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*DECK VALU5B
SUBROUTINE VALU5B (KPMAC,NX,NY,LL4F,LL4X,NUN,NMIX,X,Y,XXX,YYY,
1 EVT,ISS,KFLX,KN,IXLG,IYLG,ICORN,AXY)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Interpolation of the flux distribution for nodal method in 2D.
*
*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.
* LL4F number of averaged flux unknowns.
* LL4X number of X-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.
* XXX Cartesian coordinates along the X axis.
* YYY Cartesian coordinates along the Y 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.
* ICORN flag to activate corner flux correction (0/1: OFF/ON).
*
*Parameters: output
* AXY interpolated fluxes.
*
*----------------------------------------------------------------------
*
USE GANLIB
*----
* SUBROUTINE ARGUMENTS
*----
TYPE(C_PTR) KPMAC
INTEGER NX,NY,LL4F,LL4X,NUN,NMIX,ISS(NX*NY),KFLX(NX*NY),
1 KN(6,NX,NY),IXLG,IYLG,ICORN
REAL X(IXLG),Y(IYLG),XXX(NX+1),YYY(NY+1),EVT(NUN),AXY(IXLG,IYLG)
*----
* LOCAL VARIABLES
*----
DOUBLE PRECISION WORK1(4,5),FC2(4)
DOUBLE PRECISION GAR,COEFX,COEFY,U,V,P2U,P2V
LOGICAL LOGC1,LOGC2
*----
* 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(4,NX,NY))
DELC(:4,:NX,:NY)=0.D0
IF(ICORN==1) THEN
ALLOCATE(FCORN(4,NX,NY))
FCORN(:4,:NX,:NY)=0.D0
DO JS=1,NY
DO IS=1,NX
IEL=(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) ; JXP=KN(2,IS,JS)
JYM=KN(3,IS,JS) ; JYP=KN(4,IS,JS)
COEFX=DIFF(IBM)/(XXX(IS+1)-XXX(IS))
COEFY=DIFF(IBM)/(YYY(JS+1)-YYY(JS))
*
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(5*LL4F+JXM)
WORK1(4,1)=-COEFX
WORK1(4,2)=-3.0*COEFX
IF(JXP.NE.0) WORK1(4,5)=EVT(5*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('VALU5B: SINGULAR MATRIX(1).')
DO IC=1,4
SELECT CASE(IC)
CASE(1,3)
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)=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(5*LL4F+LL4X+JYM)
WORK1(4,1)=-COEFY
WORK1(4,2)=-3.0*COEFY
IF(JYP.NE.0) WORK1(4,5)=EVT(5*LL4F+LL4X+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('VALU5B: SINGULAR MATRIX(2).')
DO IC=1,4
SELECT CASE(IC)
CASE(1,2)
V=-0.5
CASE DEFAULT
V=0.5
END SELECT
GAR=FCORN(IC,IS,JS)+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)=GAR
ENDDO
ENDDO
ENDDO
DO JS=1,NY
DO IS=1,NX
IEL=(JS-1)*NX+IS
IND1=KFLX(IEL)
IF(IND1.EQ.0) CYCLE
! corner 1
NB=1; GAR=FCORN(1,IS,JS)
LOGC1=(IS>1) ; LOGC2=(JS>1)
IF(LOGC2) LOGC2=(KFLX((JS-2)*NX+IS)>0)
IF(LOGC1) THEN
IF(KFLX((JS-1)*NX+IS-1)>0) THEN
NB=NB+1 ;GAR=GAR+FCORN(2,IS-1,JS)
ENDIF
ENDIF
IF(LOGC2) THEN
IF(KFLX((JS-2)*NX+IS)>0) THEN
NB=NB+1 ;GAR=GAR+FCORN(3,IS,JS-1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2) THEN
IF(KFLX((JS-2)*NX+IS-1)>0) THEN
NB=NB+1 ;GAR=GAR+FCORN(4,IS-1,JS-1)
ENDIF
ENDIF
FC2(1)=GAR/REAL(NB)-FCORN(1,IS,JS)
! corner 2
NB=1 ;GAR=FCORN(2,IS,JS)
LOGC1=(IS<NX) ; LOGC2=(JS>1)
IF(LOGC1) THEN
IF(KFLX((JS-1)*NX+IS+1)>0) THEN
NB=NB+1 ;GAR=GAR+FCORN(1,IS+1,JS)
ENDIF
ENDIF
