPSJ+(NMC_NODE(IK+1)-NMC_NODE(IK))*(NMC_SURF(IK+1)-NMC_SURF(IK))
ENDDO
KNMC=INDNMC(IKK)
DO I=1,I2
DO IC=1,I3
JCC=MIX(IT+IC)
PBJ=PSJW(IPSJ+(I-1)*I3+IC)
CIT0(JCC)=CIT0(JCC)+PBJ*DVX(IT+IC)*SUNKNO(IMAC(KNMC+I))
ENDDO
ENDDO
ENDDO
!----
! COMPUTE NORMALIZATION VECTOR WCURR
!----
DO ICEL=1,NMCEL
IKK=INUM(ICEL)
IKG=IGEN(IKK)
J3=NMC_SURF(IKG+1)-NMC_SURF(IKG)
IT=0
DO IK=1,IKK-1
IT=IT+(NMC_SURF(IGEN(IK)+1)-NMC_SURF(IGEN(IK)))
ENDDO
IS=0
DO IK=1,ICEL-1
IS=IS+(NMC_SURF(IGEN(INUM(IK))+1)-NMC_SURF(IGEN(INUM(IK))))
ENDDO
IPSS=0
DO IK=1,IKG-1
IPSS=IPSS+(NMC_SURF(IK+1)-NMC_SURF(IK))**2
ENDDO
DO JC=1,J3
J1=IFR(IS+JC)
DO IC=1,J3
PSS=PSSW(IPSS+(JC-1)*J3+IC)
WCURR(J1)=WCURR(J1)-PSS*ALB(IS+JC)*DVX(IT+IC)
ENDDO
ENDDO
ENDDO
!
ISTART=1
TEST=0.0D0
ITER=0
10 ITER=ITER+1
IF(ITER.GT.MAXIT) THEN
WRITE(6,'(/47H MUSJJ2: *** WARNING *** MAXIMUM NUMBER OF ITER, &
& 15HATIONS REACHED.)')
GO TO 190
ENDIF
IT3=MOD(ITER,3)+1
IT2=MOD(ITER-1,3)+1
IT1=MOD(ITER-2,3)+1
CITR(IT3,:IJAT)=CIT0(:IJAT)
!----
! COMPUTE PSSW * J(-) CONTRIBUTION
!----
DO ICEL=1,NMCEL
IKK=INUM(ICEL)
IKG=IGEN(IKK)
J3=NMC_SURF(IKG+1)-NMC_SURF(IKG)
IT=0
DO IK=1,IKK-1
IT=IT+(NMC_SURF(IGEN(IK)+1)-NMC_SURF(IGEN(IK)))
ENDDO
IS=0
DO IK=1,ICEL-1
IS=IS+(NMC_SURF(IGEN(INUM(IK))+1)-NMC_SURF(IGEN(INUM(IK))))
ENDDO
IPSS=0
DO IK=1,IKG-1
IPSS=IPSS+(NMC_SURF(IK+1)-NMC_SURF(IK))**2
ENDDO
DO JC=1,J3
J1=IFR(IS+JC)
DO IC=1,J3
J2=MIX(IT+IC)
PSS=PSSW(IPSS+(JC-1)*J3+IC)
CITR(IT3,J2)=CITR(IT3,J2)+PSS*ALB(IS+JC)*DVX(IT+IC)*CITR(IT2,J1)
ENDDO
ENDDO
ENDDO
!----
! NORMALIZATION
!----
S1=0.0D0
S2=0.0D0
DO I=1,IJAT
S1=S1+WCURR(I)*CITR(IT3,I)
S2=S2+CIT0(I)
ENDDO
ZNORM=S2/S1
IF(ZNORM.LT.0.0D0) ZNORM=1.0D0
CITR(IT3,:IJAT)=CITR(IT3,:IJAT)*ZNORM
!----
! ONE/TWO PARAMETER ACCELERATION
!----
ALP=1.0D0
BET=0.0D0
LOGTES=(1+MOD(ITER-ISTART,ICL1+ICL2).GT.ICL1)
IF(LOGTES) THEN
AITR(1,:IJAT)=CITR(IT3,:IJAT)-CITR(IT2,:IJAT)
AITR(2,:IJAT)=CITR(IT2,:IJAT)-CITR(IT1,:IJAT)
DO ICEL=1,NMCEL
IKK=INUM(ICEL)
IKG=IGEN(IKK)
J3=NMC_SURF(IKG+1)-NMC_SURF(IKG)
IT=0
DO IK=1,IKK-1
IT=IT+(NMC_SURF(IGEN(IK)+1)-NMC_SURF(IGEN(IK)))
ENDDO
IS=0
DO IK=1,ICEL-1
IS=IS+(NMC_SURF(IGEN(INUM(IK))+1)-NMC_SURF(IGEN(INUM(IK))))
ENDDO
IPSS=0
DO IK=1,IKG-1
IPSS=IPSS+(NMC_SURF(IK+1)-NMC_SURF(IK))**2
ENDDO
DO JC=1,J3
J1=IFR(IS+JC)
DO IC=1,J3
J2=MIX(IT+IC)
PSS=PSSW(IPSS+(JC-1)*J3+IC)*ALB(IS+JC)*DVX(IT+IC)
AITR(1,J2)=AITR(1,J2)-PSS*(CITR(IT3,J1)-CITR(IT2,J1))
AITR(2,J2)=AITR(2,J2)-PSS*(CITR(IT2,J1)-CITR(IT1,J1))
ENDDO
ENDDO
ENDDO
IF((LACCFC.EQ.1).OR.(MOD(ITER-ISTART,ICL1+ICL2).EQ.ICL1)) THEN
S1=0.0D0
S2=0.0D0
DO I=1,IJAT
