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*DECK XHX2D1
SUBROUTINE XHX2D1 (NGPT,ZGAUS,WGAUS,COTE,SIGT,TRONC,PII,PIS,PSS,
+ P)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Compute DP1 collision, leakage and transmission probabilities for
* hexagonal 2D geometries.
*
*Copyright:
* Copyright (C) 2002 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): M. Ouisloumen
*
*Parameters: input
* NGPT number of Gauss integration points.
* COTE length of one of sides of the hexagon.
* SIGT total cross section.
* TRONC voided block cutoff criterion.
* ZGAUS Gauss-Legendre integration points.
* WGAUS Gauss-Legendre integration weights.
*
*Parameters: output
* PII volume to volume reduced probability.
* PIS leakage probability (PIS(i) volume to side i).
* PSS transmission probability (PSS(i,j) side i to side j).
*
*Parameters: scratch
* P undefined.
*
*Comments:
* Faces identification for hexagon
* 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
*----
REAL FUNC3,FUNC4,FUNC5,X
INTEGER NGPT
REAL ZGAUS(NGPT),WGAUS(NGPT),COTE,SIGT,TRONC,PII,PIS(18),
+ PSS(18,18)
DOUBLE PRECISION P(16)
*----
* LOCAL VARIABLES
*----
PARAMETER (MKI3=600,MKI4=600,MKI5=600)
PARAMETER (PI=3.141592653589793,SQRT3=1.732050807568877,
+ SQRT2=1.414213562373095,ALOG2=.693147180559945,
+ ALOG3=1.0986122886681097,ALOGX=.7676517525907618)
*
REAL TAU(3),FKI3(3),FKI4(3),FKI5(3),FKI6(3)
INTEGER IROT(18,18)
DOUBLE PRECISION PIS10,PIS11
*----
* ASSUME THAT BICKLEY KI TABLES HAVE THE SAME TABULATION POINTS AND
* THE SAME TRUNCATION LIMIT.
*----
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/
*
FUNC3(X,K)=BI3(K)+X*(BI31(K)+X*BI32(K))
FUNC4(X,K)=BI4(K)+X*(BI41(K)+X*BI42(K))
FUNC5(X,K)=BI5(K)+X*(BI51(K)+X*BI52(K))
*----
* INITIALIZATION OF COLLISION PROBABILITIES
*----
P(:16)=0.0D0
*----
* COMPUTE CORDE =4*V*SIGMA/S=SQRT(3)*COTE*SIGMA (AVERAGE CORDE)
*----
S2S3=SQRT2*SQRT3
S3DS2=SQRT3/SQRT2
CAUX=SQRT3*COTE
CORDE=CAUX*SIGT
IF (CORDE.LE.TRONC) GO TO 300
*----
* CONSIDER EXPLICIT INTEGRATION OF F PSS
*----
PI12=PI/12.
*
* CONSIDER TWO CASES 1) IF ZGAUS(I)<0 => 1/COSFI>1/SINA>1/COSA
* 2) IF ZGAUS(I)>0 => 1/COSFI>1/COSA>1/SINA
*
NGPT2=IFIX(FLOAT(NGPT)/2.)
DO 50 I=1,NGPT
FI=PI12*(1.+ZGAUS(I))
COSFI=COS(FI)
SINFI=SIN(FI)
AUX=SQRT3*COSFI
COSA=AUX-SINFI
COSB=AUX+SINFI
AUX=SQRT3*SINFI
SINA=AUX+COSFI
SINB=COSFI-AUX
*----
* WEIGHTS TIMES BICKLEY NAYLOR FUNCTIONS
*----
W006=SINFI*COSA
W106=W006*COSB
W005=COSFI*SINA
W105=W005*COSB
W204=COSFI*SINB
W114=SINFI*SINFI*SINB
W224=COSFI*W204
*----
* OPTICAL LENGHTS
*----
TAU(1)=CORDE/COSFI
IAUX1=2
IAUX2=3
IF(I.GT.NGPT2) THEN
IAUX1=3
IAUX2=2
ENDIF
TAU(IAUX1)=CORDE/SINA
TAU(IAUX2)=CORDE/COSA
*
LB=4
IF(TAU(1).LT.XLIM3) THEN
LB=1
ELSEIF(TAU(2).LT.XLIM3) THEN
LB=2
ELSEIF(TAU(3).LT.XLIM3) THEN
LB=3
ENDIF
*
DO 10 J=LB,3
K1=NINT(PAS3*TAU(J))
FKI3(J)=FUNC3(TAU(J),K1)
FKI4(J)=FUNC4(TAU(J),K1)
FKI5(J)=FUNC5(TAU(J),K1)
FKI6(J)=.8*FKI4(J)+.2*TAU(J)*(FKI3(J)-FKI5(J))
10 CONTINUE
WEIGHT=0.0
GO TO (20,25,30,50),LB
*----
* PSS CALCULATION
*----
20 WEIGHT=WGAUS(I)
P(13)=P(13)+WEIGHT*SINB*FKI3(1)
P(14)=P(14)+WEIGHT*W204*FKI4(1)
P(16)=P(16)+WEIGHT*W114*FKI5(1)
P(15)=P(15)+WEIGHT*W224*FKI5(1)
AUX5=WEIGHT*W005
P(7)=P(7)+AUX5*(FKI4(IAUX1)-FKI4(1))
P(9)=P(9)+WEIGHT*W105*(FKI5(IAUX1)-FKI5(1))
AUX=AUX5*(FKI6(IAUX1)-FKI6(1))
P(11)=P(11)+AUX
P(10)=P(10)+W005*AUX
GO TO 30
*
25 WEIGHT=WGAUS(I)
AUX5=WEIGHT*W005
P(7)=P(7)+AUX5*FKI4(IAUX1)
P(9)=P(9)+WEIGHT*W105*FKI5(IAUX1)
AUX=AUX5*FKI6(IAUX1)
P(11)=P(11)+AUX
P(10)=P(10)+W005*AUX
30 P(1)=P(1)+WEIGHT*W006*(BI4(0)-FKI4(IAUX2))
P(3)=P(3)+WEIGHT*W106*(BI5(0)-FKI5(IAUX2))
AUX=W006*WEIGHT*(.533333333333333-FKI6(IAUX2))
P(5)=P(5)+AUX
P(4)=P(4)+AUX*W006
50 CONTINUE
*----
* NORMALIZATION
*----
CORDI=1./CORDE
X1=CORDI/3.