IF(LOGC2) THEN
IF(KFLX((JS-2)*NX+IS)>0) THEN
NB=NB+1 ;GAR=GAR+FCORN(4,IS,JS-1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2) THEN
IF(KFLX((JS-2)*NX+IS+1)>0) THEN
NB=NB+1 ;GAR=GAR+FCORN(3,IS+1,JS-1)
ENDIF
ENDIF
FC2(2)=GAR/REAL(NB)-FCORN(2,IS,JS)
! corner 3
NB=1 ; GAR=FCORN(3,IS,JS)
LOGC1=(IS>1) ; LOGC2=(JS<NY)
IF(LOGC1) THEN
IF(KFLX((JS-1)*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(4,IS-1,JS)
ENDIF
ENDIF
IF(LOGC2) THEN
IF(KFLX(JS*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(1,IS,JS+1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2) THEN
IF(KFLX(JS*NX+IS-1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(2,IS-1,JS+1)
ENDIF
ENDIF
FC2(3)=GAR/REAL(NB)-FCORN(3,IS,JS)
! corner 4
NB=1
GAR=FCORN(4,IS,JS)
LOGC1=(IS<NX)
IF(LOGC1) LOGC1=(KFLX((JS-1)*NX+IS+1)>0)
LOGC2=(JS<NY)
IF(LOGC2) LOGC2=(KFLX(JS*NX+IS)>0)
IF(LOGC1) THEN
IF(KFLX((JS-1)*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(3,IS+1,JS)
ENDIF
ENDIF
IF(LOGC2) THEN
IF(KFLX(JS*NX+IS)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(2,IS,JS+1)
ENDIF
ENDIF
IF(LOGC1.AND.LOGC2) THEN
IF(KFLX(JS*NX+IS+1)>0) THEN
NB=NB+1 ; GAR=GAR+FCORN(1,IS+1,JS+1)
ENDIF
ENDIF
FC2(4)=GAR/REAL(NB)-FCORN(4,IS,JS)
! polynomial coefficients of correction terms
DELC(1,IS,JS)= FC2(1)-FC2(2)-FC2(3)+FC2(4)
DELC(2,IS,JS)=-FC2(1)-FC2(2)+FC2(3)+FC2(4)
DELC(3,IS,JS)=-FC2(1)+FC2(2)-FC2(3)+FC2(4)
DELC(4,IS,JS)= FC2(1)+FC2(2)+FC2(3)+FC2(4)
ENDDO
ENDDO
DEALLOCATE(FCORN)
ENDIF
*----
* PERFORM INTERPOLATION
*----
DO J=1,IYLG
ORDO=Y(J)
DO I=1,IXLG
ABSC=X(I)
GAR=0.0D0
*
* Find the node index containing the interpolation point
IS=0; JS=0
DO L=1,NX
IS=L
IF((ABSC.GE.XXX(L)).AND.(ABSC.LE.XXX(L+1))) GO TO 10
ENDDO
CALL XABORT('VALU5B: 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('VALU5B: WRONG INTERPOLATION(2).')
20 IEL=(JS-1)*NX+IS
IND1=KFLX(IEL)
IF(IND1.EQ.0) GO TO 30
IBM=ISS(IEL)
IF(IBM.LE.0) GO TO 30
JXM=KN(1,IS,JS) ; JXP=KN(2,IS,JS)
JYM=KN(3,IS,JS) ; JYP=KN(4,IS,JS)
COEFX=DIFF(IBM)/(XXX(IS+1)-XXX(IS))
COEFY=DIFF(IBM)/(YYY(JS+1)-YYY(JS))
U=(ABSC-XXX(IS))/(XXX(IS+1)-XXX(IS))-0.5
V=(ORDO-YYY(JS))/(YYY(JS+1)-YYY(JS))-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(5*LL4F+JXM)
WORK1(4,1)=-COEFX
WORK1(4,2)=-3.0*COEFX
IF(JXP.NE.0) WORK1(4,5)=EVT(5*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('VALU5B: SINGULAR MATRIX(3).')
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(5*LL4F+LL4X+JYM)
WORK1(4,1)=-COEFY
WORK1(4,2)=-3.0*COEFY
IF(JYP.NE.0) WORK1(4,5)=EVT(5*LL4F+LL4X+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('VALU5B: SINGULAR MATRIX(4).')
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)
*
IF(ICORN==1) THEN
! perform interpolation of corner flux correction
P2U=3.0*U**2-0.25 ; P2V=3.0*V**2-0.25
GAR=GAR+DELC(1,IS,JS)*U*V + DELC(2,IS,JS)*P2U*V+
1 DELC(3,IS,JS)*U*P2V + DELC(4,IS,JS)*P2U*P2V
ENDIF
30 AXY(I,J)=REAL(GAR)
ENDDO
ENDDO
DEALLOCATE(DELC,DIFF)
RETURN
END
|
