*DECK NSS1TR SUBROUTINE NSS1TR(ITRIAL,NEL,NMIX,MAT,XX,IQFR,QFR,DIFF,SIGR,FD, 1 A11) * *----------------------------------------------------------------------- * *Purpose: * Assembly of leakage system matrices for the nodal expansion method. * *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 * ITRIAL type of base (=1: polynomial; =2: hyperbolic). * NEL number of nodes * NMIX number of mixtures * MAT node mixtures * XX node widths * IQFR boundary conditions * QFR albedo functions * DIFF diffusion coefficients * SIGR macroscopic removal cross sections * FD discontinuity factors * *Parameters: output * A11 assembly matrix. * *----------------------------------------------------------------------- * INTEGER ITRIAL(NMIX),NEL,NMIX,MAT(NEL),IQFR(6,NEL) REAL XX(NEL),QFR(6,NEL),DIFF(NMIX),SIGR(NMIX),FD(NMIX,2), 1 A11(5*NEL,5*NEL) * A11(:5*NEL,:5*NEL)=0.0 ! WEIGHT RESIDUAL EQUATIONS: NUM1=0 DO KEL=1,NEL IBM=MAT(KEL) DX2=XX(KEL)**2 SIGG=SIGR(IBM) DIDD=DIFF(IBM) ETA=XX(KEL)*SQRT(SIGG/DIDD) A11(NUM1+1,NUM1+1)=SIGG A11(NUM1+1,NUM1+3)=-6.0*DIDD/DX2 A11(NUM1+2,NUM1+2)=SIGG/12.0 A11(NUM1+3,NUM1+3)=SIGG/20.0 IF(ITRIAL(IBM) == 1) THEN A11(NUM1+1,NUM1+5)=-2.0*DIDD/(5.0*DX2) A11(NUM1+2,NUM1+4)=-SIGG/120.0-DIDD/(2.0*DX2) A11(NUM1+3,NUM1+5)=-SIGG/700.0-DIDD/(5.0*DX2) ELSE ALP0=2.0*ETA*SINH(ETA/2.0) A11(NUM1+1,NUM1+5)=-DIDD*ALP0/DX2 ENDIF NUM1=NUM1+5 ENDDO ! continuity relations: NUM1=0 DO KEL=1,NEL-1 IBM=MAT(KEL) IBMP=MAT(KEL+1) DIDD=DIFF(IBM) DIDDP=DIFF(IBMP) ETA=XX(KEL)*SQRT(SIGR(IBM)/DIDD) ETAP=XX(KEL+1)*SQRT(SIGR(IBMP)/DIDDP) NUM2=NUM1+5 ! flux continuity: FDP=FD(IBM,2) FDM=FD(IBMP,1) A11(NUM1+4,NUM1+1)=FDP A11(NUM1+4,NUM1+2)=FDP/2.0 A11(NUM1+4,NUM1+3)=FDP/2.0 A11(NUM1+4,NUM2+1)=-FDM A11(NUM1+4,NUM2+2)=FDM/2.0 A11(NUM1+4,NUM2+3)=-FDM/2.0 IF(ITRIAL(IBM) == 2) THEN ALP1=ETA*COSH(ETA/2.0)-2.0*SINH(ETA/2.0) A11(NUM1+4,NUM1+4)=FDP*SINH(ETA/2.0) A11(NUM1+4,NUM1+5)=FDP*ALP1/ETA ENDIF IF(ITRIAL(IBMP) == 2) THEN ALP1P=ETAP*COSH(ETAP/2.0)-2.0*SINH(ETAP/2.0) A11(NUM1+4,NUM2+4)=FDM*SINH(ETAP/2.0) A11(NUM1+4,NUM2+5)=-FDM*ALP1P/ETAP ENDIF ! current contunuity: A11(NUM1+5,NUM1+2)=DIDD/XX(KEL) A11(NUM1+5,NUM1+3)=3.0*DIDD/XX(KEL) A11(NUM1+5,NUM2+2)=-DIDDP/XX(KEL+1) A11(NUM1+5,NUM2+3)=3.0*DIDDP/XX(KEL+1) IF(ITRIAL(IBM) == 1) THEN A11(NUM1+5,NUM1+4)=DIDD/(2.0*XX(KEL)) A11(NUM1+5,NUM1+5)=DIDD/(5.0*XX(KEL)) ELSE A11(NUM1+5,NUM1+4)=(DIDD/XX(KEL))*ETA*COSH(ETA/2.0) A11(NUM1+5,NUM1+5)=(DIDD/XX(KEL))*ETA*SINH(ETA/2.0) ENDIF IF(ITRIAL(IBMP) == 1) THEN A11(NUM1+5,NUM2+4)=-DIDDP/(2.0*XX(KEL+1)) A11(NUM1+5,NUM2+5)=DIDDP/(5.0*XX(KEL+1)) ELSE A11(NUM1+5,NUM2+4)=-(DIDDP/XX(KEL+1))*ETAP*COSH(ETAP/2.0) A11(NUM1+5,NUM2+5)=(DIDDP/XX(KEL+1))*ETAP*SINH(ETAP/2.0) ENDIF NUM1=NUM1+5 ENDDO ! left boundary condition: IBM=MAT(1) ETA=XX(1)*SQRT(SIGR(MAT(1))/DIFF(IBM)) IF((IQFR(1,1) == -1).OR.