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|
*DECK VALU5
SUBROUTINE VALU5 (KPMAC,NX,NY,NZ,LL4F,LL4X,LL4Y,NUN,NMIX,X,Y,Z,
1 XXX,YYY,ZZZ,EVT,ISS,KFLX,KN,IXLG,IYLG,IZLG,ICORN,AXYZ)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Interpolation of the flux distribution for nodal method in 3D.
*
*Copyright:
* Copyright (C) 2021 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
* KPMAC group directory in the macrolib.
* NX number of elements along the X axis.
* NY number of elements along the Y axis.
* NY number of elements along the Z axis.
* LL4F number of averaged flux unknowns.
* LL4X number of X-directed net currents.
* LL4Y number of Y-directed net currents.
* NUN dimension of unknown array EVT.
* NMIX number of mixtures.
* X Cartesian coordinates along the X axis where the flux is
* interpolated.
* Y Cartesian coordinates along the Y axis where the flux is
* interpolated.
* Z Cartesian coordinates along the Z axis where the flux is
* interpolated.
* XXX Cartesian coordinates along the X axis.
* YYY Cartesian coordinates along the Y axis.
* ZZZ Cartesian coordinates along the Z axis.
* EVT reconstruction coefficients of the flux.
* ISS mixture index assigned to each element.
* KFLX correspondence between local and global numbering.
* KN element-ordered interface net current unknown list.
* IXLG number of interpolated points according to X.
* IYLG number of interpolated points according to Y.
* IZLG number of interpolated points according to Z.
* ICORN flag to activate corner flux correction (0/1: ON/OFF).
*
*Parameters: output
* AXYZ interpolated fluxes.
*
*----------------------------------------------------------------------
*
USE GANLIB
*----
* SUBROUTINE ARGUMENTS
*----
TYPE(C_PTR) KPMAC
INTEGER NX,NY,NZ,LL4F,LL4X,LL4Y,NUN,NMIX,ISS(NX*NY*NZ),
1 KFLX(NX*NY*NZ),KN(6,NX,NY,NZ),IXLG,IYLG,IZLG,ICORN
REAL X(IXLG),Y(IYLG),Z(IZLG),XXX(NX+1),YYY(NY+1),ZZZ(NZ+1),
1 EVT(NUN),AXYZ(IXLG,IYLG,IZLG)
*----
* LOCAL VARIABLES
*----
DOUBLE PRECISION WORK1(4,5),FC2(8)
DOUBLE PRECISION GAR,COEFX,COEFY,COEFZ,U,V,W,P2U,P2V,P2W
LOGICAL LOGC1,LOGC2,LOGC3
*----
* ALLOCATABLE ARRAYS
*----
REAL, ALLOCATABLE, DIMENSION(:) :: DIFF
DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:,:,:,:) :: FCORN,DELC
*----
* RECOVER DIFFUSION COEFFICIENTS
*----
ALLOCATE(DIFF(NMIX))
CALL LCMGET(KPMAC,'DIFF',DIFF)
*----
* COMPUTE CORNER FLUXES
*----
ALLOCATE(DELC(8,NX,NY,NZ))
DELC(:8,:NX,:NY,:NZ)=0.D0
IOFY=7*LL4F+LL4X
IOFZ=7*LL4F+LL4X+LL4Y
IF(ICORN==1) THEN
ALLOCATE(FCORN(8,NX,NY,NZ))
FCORN(:8,:NX,:NY,:NZ)=0.D0
DO KS=1,NZ
DO JS=1,NY
DO IS=1,NX
IEL=(KS-1)*NX*NY+(JS-1)*NX+IS
IND1=KFLX(IEL)
IF(IND1.EQ.0) CYCLE
IBM=ISS(IEL)
IF(IBM.LE.0) CYCLE
JXM=KN(1,IS,JS,KS) ; JXP=KN(2,IS,JS,KS)
JYM=KN(3,IS,JS,KS) ; JYP=KN(4,IS,JS,KS)
JZM=KN(5,IS,JS,KS) ; JZP=KN(6,IS,JS,KS)
COEFX=DIFF(IBM)/(XXX(IS+1)-XXX(IS))
COEFY=DIFF(IBM)/(YYY(JS+1)-YYY(JS))
COEFZ=DIFF(IBM)/(ZZZ(KS+1)-ZZZ(KS))
*
WORK1(:,:)=0.0
WORK1(1,1)=-0.5
WORK1(1,2)=0.5
WORK1(1,5)=EVT(LL4F+IND1)-EVT(IND1)
WORK1(2,1)=0.5
WORK1(2,2)=0.5
WORK1(2,5)=EVT(2*LL4F+IND1)-EVT(IND1)
WORK1(3,1)=-COEFX
WORK1(3,2)=3.0*COEFX
IF(JXM.NE.0) WORK1(3,5)=EVT(7*LL4F+JXM)
WORK1(4,1)=-COEFX
WORK1(4,2)=-3.0*COEFX
IF(JXP.NE.0) WORK1(4,5)=EVT(7*LL4F+JXP)
WORK1(3,3)=-0.5*COEFX
WORK1(3,4)=0.2*COEFX
WORK1(4,3)=-0.5*COEFX
WORK1(4,4)=-0.2*COEFX
CALL ALSBD(4,1,WORK1,IER,4)
IF(IER.NE.0) CALL XABORT('VALU5: SINGULAR MATRIX(1).')
