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*DECK SYBHN2
SUBROUTINE SYBHN2(NREG,NSURF,SIDE,Z,IZ,VOL,SIGT,TRONC,PVS,PSS)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Compute the DP-1 leakage and transmission probabilities for an
* heterogeneous non-sectorized hexagonal cell. The tracks are computed
* by SYBHTK.
*
*Copyright:
* Copyright (C) 2008 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
* NREG number regions in the cell.
* NSURF number of surfaces.
* SIDE length of one of sides of the hexagon.
* Z real integration mesh.
* IZ integer integration mesh.
* VOL volumes.
* SIGT total cross sections.
* TRONC voided block cutoff criterion.
*
*Parameters: output
* PVS leakage probability:
* PVS(i,j) for volume i to side j with i=1,nr and j=1,18.
* PSS transmission probability:
* PSS(i,j) for side i to side j with i=1,18 and j=1,18.
*
*Reference:
* M. Ouisloumen, Resolution par la methode des probabilites de
* collision de l'equation integrale du transport a deux et trois
* dimensions en geometrie hexagonale, Ph. D. thesis, Ecole
* Polytechnique de Montreal, Montreal, October 1993.
*
*Comments:
* hexagone surface identification.
* side a,b,c
* side 4,5,6 dir a -> isotropic
* xxxxxxxx dir c -> tangent to surface
* x x dir b -> normal to surface
* side 7,8,9 x x side 1,2,3
* x x
* x x
* x x
* side 10,11,12 x x side 16,17,18
* x x
* xxxxxxxx
* side 13,14,15
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER NREG,NSURF,IZ(*)
REAL Z(*),SIDE,SIGT(NREG),TRONC,VOL(NREG),PVS(NREG,3*NSURF),
1 PSS(3*NSURF,3*NSURF)
*----
* LOCAL VARIABLES
*----
PARAMETER (MKI3=600,MKI4=600,MKI5=600)
PARAMETER (SQ3=1.732050807568877,SQ2=1.414213562373095,
1 PI=3.141592653589793,ZI30=0.785398164,ZI40=0.666666667)
REAL KI3,KI4,KI5
REAL PBB(16)
INTEGER IROT(18,18)
REAL, ALLOCATABLE, DIMENSION(:,:) :: COSINU
*----
* BICKLEY TABLES
*----
COMMON /BICKL3/BI3(0:MKI3),BI31(0:MKI3),BI32(0:MKI3),PAS3,XLIM3,L3
COMMON /BICKL4/BI4(0:MKI4),BI41(0:MKI4),BI42(0:MKI4),PAS4,XLIM4,L4
COMMON /BICKL5/BI5(0:MKI5),BI51(0:MKI5),BI52(0:MKI5),PAS5,XLIM5,L5
*
SAVE IROT
DATA IROT /
+ 0, 0, 0, 1, 2,-3, 7, 8,-9,13,14, 0, 7, 8, 9, 1, 2, 3,
+ 0, 0, 0, 2, 4, 5, 8,10,11,14,15, 0, 8,10,-11, 2, 4,-5,
+ 0, 0, 0, 3,-5, 6, 9,-11,12,0, 0,16,-9,11,12,-3, 5,6,
+ 1, 2, 3, 0, 0, 0, 1, 2,-3, 7, 8,-9,13,14, 0, 7, 8, 9,