S1=S1+(CITR(IT3,I)-CITR(IT2,I))*AITR(1,I)
S2=S2+AITR(1,I)*AITR(1,I)
ENDDO
IF(S2.EQ.0.0D0) THEN
ISTART=ITER+1
ELSE
ALP=S1/S2
IF(ALP.LE.0.0D0) THEN
ISTART=ITER+1
ALP=1.0D0
ENDIF
ENDIF
DO I=1,IJAT
CITR(IT3,I)=CITR(IT2,I)+ALP*(CITR(IT3,I)-CITR(IT2,I))
ENDDO
ELSE IF(LACCFC.EQ.2) THEN
S1=0.0D0
S2=0.0D0
S3=0.0D0
S4=0.0D0
S5=0.0D0
DO I=1,IJAT
S1=S1+(CITR(IT3,I)-CITR(IT2,I))*AITR(1,I)
S2=S2+AITR(1,I)*AITR(1,I)
S3=S3+(CITR(IT3,I)-CITR(IT2,I))*AITR(2,I)
S4=S4+AITR(1,I)*AITR(2,I)
S5=S5+AITR(2,I)*AITR(2,I)
ENDDO
DET=S2*S5-S4*S4
IF(DET.EQ.0.0D0) THEN
ISTART=ITER+1
ELSE
ALP=(S5*S1-S4*S3)/DET
BET=(S2*S3-S4*S1)/DET
IF(ALP.LE.0.0D0) THEN
ISTART=ITER+1
ALP=1.0D0
BET=0.0D0
ENDIF
ENDIF
DO I=1,IJAT
CITR(IT3,I)=CITR(IT2,I)+ALP*(CITR(IT3,I)-CITR(IT2,I))+ &
& BET*(CITR(IT2,I)-CITR(IT1,I))
ENDDO
ENDIF
ENDIF
!----
! CHECK THE CONVERGENCE ERROR
!----
ERR1=0.0D0
ERR2=0.0D0
DO I=1,IJAT
ERR1=MAX(ERR1,ABS(CITR(IT3,I)-CITR(IT2,I)))
ERR2=MAX(ERR2,ABS(CITR(IT3,I)))
ENDDO
IF(IMPX.GT.3) WRITE(6,'(30H MUSJJ2: CURRENT ITERATION NB.,I4, &
& 7H ERROR=,1P,E10.3,5H OVER,E10.3,15H NORMALIZATION=,E10.3, &
& 14H ACCELERATION=,2E11.3,1H.)') ITER,ERR1,ERR2,ZNORM,ALP,BET/ALP
IF(ITER.EQ.1) TEST=ERR1/ERR2
IF((ITER.GT.20).AND.(ERR1/ERR2.GT.TEST)) THEN
WRITE(6,'(/50H MUSJJ2: *** WARNING *** CONVERGENCE DIFFICULTIES.)')
GO TO 190
ENDIF
IF(LOGTES.OR.(ERR1.GT.EPSJ*ERR2)) GO TO 10
IF(IMPX.GT.2) WRITE(6,'(40H MUSJJ2: CURRENT CONVERGENCE AT ITERATIO, &
& 5HN NB.,I4,7H ERROR=,1P,E10.3,5H OVER,E10.3,1H.)') ITER,ERR1,ERR2
!
190 FUNKNO(:IPAS)=0.0
DO I=1,IJAT
FUNKNO(IPAS+I)=REAL(CITR(IT3,I))
ENDDO
!----
! COMPUTE PISW * J(-) CONTRIBUTION
!----
DO ICEL=1,NMCEL
IKK=INUM(ICEL)
IKG=IGEN(IKK)
I2=NMC_NODE(IKG+1)-NMC_NODE(IKG)
I3=NMC_SURF(IKG+1)-NMC_SURF(IKG)
IS=0
DO IK=1,ICEL-1
IS=IS+(NMC_SURF(IGEN(INUM(IK))+1)-NMC_SURF(IGEN(INUM(IK))))
ENDDO
IPIS=0
DO IK=1,IKG-1
IPIS=IPIS+(NMC_NODE(IK+1)-NMC_NODE(IK))*(NMC_SURF(IK+1)-NMC_SURF(IK))
ENDDO
KNMC=INDNMC(IKK)
DO J=1,I2
DO JC=1,I3
J1=IFR(IS+JC)
PIS=PISW(IPIS+(JC-1)*I2+J)
FUNKNO(IMAC(KNMC+J))=FUNKNO(IMAC(KNMC+J))+PIS*ALB(IS+JC)*FUNKNO(IPAS+J1)
ENDDO
ENDDO
ENDDO
!----
! COMPUTE PIJW * Q(*) CONTRIBUTION
!----
DO IKK=1,NMERGE
IKG=IGEN(IKK)
I2=NMC_NODE(IKG+1)-NMC_NODE(IKG)
IPIJ=0
DO IK=1,IKG-1
IPIJ=IPIJ+(NMC_NODE(IK+1)-NMC_NODE(IK))**2
ENDDO
KNMC=INDNMC(IKK)
DO I=1,I2
DO J=1,I2
PIJ=PIJW(IPIJ+(I-1)*I2+J)
FUNKNO(IMAC(KNMC+J))=FUNKNO(IMAC(KNMC+J))+PIJ*SUNKNO(IMAC(KNMC+I))
ENDDO
ENDDO
ENDDO
!----
! SCRATCH STORAGE DEALLOCATION
!----
DEALLOCATE(WCURR)
DEALLOCATE(AITR,CIT0,CITR)
DEALLOCATE(INDNMC)
RETURN
END
|