DO IC=1,8
SELECT CASE(IC)
CASE(1,3,5,7)
U=-0.5
CASE DEFAULT
U=0.5
END SELECT
GAR=EVT(IND1)+WORK1(1,5)*U+WORK1(2,5)*(3.0*U**2-0.25)
GAR=GAR+WORK1(3,5)*(U**2-0.25)*U+WORK1(4,5)*(U**2-0.25)*
1 (U**2-0.05)
FCORN(IC,IS,JS,KS)=GAR
ENDDO
*
WORK1(:,:)=0.0
WORK1(1,1)=-0.5
WORK1(1,2)=0.5
WORK1(1,5)=EVT(3*LL4F+IND1)-EVT(IND1)
WORK1(2,1)=0.5
WORK1(2,2)=0.5
WORK1(2,5)=EVT(4*LL4F+IND1)-EVT(IND1)
WORK1(3,1)=-COEFY
WORK1(3,2)=3.0*COEFY
IF(JYM.NE.0) WORK1(3,5)=EVT(IOFY+JYM)
WORK1(4,1)=-COEFY
WORK1(4,2)=-3.0*COEFY
IF(JYP.NE.0) WORK1(4,5)=EVT(IOFY+JYP)
WORK1(3,3)=-0.5*COEFY
WORK1(3,4)=0.2*COEFY
WORK1(4,3)=-0.5*COEFY
WORK1(4,4)=-0.2*COEFY
CALL ALSBD(4,1,WORK1,IER,4)
IF(IER.NE.0) CALL XABORT('VALU5: SINGULAR MATRIX(2).')
DO IC=1,8
SELECT CASE(IC)
CASE(1,2,5,6)
V=-0.5
CASE DEFAULT
V=0.5
END SELECT
GAR=FCORN(IC,IS,JS,KS)+WORK1(1,5)*V+WORK1(2,5)*
1 (3.0*V**2-0.25)
GAR=GAR+WORK1(3,5)*(V**2-0.25)*V+WORK1(4,5)*(V**2-0.25)*
1 (V**2-0.05)
FCORN(IC,IS,JS,KS)=GAR
ENDDO
*
WORK1(:,:)=0.0
WORK1(1,1)=-0.5
WORK1(1,2)=0.5
WORK1(1,5)=EVT(7*LL4F+IND1)-EVT(IND1)
WORK1(2,1)=0.5
WORK1(2,2)=0.5
WORK1(2,5)=EVT(6*LL4F+IND1)-EVT(IND1)
WORK1(3,1)=-COEFZ
WORK1(3,2)=3.0*COEFZ
IF(JZM.NE.0) WORK1(3,5)=EVT(IOFZ+JZM)
WORK1(4,1)=-COEFZ
WORK1(4,2)=-3.0*COEFZ
IF(JZP.NE.0) WORK1(4,5)=EVT(IOFZ+JZP)
WORK1(3,3)=-0.5*COEFZ
WORK1(3,4)=0.2*COEFZ
WORK1(4,3)=-0.5*COEFZ
WORK1(4,4)=-0.2*COEFZ
CALL ALSBD(4,1,WORK1,IER,4)
IF(IER.NE.0) CALL XABORT('VALU5: SINGULAR MATRIX(3).')