+ 2, 4,-5, 0, 0, 0, 2, 4, 5, 8,10,11,14,15, 0, 8,10,-11,
+ -3, 5, 6, 0, 0, 0, 3,-5, 6, 9,-11,12,0, 0,16,-9,11,12,
+ 7, 8, 9, 1, 2, 3, 0, 0, 0, 1, 2,-3, 7, 8,-9,13,14, 0,
+ 8,10,-11, 2, 4,-5, 0, 0, 0, 2, 4, 5, 8,10,11,14,15, 0,
+ -9,11,12,-3, 5, 6, 0, 0, 0, 3,-5, 6, 9,-11,12,0, 0,16,
+ 13,14, 0, 7, 8, 9, 1, 2, 3, 0, 0, 0, 1, 2,-3, 7, 8,-9,
+ 14,15, 0, 8,10,-11, 2, 4,-5, 0, 0, 0, 2, 4, 5, 8,10,11,
+ 0, 0,16,-9,11,12,-3, 5, 6, 0, 0, 0, 3,-5, 6, 9,-11,12,
+ 7, 8,-9, 13,14, 0, 7, 8, 9, 1, 2, 3, 0, 0, 0, 1, 2,-3,
+ 8,10,11,14,15, 0, 8,10,-11, 2, 4,-5, 0, 0, 0, 2, 4, 5,
+ 9,-11,12, 0, 0,16,-9,11,12,-3, 5, 6, 0, 0, 0, 3,-5, 6,
+ 1, 2,-3, 7, 8,-9, 13,14, 0, 7, 8, 9, 1, 2, 3, 0, 0, 0,
+ 2, 4, 5, 8,10,11,14,15, 0, 8,10,-11, 2, 4,-5, 0, 0, 0,
+ 3,-5, 6, 9,-11,12, 0, 0,16,-9,11,12,-3, 5, 6, 0, 0, 0/
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(COSINU(2,NSURF))
*----
* INTEGRATION USING THE TRACKING
*----
ZERO=TRONC/(SQ3*SIDE)
PBB(:16)=0.0
PVS(:NREG,:18)=0.0
IZ0=2
IZR=4
DO 205 IA=1,IZ(2)
DO 20 I=1,NSURF
COSINU(1,I)=Z(IZR+1)
COSINU(2,I)=Z(IZR+2)
IZR=IZR+2
20 CONTINUE
MNT=IZ(IZ0+1)
IZ0=IZ0+2
IZR=IZR+1
DO 200 IMNT=1,MNT
NH=IZ(IZ0+1)
NX=IZ(IZ0+2)
ISURF=IZ(IZ0+3)+1
JSURF=IZ(IZ0+NH+4)+1
DO 190 INX=1,NX
Z1=Z(IZR+1)/SIDE
IZR=IZR+1
DW1=Z1*COSINU(1,ISURF)
DW2=Z1*COSINU(1,JSURF)
IF((ISURF.EQ.5).AND.(JSURF.EQ.6)) THEN
W610=SQ3*COSINU(2,ISURF)+COSINU(1,ISURF)
W611=2.0*COSINU(2,JSURF)*COSINU(2,ISURF)
Z2=Z1*W611
Z3=Z1*W610
KI3=ZI30
KI4=ZI40
POP=0.0
DO 40 I=1,NH
III=IZ(IZ0+3+I)-NSURF+1
SIGTI=SIGT(III)
POP0=POP
POP=POP+SIGTI*Z(IZR+I)
IF(POP.LT.XLIM3) GO TO 30
IF(SIGTI.LE.ZERO) GO TO 50
PVS(III,1)=PVS(III,1)+KI3*Z1
PVS(III,2)=PVS(III,2)+KI4*DW1
GO TO 50
30 K=NINT(POP*PAS3)
WI3=BI3(K)+POP*(BI31(K)+POP*BI32(K))
WI4=BI4(K)+POP*(BI41(K)+POP*BI42(K))
IF(SIGTI.LE.ZERO) THEN
PVS(III,1)=PVS(III,1)+TABKI(2,POP0)*Z(IZR+I)*Z1
PVS(III,2)=PVS(III,2)+KI3*Z(IZR+I)*DW1
ELSE
PVS(III,1)=PVS(III,1)+(KI3-WI3)*Z1
PVS(III,2)=PVS(III,2)+(KI4-WI4)*DW1
ENDIF
KI3=WI3
KI4=WI4
40 CONTINUE
50 KI3=ZI30
KI4=ZI40
POP=0.0
K=0
DO 80 I=1,NH
III=IZ(IZ0+3+I)-NSURF+1
SIGTI=SIGT(III)
POP0=POP
POP=POP+SIGTI*Z(IZR+NH+1-I)
IF(POP.LT.XLIM3) GO TO 70
IF(SIGTI.LE.ZERO) GO TO 185
PVS(III,1)=PVS(III,1)+KI3*Z1
PVS(III,2)=PVS(III,2)+KI4*DW2
GO TO 185
70 K=NINT(POP*PAS3)
WI3=BI3(K)+POP*(BI31(K)+POP*BI32(K))