(IQFR(1,1) > 0)) THEN ! VOID AFACTOR=QFR(1,1) A11(NUM1+4,1)=AFACTOR A11(NUM1+4,2)=-(AFACTOR/2.0+DIFF(IBM)/XX(1)) A11(NUM1+4,3)=(AFACTOR/2.0+3.0*DIFF(IBM)/XX(1)) IF(ITRIAL(IBM) == 1) THEN A11(NUM1+4,4)=-DIFF(IBM)/(2.0*XX(1)) A11(NUM1+4,5)=DIFF(IBM)/(5.0*XX(1)) ELSE ALP1=ETA*COSH(ETA/2.0)-2.0*SINH(ETA/2.0) A11(NUM1+4,4)=-(AFACTOR*SINH(ETA/2.0)+(DIFF(IBM)/XX(1))* 1 ETA*COSH(ETA/2.0)) A11(NUM1+4,5)=AFACTOR*ALP1/ETA+(DIFF(IBM)/XX(1))*ETA* 1 SINH(ETA/2.0) ENDIF ELSE IF(IQFR(1,1) == -2) THEN ! REFL A11(NUM1+4,2)=1.0 A11(NUM1+4,3)=-3.0 IF(ITRIAL(IBM) == 1) THEN A11(NUM1+4,4)=1.0/2.0 A11(NUM1+4,5)=-1.0/5.0 ELSE A11(NUM1+4,4)=ETA*COSH(ETA/2.0) A11(NUM1+4,5)=-ETA*SINH(ETA/2.0) ENDIF ELSE IF(IQFR(1,1) == -3) THEN ! ZERO A11(NUM1+4,1)=1.0 A11(NUM1+4,2)=-1.0/2.0 A11(NUM1+4,3)=1.0/2.0 IF(ITRIAL(IBM) == 2) THEN ALP1=ETA*COSH(ETA/2.0)-2.0*SINH(ETA/2.0) A11(NUM1+4,4)=-SINH(ETA/2.0) A11(NUM1+4,5)=ALP1/ETA ENDIF ENDIF ! right boundary condition: IBM=MAT(NEL) ETA=XX(NEL)*SQRT(SIGR(IBM)/DIFF(IBM)) IF((IQFR(2,NEL) == -1).OR.(IQFR(2,NEL) > 0)) THEN NUM2=5*(NEL-1) ! VOID AFACTOR=QFR(2,NEL) A11(NUM1+5,NUM2+1)=AFACTOR A11(NUM1+5,NUM2+2)=(AFACTOR/2.0+DIFF(IBM)/XX(NEL)) A11(NUM1+5,NUM2+3)=(AFACTOR/2.0+3.0*DIFF(IBM)/XX(NEL)) IF(ITRIAL(IBM) == 1) THEN A11(NUM1+5,NUM2+4)=DIFF(IBM)/(2.0*XX(NEL)) A11(NUM1+5,NUM2+5)=DIFF(IBM)/(5.0*XX(NEL)) ELSE ALP1=ETA*COSH(ETA/2.0)-2.0*SINH(ETA/2.0) A11(NUM1+5,NUM2+4)=AFACTOR*SINH(ETA/2.0)+(DIFF(IBM)/ 1 XX(NEL))*ETA*COSH(ETA/2.0) A11(NUM1+5,NUM2+5)=AFACTOR*ALP1/ETA+(DIFF(IBM)/ 1 XX(NEL))*ETA*SINH(ETA/2.0) ENDIF ELSE IF(IQFR(2,NEL) == -2) THEN NUM2=5*(NEL-1) ! REFL A11(NUM1+5,NUM2+2)=1.0 A11(NUM1+5,NUM2+3)=3.0 IF(ITRIAL(IBM) == 1) THEN A11(NUM1+5,NUM2+4)=1.0/2.0 A11(NUM1+5,NUM2+5)=1.0/5.0 ELSE A11(NUM1+5,NUM2+4)=ETA*COSH(ETA/2.0) A11(NUM1+5,NUM2+5)=ETA*SINH(ETA/2.0) ENDIF ELSE IF(IQFR(2,NEL) == -3) THEN NUM2=5*(NEL-1) ! ZERO A11(NUM1+5,NUM2+1)=1.0 A11(NUM1+5,NUM2+2)=1.0/2.0 A11(NUM1+5,NUM2+3)=1.0/2.0 IF(ITRIAL(IBM) == 2) THEN ALP1=ETA*COSH(ETA/2.0)-2.0*SINH(ETA/2.0) A11(NUM1+5,NUM2+4)=SINH(ETA/2.0) A11(NUM1+5,NUM2+5)=ALP1/ETA ENDIF ENDIF END SUBROUTINE NSS1TR