DO IC=1,8
SELECT CASE(IC)
CASE(1,2,3,4)
W=-0.5
CASE DEFAULT
W=0.5
END SELECT
GAR=FCORN(IC,IS,JS,KS)+WORK1(1,5)*W+WORK1(2,5)*
1 (3.0*W**2-0.25)
GAR=GAR+WORK1(3,5)*(W**2-0.25)*W+WORK1(4,5)*(W**2-0.25)*
1 (W**2-0.05)
FCORN(IC,IS,JS,KS)=GAR
ENDDO
ENDDO
ENDDO
ENDDO
DO KS=1,NZ
DO JS=1,NY
DO IS=1,NX
IEL=(KS-1)*NX*NY+(JS-1)*NX+IS
IND1=KFLX(IEL)
IF(IND1.EQ.0) CYCLE
! corner 1
NB=1 ; GAR=FCORN(1,IS,JS,KS)
LOGC1=(IS>1) ; LOGC2=(JS>1) ; LOGC3=(KS>1)
IF(LOGC1) THEN
IF(KFLX((KS-1)*NX*NY+(JS-1)*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(2,IS-1,JS,KS)
ENDIF
ENDIF
IF(LOGC2) THEN
IF(KFLX((KS-1)*NX*NY+(JS-2)*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(3,IS,JS-1,KS)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2) THEN
IF(KFLX((KS-1)*NX*NY+(JS-2)*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(4,IS-1,JS-1,KS)
ENDIF
ENDIF
IF(LOGC3) THEN
IF(KFLX((KS-2)*NX*NY+(JS-1)*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(5,IS,JS,KS-1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC3) THEN
IF(KFLX((KS-2)*NX*NY+(JS-1)*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(6,IS-1,JS,KS-1)
ENDIF
ENDIF
IF(LOGC2.AND.LOGC3) THEN
IF(KFLX((KS-2)*NX*NY+(JS-2)*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(7,IS,JS-1,KS-1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2.AND.LOGC3) THEN
IF(KFLX((KS-2)*NX*NY+(JS-2)*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(8,IS-1,JS-1,KS-1)
ENDIF
ENDIF
FC2(1)=GAR/REAL(NB)-FCORN(1,IS,JS,KS)
! corner 2
NB=1 ; GAR=FCORN(2,IS,JS,KS)
LOGC1=(IS<NX); LOGC2=(JS>1) ; LOGC3=(KS>1)
IF(LOGC1) THEN
IF(KFLX((KS-1)*NX*NY+(JS-1)*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(1,IS+1,JS,KS)
ENDIF
ENDIF
IF(LOGC2) THEN
IF(KFLX((KS-1)*NX*NY+(JS-2)*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(4,IS,JS-1,KS)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2) THEN
IF(KFLX((KS-1)*NX*NY+(JS-2)*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(3,IS+1,JS-1,KS)
ENDIF
ENDIF
IF(LOGC3) THEN
IF(KFLX((KS-2)*NX*NY+(JS-1)*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(6,IS,JS,KS-1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC3) THEN
IF(KFLX((KS-2)*NX*NY+(JS-1)*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(5,IS+1,JS,KS-1)
ENDIF
ENDIF
IF(LOGC2.AND.LOGC3) THEN
IF(KFLX((KS-2)*NX*NY+(JS-2)*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(8,IS,JS-1,KS-1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2.AND.LOGC3) THEN
IF(KFLX((KS-2)*NX*NY+(JS-2)*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(7,IS+1,JS-1,KS-1)
ENDIF
ENDIF
FC2(2)=GAR/REAL(NB)-FCORN(2,IS,JS,KS)
! corner 3
NB=1 ; GAR=FCORN(3,IS,JS,KS)
LOGC1=(IS>1) ; LOGC2=(JS<NY) ; LOGC3=(KS>1)
IF(LOGC1) THEN
IF(KFLX((KS-1)*NX*NY+(JS-1)*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(4,IS-1,JS,KS)
ENDIF
ENDIF
IF(LOGC2) THEN