WI4=BI4(K)+POP*(BI41(K)+POP*BI42(K))
IF(SIGTI.LE.ZERO) THEN
PVS(III,1)=PVS(III,1)+TABKI(2,POP0)*Z(IZR+NH+1-I)*Z1
PVS(III,2)=PVS(III,2)+KI3*Z(IZR+NH+1-I)*DW2
ELSE
PVS(III,1)=PVS(III,1)+(KI3-WI3)*Z1
PVS(III,2)=PVS(III,2)+(KI4-WI4)*DW2
ENDIF
KI3=WI3
KI4=WI4
80 CONTINUE
KI5=BI5(K)+POP*(BI51(K)+POP*BI52(K))
PBB(1)=PBB(1)+KI3*Z1
PBB(3)=PBB(3)+KI4*Z3
PBB(5)=PBB(5)+KI5*Z1
PBB(6)=PBB(6)+KI5*Z2
ELSE IF((ISURF.EQ.5).AND.(JSURF.EQ.1)) THEN
W610=SQ3*COSINU(1,JSURF)+COSINU(2,JSURF)
W511=2.0*COSINU(2,ISURF)*COSINU(2,JSURF)
Z2=Z1*W511
Z3=Z1*W610
KI3=ZI30
KI4=ZI40
POP=0.0
K=0
DO 100 I=1,NH
III=IZ(IZ0+3+I)-NSURF+1
SIGTI=SIGT(III)
POP0=POP
POP=POP+SIGTI*Z(IZR+I)
IF(POP.LT.XLIM3) GO TO 90
IF(SIGTI.LE.ZERO) GO TO 110
PVS(III,1)=PVS(III,1)+KI3*Z1
PVS(III,2)=PVS(III,2)+KI4*DW1
GO TO 110
90 K=NINT(POP*PAS3)
WI3=BI3(K)+POP*(BI31(K)+POP*BI32(K))
WI4=BI4(K)+POP*(BI41(K)+POP*BI42(K))
IF(SIGTI.LE.ZERO) THEN
PVS(III,1)=PVS(III,1)+TABKI(2,POP0)*Z(IZR+I)*Z1
PVS(III,2)=PVS(III,2)+KI3*Z(IZR+I)*DW1
ELSE
PVS(III,1)=PVS(III,1)+(KI3-WI3)*Z1
PVS(III,2)=PVS(III,2)+(KI4-WI4)*DW1
ENDIF
KI3=WI3
KI4=WI4
100 CONTINUE
110 KI3=ZI30
KI4=ZI40
POP=0.0
DO 130 I=1,NH
III=IZ(IZ0+3+I)-NSURF+1
SIGTI=SIGT(III)
POP0=POP
POP=POP+SIGTI*Z(IZR+NH+1-I)
IF(POP.LT.XLIM3) GO TO 120
IF(SIGTI.LE.ZERO) GO TO 185
PVS(III,1)=PVS(III,1)+KI3*Z1
PVS(III,2)=PVS(III,2)+KI4*DW2
GO TO 185
120 K=NINT(POP*PAS3)
WI3=BI3(K)+POP*(BI31(K)+POP*BI32(K))
WI4=BI4(K)+POP*(BI41(K)+POP*BI42(K))
IF(SIGTI.LE.ZERO) THEN
PVS(III,1)=PVS(III,1)+TABKI(2,POP0)*Z(IZR+NH+1-I)*Z1
PVS(III,2)=PVS(III,2)+KI3*Z(IZR+NH+1-I)*DW2
ELSE
PVS(III,1)=PVS(III,1)+(KI3-WI3)*Z1
PVS(III,2)=PVS(III,2)+(KI4-WI4)*DW2
ENDIF
KI3=WI3
KI4=WI4
130 CONTINUE
KI5=BI5(K)+POP*(BI51(K)+POP*BI52(K))
PBB(7)=PBB(7)+KI3*Z1
PBB(9)=PBB(9)+KI4*Z3
PBB(11)=PBB(11)+KI5*Z1
PBB(12)=PBB(12)+KI5*Z2
ELSE IF((ISURF.EQ.5).AND.(JSURF.EQ.2)) THEN
Z2=Z1*COSINU(1,ISURF)
Z3=Z1*COSINU(1,ISURF)*COSINU(1,JSURF)
KI3=ZI30
KI4=ZI40
POP=0.0
K=0
DO 150 I=1,NH
III=IZ(IZ0+3+I)-NSURF+1
SIGTI=SIGT(III)
POP0=POP
POP=POP+SIGTI*Z(IZR+I)
IF(POP.LT.XLIM3) GO TO 140
IF(SIGTI.LE.ZERO) GO TO 160
PVS(III,1)=PVS(III,1)+KI3*Z1
PVS(III,2)=PVS(III,2)+KI4*Z2
GO TO 160
140 K=NINT(POP*PAS3)
WI3=BI3(K)+POP*(BI31(K)+POP*BI32(K))
WI4=BI4(K)+POP*(BI41(K)+POP*BI42(K))
IF(SIGTI.LE.ZERO) THEN
PVS(III,1)=PVS(III,1)+TABKI(2,POP0)*Z(IZR+I)*Z1
