*DECK SYBALS SUBROUTINE SYBALS(NPIJ,MAXPTS,RAYRE,SIG,NGAUSS,ALBEDO,Z,PIJ) * *----------------------------------------------------------------------- * *Purpose: * Pij calculation in 1D spherical geometry. The tracking is computed * by subroutine SYBT1D. * *Copyright: * Copyright (C) 2005 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 * NPIJ number of regions. * MAXPTS first dimension of matrix PIJ. * RAYRE radius of regions array. * SIG total cross section array. * NGAUSS number of Gauss points. * ALBEDO outside albedo. * Z tracking information. * *Parameters: output * PIJ reduced collision probability matrix. * *Reference: * A. Kavenoky, 'Calcul et utilisation des probabilites de premiere * collision pour les milieux heterogenes a une dimension: Les programmes * ALCOLL et CORTINA', note CEA-N-1077, Commissariat a l'energie * atomique, mars 1969. * *---- * SUBROUTINE ARGUMENTS *---- INTEGER NPIJ,MAXPTS,NGAUSS REAL RAYRE(NPIJ+1),SIG(NPIJ),PIJ(MAXPTS,NPIJ),ALBEDO,Z(*) *---- * LOCAL VARIABLES *---- PARAMETER (PI=3.1415926535) LOGICAL LGEMPT REAL, ALLOCATABLE, DIMENSION(:,:) :: AUXI *---- * SCRATCH STORAGE ALLOCATION *---- ALLOCATE(AUXI(NPIJ,3)) *---- * TEST FOR VOIDED REGIONS *---- LGEMPT=.FALSE. VOLI=PI*RAYRE(1)**2 DO 10 IP=1,NPIJ LGEMPT=LGEMPT.OR.(2.0*(RAYRE(IP+1)-RAYRE(IP))*SIG(IP).LE.0.004) AUXI(IP,1)=(4.0/3.0)*PI*RAYRE(IP+1)**3-VOLI AUXI(IP,2)=MAX(1.0E-10,SIG(IP)) VOLI=(4.0/3.0)*PI*RAYRE(IP+1)**3 10 CONTINUE SURF=4.0*PI*RAYRE(NPIJ+1)**2 PIJ(:MAXPTS,:NPIJ)=0.0 IZ=1 IF(.NOT.LGEMPT) THEN * NO VOIDED REGIONS DETECTED. DO 42 IX=1,NPIJ DO 41 I=1,NGAUSS IZ=IZ+2 W=Z(IZ) DO 20 ITR=IX,NPIJ IZ=IZ+1 AUXI(ITR,3)=AUXI(ITR,2)*Z(IZ) 20 CONTINUE AUX0=2.0*AUXI(IX,3) EXP0=EXP(-AUX0) DII=AUX0-1.0+EXP0 PIJ(IX,IX)=PIJ(IX,IX)+W*DII/AUXI(IX,2)**2 TAU=AUX0 TAU1J=0.0 DO 40 IP=IX+1,NPIJ AUX1=AUXI(IP,3) EXP1=EXP(-TAU) EXP2=EXP(-AUX1) EXP3=EXP(-TAU1J) DII=AUX1-1.0+EXP2 CII=EXP1*(1.0-2.0*EXP2+EXP2*EXP2) CIJ1=EXP3*(1.0-EXP0-EXP2+EXP0*EXP2) PIJ(IP,IP)=PIJ(IP,IP)+W*(2.0*DII+CII)/AUXI(IP,2)**2 PIJ(IX,IP)=PIJ(IX,IP)+W*CIJ1/(AUXI(IX,2)*AUXI(IP,2)) TAUIJ=0.0 DO 30 JP=IP+1,NPIJ EXP4=EXP(-TAUIJ) EXP5=EXP(-AUXI(JP,3)) CIJ2=EXP4*(1.0-EXP2-EXP5+EXP2*EXP5) CIJ3=EXP1*EXP2*EXP4*(1.0-EXP2-EXP5+EXP2*EXP5) PIJ(IP,JP)=PIJ(IP,JP)+W*(CIJ2+CIJ3)/(AUXI(IP,2)*AUXI(JP,2)) TAUIJ=TAUIJ+AUXI(JP,3) 30 CONTINUE TAU=TAU+2.0*AUX1 TAU1J=TAU1J+AUX1 40 CONTINUE 41 CONTINUE 42 CONTINUE ELSE DO 72 IX=1,NPIJ DO 71 I=1,NGAUSS IZ=IZ+2 W=Z(IZ) DO 50 ITR=IX,NPIJ IZ=IZ+1 AUXI(ITR,3)=AUXI(ITR,2)*Z(IZ) 50 CONTINUE CALL SYB43C(DII,2.0*AUXI(IX,3)) PIJ(IX,IX)=PIJ(IX,IX)+W*DII/AUXI(IX,2)**2 TAU=2.0*AUXI(IX,3) TAU1J=0.0 DO 70 IP=IX+1,NPIJ CALL SYB43C(DII,AUXI(IP,3)) CALL SYB41C(CII,TAU,AUXI(IP,3),AUXI(IP,3)) CALL SYB41C(CIJ1,TAU1J,2.0*AUXI(IX,3),AUXI(IP,3)) PIJ(IP,IP)=PIJ(IP,IP)+W*(2.0*DII+CII)/AUXI(IP,2)**2 PIJ(IX,IP)=PIJ(IX,IP)+W*CIJ1/(AUXI(IX,2)*AUXI(IP,2)) TAUIJ=0.0 DO 60 JP=IP+1,NPIJ CALL SYB41C(CIJ2,TAUIJ,AUXI(IP,3),AUXI(JP,3)) CALL SYB41C(CIJ3,TAUIJ+TAU+AUXI(IP,3),AUXI(IP,3),AUXI(JP,3)) PIJ(IP,JP)=PIJ(IP,JP)+W*(CIJ2+CIJ3)/(AUXI(IP,2)*AUXI(JP,2)) TAUIJ=TAUIJ+AUXI(JP,3) 60 CONTINUE TAU=TAU+2*AUXI(IP,3) TAU1J=TAU1J+AUXI(IP,3) 70 CONTINUE 71 CONTINUE 72 CONTINUE ENDIF * DO 85 I=1,NPIJ DO 80 J=I,NPIJ VAL=PIJ(I,J) PIJ(I,J)=VAL/AUXI(I,1) PIJ(J,I)=VAL/AUXI(J,1) 80 CONTINUE 85 CONTINUE *---- * COMPUTING REFLECTED PROBABILITIES ASSUMING WHITE BOUNDARY CONDITION. *---- IF(ALBEDO.NE.0.0) THEN PSS=1.0 DO 100 IK=1,NPIJ AUXI(IK,3)=1.0 DO 90 JK=1,NPIJ AUXI(IK,3)=AUXI(IK,3)-PIJ(IK,JK)*AUXI(JK,2) 90 CONTINUE PSS=PSS-4.0*AUXI(IK,1)*AUXI(IK,2)*AUXI(IK,3)/SURF 100 CONTINUE AUX0=ALBEDO/(1.0-ALBEDO*PSS) DO 120 JK=1,NPIJ AUX1=AUX0*(4.0*AUXI(JK,1)/SURF)*AUXI(JK,3) DO 110 IK=1,NPIJ PIJ(IK,JK)=PIJ(IK,JK)+AUXI(IK,3)*AUX1 110 CONTINUE 120 CONTINUE ENDIF *---- * SCRATCH STORAGE DEALLOCATION *---- DEALLOCATE(AUXI) RETURN END