IF(KFLX((KS-1)*NX*NY+JS*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(1,IS,JS+1,KS)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2) THEN
IF(KFLX((KS-1)*NX*NY+JS*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(2,IS-1,JS+1,KS)
ENDIF
ENDIF
IF(LOGC3) THEN
IF(KFLX((KS-2)*NX*NY+(JS-1)*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(7,IS,JS,KS-1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC3) THEN
IF(KFLX((KS-2)*NX*NY+(JS-1)*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(8,IS-1,JS,KS-1)
ENDIF
ENDIF
IF(LOGC2.AND.LOGC3) THEN
IF(KFLX((KS-2)*NX*NY+JS*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(5,IS,JS+1,KS-1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2.AND.LOGC3) THEN
IF(KFLX((KS-2)*NX*NY+JS*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(6,IS-1,JS+1,KS-1)
ENDIF
ENDIF
FC2(3)=GAR/REAL(NB)-FCORN(3,IS,JS,KS)
! corner 4
NB=1 ; GAR=FCORN(4,IS,JS,KS)
LOGC1=(IS<NX) ; LOGC2=(JS<NY) ; LOGC3=(KS>1)
IF(LOGC1) THEN
IF(KFLX((KS-1)*NX*NY+(JS-1)*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(3,IS+1,JS,KS)
ENDIF
ENDIF
IF(LOGC2) THEN
IF(KFLX((KS-1)*NX*NY+JS*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(2,IS,JS+1,KS)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2) THEN
IF(KFLX((KS-1)*NX*NY+JS*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(1,IS+1,JS+1,KS)
ENDIF
ENDIF
IF(LOGC3) THEN
IF(KFLX((KS-2)*NX*NY+(JS-1)*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(8,IS,JS,KS-1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC3) THEN
IF(KFLX((KS-2)*NX*NY+(JS-1)*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(7,IS+1,JS,KS-1)
ENDIF
ENDIF
IF(LOGC2.AND.LOGC3) THEN
IF(KFLX((KS-2)*NX*NY+JS*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(6,IS,JS+1,KS-1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2.AND.LOGC3) THEN
IF(KFLX((KS-2)*NX*NY+JS*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(5,IS+1,JS+1,KS-1)
ENDIF
ENDIF
FC2(4)=GAR/REAL(NB)-FCORN(4,IS,JS,KS)
! corner 5
NB=1 ; GAR=FCORN(5,IS,JS,KS)
LOGC1=(IS>1) ; LOGC2=(JS>1) ; LOGC3=(KS<NZ)
IF(LOGC1) THEN
IF(KFLX((KS-1)*NX*NY+(JS-1)*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(6,IS-1,JS,KS)
ENDIF
ENDIF
IF(LOGC2) THEN
IF(KFLX((KS-1)*NX*NY+(JS-2)*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(7,IS,JS-1,KS)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2) THEN
IF(KFLX((KS-1)*NX*NY+(JS-2)*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(8,IS-1,JS-1,KS)
ENDIF
ENDIF
IF(LOGC3) THEN
IF(KFLX(KS*NX*NY+(JS-1)*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(1,IS,JS,KS+1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC3) THEN
IF(KFLX(KS*NX*NY+(JS-1)*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(2,IS-1,JS,KS+1)
ENDIF
ENDIF
IF(LOGC2.AND.LOGC3) THEN
IF(KFLX(KS*NX*NY+(JS-2)*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(3,IS,JS-1,KS+1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2.AND.LOGC3) THEN