PVS(III,2)=PVS(III,2)+KI3*Z(IZR+I)*Z2
ELSE
PVS(III,1)=PVS(III,1)+(KI3-WI3)*Z1
PVS(III,2)=PVS(III,2)+(KI4-WI4)*Z2
ENDIF
KI3=WI3
KI4=WI4
150 CONTINUE
160 KI3=ZI30
KI4=ZI40
POP=0.0
K=0
DO 180 I=1,NH
III=IZ(IZ0+3+I)-NSURF+1
SIGTI=SIGT(III)
POP0=POP
POP=POP+SIGTI*Z(IZR+NH+1-I)
IF(POP.LT.XLIM3) GO TO 170
IF(SIGTI.LE.ZERO) GO TO 185
PVS(III,1)=PVS(III,1)+KI3*Z1
PVS(III,2)=PVS(III,2)+KI4*Z2
GO TO 185
170 K=NINT(POP*PAS3)
WI3=BI3(K)+POP*(BI31(K)+POP*BI32(K))
WI4=BI4(K)+POP*(BI41(K)+POP*BI42(K))
IF(SIGTI.LE.ZERO) THEN
PVS(III,1)=PVS(III,1)+TABKI(2,POP0)*Z(IZR+NH+1-I)*Z1
PVS(III,2)=PVS(III,2)+KI3*Z(IZR+NH+1-I)*Z2
ELSE
PVS(III,1)=PVS(III,1)+(KI3-WI3)*Z1
PVS(III,2)=PVS(III,2)+(KI4-WI4)*Z2
ENDIF
KI3=WI3
KI4=WI4
180 CONTINUE
KI5=BI5(K)+POP*(BI51(K)+POP*BI52(K))
PBB(13)=PBB(13)+2.0*KI3*Z1
PBB(14)=PBB(14)+2.0*KI4*Z2
PBB(15)=PBB(15)+2.0*KI5*Z3
PBB(16)=PBB(16)+2.0*KI5*(Z1-Z3)
ENDIF
185 IZR=IZR+NH
190 CONTINUE
IZ0=IZ0+NH+4
200 CONTINUE
205 CONTINUE
*----
* PSS ORTHONORMALIZATION
*----
E1=Z(1)
E2=Z(2)
E3=Z(3)
E4=Z(4)
P13=PBB(13)
PBB(1)=PBB(1)*E1*E1
PBB(7)=PBB(7)*E1*E1
PBB(13)=P13*E1*E1
PBB(3)=-0.25*PBB(3)*E1*E4*SQ3
PBB(9)=-0.25*PBB(9)*E1*E4
PBB(14)=E1*(PBB(14)*E2-E3*P13)
SQRT6=.25*SQ3*E4*E2
PBB(5)=SQRT6*PBB(5)+E3*PBB(3)/E1
PBB(11)=SQRT6*PBB(11)+E3*PBB(9)/E1
PBB(6)=-0.5*E4*E4*PBB(6)
PBB(12)=-0.5*E4*E4*PBB(12)
PBB(16)=E4*E4*PBB(16)
PBB(15)=E2*E2*PBB(15)-E3*(2.*PBB(14)/E1+E3*P13)
*----
* PIS NORMALIZATION
*----
DO 210 I=1,NREG
COEF=0.25*SIDE/VOL(I)
IF(SIGT(I).LE.ZERO) THEN
PVS(I,2)=COEF*E1*(E2*PVS(I,2)-E3*PVS(I,1))
PVS(I,1)=COEF*PVS(I,1)*E1*E1
ELSE
SIGTI=COEF/SIGT(I)
PVS(I,2)=SIGTI*E1*(E2*PVS(I,2)-E3*PVS(I,1))
PVS(I,1)=SIGTI*PVS(I,1)*E1*E1
ENDIF
210 CONTINUE
*----
* OTHER PROBABILITIES COMPUTATION
*----
PBB(2)=(-SQ3*PBB(3)-4.*PBB(1))/SQ2
PBB(4)=-4.5*PBB(6)+SQ3*(-SQ2*PBB(5)+8.*PBB(3))+8.*PBB(1)
PBB(8)=(-3.*SQ3*PBB(9)-4.*PBB(7))/SQ2
PBB(10)=-4.5*PBB(12)+SQ3*(SQ2*PBB(11)+8.*PBB(9))+8.*PBB(7)
*----
* TRANSMISSION MATRIX
*----
DO 225 I=1,18
DO 220 J=1,18
IB=IROT(J,I)
IF(IB.LT.0) THEN
PSS(I,J)=-PBB(-IB)
ELSEIF(IB.GT.0) THEN
PSS(I,J)=PBB(IB)
ELSE
PSS(I,J)=0.
ENDIF
220 CONTINUE
225 CONTINUE
*----
* LEAKAGE MARTIX
*----
DO 235 J=1,NREG
K=3
DO 230 I=1,5
K=K+3
PVS(J,K-1)=PVS(J,2)
PVS(J,K-2)=PVS(J,1)
230 CONTINUE
235 CONTINUE
*----
* SCRATCH STORAGE DEALLOCATION
*----
DEALLOCATE(COSINU)
RETURN
END
|