IF(KFLX(KS*NX*NY+(JS-2)*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(4,IS-1,JS-1,KS+1)
ENDIF
ENDIF
FC2(5)=GAR/REAL(NB)-FCORN(5,IS,JS,KS)
! corner 6
NB=1 ; GAR=FCORN(6,IS,JS,KS)
LOGC1=(IS<NX); LOGC2=(JS>1) ; LOGC3=(KS<NZ)
IF(LOGC1) THEN
IF(KFLX((KS-1)*NX*NY+(JS-1)*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(5,IS+1,JS,KS)
ENDIF
ENDIF
IF(LOGC2) THEN
IF(KFLX((KS-1)*NX*NY+(JS-2)*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(8,IS,JS-1,KS)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2) THEN
IF(KFLX((KS-1)*NX*NY+(JS-2)*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(7,IS+1,JS-1,KS)
ENDIF
ENDIF
IF(LOGC3) THEN
IF(KFLX(KS*NX*NY+(JS-1)*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(2,IS,JS,KS+1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC3) THEN
IF(KFLX(KS*NX*NY+(JS-1)*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(1,IS+1,JS,KS+1)
ENDIF
ENDIF
IF(LOGC2.AND.LOGC3) THEN
IF(KFLX(KS*NX*NY+(JS-2)*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(4,IS,JS-1,KS+1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2.AND.LOGC3) THEN
IF(KFLX(KS*NX*NY+(JS-2)*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(3,IS+1,JS-1,KS+1)
ENDIF
ENDIF
FC2(6)=GAR/REAL(NB)-FCORN(6,IS,JS,KS)
! corner 7
NB=1 ; GAR=FCORN(7,IS,JS,KS)
LOGC1=(IS>1) ; LOGC2=(JS<NY) ; LOGC3=(KS<NZ)
IF(LOGC1) THEN
IF(KFLX((KS-1)*NX*NY+(JS-1)*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(8,IS-1,JS,KS)
ENDIF
ENDIF
IF(LOGC2) THEN
IF(KFLX((KS-1)*NX*NY+JS*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(5,IS,JS+1,KS)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2) THEN
IF(KFLX((KS-1)*NX*NY+JS*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(6,IS-1,JS+1,KS)
ENDIF
ENDIF
IF(LOGC3) THEN
IF(KFLX(KS*NX*NY+(JS-1)*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(3,IS,JS,KS+1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC3) THEN
IF(KFLX(KS*NX*NY+(JS-1)*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(4,IS-1,JS,KS+1)
ENDIF
ENDIF
IF(LOGC2.AND.LOGC3) THEN
IF(KFLX(KS*NX*NY+JS*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(1,IS,JS+1,KS+1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2.AND.LOGC3) THEN
IF(KFLX(KS*NX*NY+JS*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(2,IS-1,JS+1,KS+1)
ENDIF
ENDIF
FC2(7)=GAR/REAL(NB)-FCORN(7,IS,JS,KS)
! corner 8
NB=1 ; GAR=FCORN(8,IS,JS,KS)
LOGC1=(IS<NX) ; LOGC2=(JS<NY) ; LOGC3=(KS<NZ)
IF(LOGC1) THEN
IF(KFLX((KS-1)*NX*NY+(JS-1)*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(7,IS+1,JS,KS)
ENDIF
ENDIF
IF(LOGC2) THEN
IF(KFLX((KS-1)*NX*NY+JS*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(6,IS,JS+1,KS)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2) THEN
IF(KFLX((KS-1)*NX*NY+JS*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(5,IS+1,JS+1,KS)
ENDIF
ENDIF
IF(LOGC3) THEN
IF(KFLX(KS*NX*NY+(JS-1)*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(4,IS,JS,KS+1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC3) THEN
IF(KFLX(KS*NX*NY+(JS-1)*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(3,IS+1,JS,KS+1)
ENDIF
ENDIF
IF(LOGC2.AND.LOGC3) THEN
IF(KFLX(KS*NX*NY+JS*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(2,IS,JS+1,KS+1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2.AND.LOGC3) THEN
IF(KFLX(KS*NX*NY+JS*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(1,IS+1,JS+1,KS+1)
ENDIF
ENDIF
FC2(8)=GAR/REAL(NB)-FCORN(8,IS,JS,KS)
! polynomial coefficients of correction terms
DELC(1,IS,JS,KS)=-FC2(1)+FC2(2)+FC2(3)-FC2(4)+FC2(5)-
1 FC2(6)-FC2(7)+FC2(8)
DELC(2,IS,JS,KS)= FC2(1)+FC2(2)-FC2(3)-FC2(4)-FC2(5)-
1 FC2(6)+FC2(7)+FC2(8)
DELC(3,IS,JS,KS)= FC2(1)-FC2(2)+FC2(3)-FC2(4)-FC2(5)+
1 FC2(6)-FC2(7)+FC2(8)
DELC(4,IS,JS,KS)=-FC2(1)-FC2(2)-FC2(3)-FC2(4)+FC2(5)+
1 FC2(6)+FC2(7)+FC2(8)
DELC(5,IS,JS,KS)= FC2(1)-FC2(2)-FC2(3)+FC2(4)+FC2(5)-
1 FC2(6)-FC2(7)+FC2(8)
DELC(6,IS,JS,KS)=-FC2(1)-FC2(2)+FC2(3)+FC2(4)-FC2(5)-
1 FC2(6)+FC2(7)+FC2(8)
DELC(7,IS,JS,KS)=-FC2(1)+FC2(2)-FC2(3)+FC2(4)-FC2(5)+
1 FC2(6)-FC2(7)+FC2(8)
DELC(8,IS,JS,KS)= FC2(1)+FC2(2)+FC2(3)+FC2(4)+FC2(5)+
1 FC2(6)+FC2(7)+FC2(8)
ENDDO
ENDDO
ENDDO
DEALLOCATE(FCORN)
ENDIF
*----
* PERFORM INTERPOLATION
*----
DO K=1,IZLG
COTE=Z(K)
DO J=1,IYLG
ORDO=Y(J)
DO I=1,IXLG
ABSC=X(I)
GAR=0.0D0
AXYZ(I,J,K)=REAL(GAR)
*
* Find the node index containing the interpolation point
IS=0
JS=0
KS=0
DO L=1,NX
IS=L
IF((ABSC.GE.XXX(L)).AND.(ABSC.LE.XXX(L+1))) GO TO 10
ENDDO
CALL XABORT('VALU5: WRONG INTERPOLATION(1).')
10 DO L=1,NY
JS=L
IF((ORDO.GE.YYY(L)).AND.(ORDO.LE.YYY(L+1))) GO TO 20
ENDDO
CALL XABORT('VALU5: WRONG INTERPOLATION(2).')
20 DO L=1,NZ
KS=L
IF((COTE.GE.ZZZ(L)).AND.(COTE.LE.ZZZ(L+1))) GO TO 30
ENDDO
CALL XABORT('VALU5: WRONG INTERPOLATION(3).')
30 IEL=(KS-1)*NX*NY+(JS-1)*NX+IS
IND1=KFLX(IEL)
IF(IND1.EQ.0) GO TO 40
IBM=ISS(IEL)
IF(IBM.LE.0) GO TO 40
JXM=KN(1,IS,JS,KS) ; JXP=KN(2,IS,JS,KS)
JYM=KN(3,IS,JS,KS) ; JYP=KN(4,IS,JS,KS)
JZM=KN(5,IS,JS,KS) ; JZP=KN(6,IS,JS,KS)
COEFX=DIFF(IBM)/(XXX(IS+1)-XXX(IS))
COEFY=DIFF(IBM)/(YYY(JS+1)-YYY(JS))
COEFZ=DIFF(IBM)/(ZZZ(KS+1)-ZZZ(KS))
U=(ABSC-XXX(IS))/(XXX(IS+1)-XXX(IS))-0.5
V=(ORDO-YYY(JS))/(YYY(JS+1)-YYY(JS))-0.5
W=(COTE-ZZZ(KS))/(ZZZ(KS+1)-ZZZ(KS))-0.5
GAR=EVT(IND1)
*
WORK1(:,:)=0.0
WORK1(1,1)=-0.5
WORK1(1,2)=0.5
WORK1(1,5)=EVT(LL4F+IND1)-EVT(IND1)
WORK1(2,1)=0.5
WORK1(2,2)=0.5
WORK1(2,5)=EVT(2*LL4F+IND1)-EVT(IND1)
WORK1(3,1)=-COEFX
WORK1(3,2)=3.0*COEFX
IF(JXM.NE.0) WORK1(3,5)=EVT(7*LL4F+JXM)
WORK1(4,1)=-COEFX
WORK1(4,2)=-3.0*COEFX
IF(JXP.NE.0) WORK1(4,5)=EVT(7*LL4F+JXP)
WORK1(3,3)=-0.5*COEFX
WORK1(3,4)=0.2*COEFX
WORK1(4,3)=-0.5*COEFX
WORK1(4,4)=-0.2*COEFX
CALL ALSBD(4,1,WORK1,IER,4)
IF(IER.NE.0) CALL XABORT('VALU5: SINGULAR MATRIX(4).')
GAR=GAR+WORK1(1,5)*U+WORK1(2,5)*(3.0*U**2-0.25)
GAR=GAR+WORK1(3,5)*(U**2-0.25)*U+WORK1(4,5)*(U**2-0.25)*
1 (U**2-0.05)
*
WORK1(:,:)=0.0
WORK1(1,1)=-0.5
WORK1(1,2)=0.5
WORK1(1,5)=EVT(3*LL4F+IND1)-EVT(IND1)
WORK1(2,1)=0.5
WORK1(2,2)=0.5
WORK1(2,5)=EVT(4*LL4F+IND1)-EVT(IND1)
WORK1(3,1)=-COEFY
WORK1(3,2)=3.0*COEFY
IF(JYM.NE.0) WORK1(3,5)=EVT(IOFY+JYM)
WORK1(4,1)=-COEFY
WORK1(4,2)=-3.0*COEFY
IF(JYP.NE.0) WORK1(4,5)=EVT(IOFY+JYP)
WORK1(3,3)=-0.5*COEFY
WORK1(3,4)=0.2*COEFY
WORK1(4,3)=-0.5*COEFY
WORK1(4,4)=-0.2*COEFY
CALL ALSBD(4,1,WORK1,IER,4)
IF(IER.NE.0) CALL XABORT('VALU5: SINGULAR MATRIX(5).')
GAR=GAR+WORK1(1,5)*V+WORK1(2,5)*(3.0*V**2-0.25)
GAR=GAR+WORK1(3,5)*(V**2-0.25)*V+WORK1(4,5)*(V**2-0.25)*
1 (V**2-0.05)
*
WORK1(:,:)=0.0
WORK1(1,1)=-0.5
WORK1(1,2)=0.5
WORK1(1,5)=EVT(5*LL4F+IND1)-EVT(IND1)
WORK1(2,1)=0.5
WORK1(2,2)=0.5
WORK1(2,5)=EVT(6*LL4F+IND1)-EVT(IND1)
WORK1(3,1)=-COEFZ
WORK1(3,2)=3.0*COEFZ
IF(JZM.NE.0) WORK1(3,5)=EVT(IOFZ+JZM)
WORK1(4,1)=-COEFZ
WORK1(4,2)=-3.0*COEFZ
IF(JZP.NE.0) WORK1(4,5)=EVT(IOFZ+JZP)
WORK1(3,3)=-0.5*COEFZ
WORK1(3,4)=0.2*COEFZ
WORK1(4,3)=-0.5*COEFZ
WORK1(4,4)=-0.2*COEFZ
CALL ALSBD(4,1,WORK1,IER,4)
IF(IER.NE.0) CALL XABORT('VALU5: SINGULAR MATRIX(6).')
GAR=GAR+WORK1(1,5)*W+WORK1(2,5)*(3.0*W**2-0.25)
GAR=GAR+WORK1(3,5)*(W**2-0.25)*W+WORK1(4,5)*(W**2-0.25)*
1 (W**2-0.05)
*
IF(ICORN==1) THEN
! perform interpolation of corner flux correction
P2U=3.0*U**2-0.25 ; P2V=3.0*V**2-0.25 ; P2W=3.0*W**2-0.25
GAR=GAR+DELC(1,IS,JS,KS)*U*V*W + DELC(2,IS,JS,KS)*P2U*V*W+
1 DELC(3,IS,JS,KS)*U*P2V*W + DELC(4,IS,JS,KS)*P2U*P2V*W+
2 DELC(5,IS,JS,KS)*U*V*P2W + DELC(6,IS,JS,KS)*P2U*V*P2W+
3 DELC(7,IS,JS,KS)*U*P2V*P2W + DELC(8,IS,JS,KS)*P2U*P2V*P2W
ENDIF
40 AXYZ(I,J,K)=REAL(GAR)
ENDDO
ENDDO
ENDDO
DEALLOCATE(DELC,DIFF)
RETURN
END
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