X2=CORDI*SQRT3
X3=3.*CORDI
X4=X2/SQRT2
P(1)=X1*P(1)
P(3)=X2*P(3)/6.
P(5)=-X4*P(5)
P(4)=X3*P(4)
P(7)=X1*P(7)
P(9)=X1*P(9)*.5
P(11)=-X4*P(11)
P(10)=X3*P(10)
P(13)=P(13)/3.
P(14)=SQRT2*P(14)
P(16)=4.*P(16)/3.
P(15)=6.*P(15)
AUX=2.*SQRT2
P(2)=S3DS2*P(3)-AUX*P(1)
P(8)=3.*S3DS2*P(9)-AUX*P(7)
P(14)=P(14)-AUX*P(13)
COEF=1./(6.*CORDE)
PIS10=(1.-2.*(P(1)+P(7))-P(13))*COEF
PIS(1)=REAL(PIS10)
PIS11=-(2.*(P(2)+P(8))+P(14))*COEF
PIS(2)=REAL(PIS11)
PII=(1.-6.*PIS(1))/SIGT
*
GO TO 350
*----
* USE SERIES EXPANSION FOR CORDE->0: TAYLOR SERIES OF KI FUNCTIONS
*----
300 TAU0=CORDE*.5
TAU02=TAU0*TAU0
AUX=SQRT3/PI
AUX0=1.-.5*SQRT3
AUX1=AUX*ALOG3-.33333333333333333
AUX2=2./SQRT3-(2.+ALOGX)/3.
P(1)=AUX0-.5*(TAU0*AUX1-TAU02*AUX2)
P(5)=-S2S3*(1.125*AUX0-.5*TAU0*AUX1+.375*TAU02*AUX2)
P(3)=(-(1.5*ALOGX+1.-SQRT3)*TAU0*.25+(1.-TAU02)/9+
+ AUX*TAU02/3.)*SQRT3
P(4)=2.25*(1.25*SQRT3-2.)-TAU0*(2.-3.*AUX)+TAU02*
+ (2.25*ALOGX-1.5)
XAUX=5.*SQRT3-9.
XAUX0=SQRT3-1.5
AUX1=AUX*(2.5*ALOG3-4.*ALOG2)-.5
AUX2=XAUX-2.*ALOG3+.5*ALOGX
P(7)=XAUX0+TAU0*AUX1-TAU02*AUX2/3.
P(11)=-S2S3*(1.125*XAUX0+TAU0*AUX1-.25*AUX2*TAU02)
P(9)=SQRT3/9.+.25*(XAUX-.5*SQRT3*(2.*ALOG3-ALOGX))*TAU0-
+ (9.*ALOG3-16.*ALOG2-3.)*TAU02/(3.*PI)
P(10)=2.25*(SQRT3-.75)+TAU0*(3.*AUX-6.)-1.5*TAU02*
+ (9.*(2.-SQRT3)+1.5*ALOGX-6.*ALOG3)
AUX0=2.*AUX0
AUX1=AUX*(.5*ALOG3-ALOG2)
P(13)=AUX0-8.*(1./6.+AUX1)*TAU0-4.*TAU02*(AUX0-.5*ALOG3)
P(15)=4.5*(2.5-SQRT3)-8.*TAU0+36.*TAU02*AUX0
AUX2=XAUX-2.*ALOG3+.5*ALOGX
P(16)=3.5-2.*SQRT3-64.*TAU0*(AUX1+1./12.)/3.+8.*TAU02*
+ (.5*ALOG3-2.*AUX0)
PSQ3=SQRT3/PI
P(14)=SQRT2*(2./3.-6.*TAU0*AUX0+TAU02*(4.+24.*PSQ3*
+ (.5*ALOG3-ALOG2)))
PII=COTE*SQRT3*(4.*SQRT3-8.-2.*ALOGX+10.*ALOG3)/12.
PIS(1)=(1.-SIGT*PII)/6.
PIS(2)=-SQRT2*(2.5-2.25*ALOG3+TAU0*(9.+PSQ3*(4.-8.*ALOG2+
+ 3.*ALOG3)-8./SQRT3-(20.*ALOG3-4.*ALOGX)/3.))/12.
AUX=2.*SQRT2
P(2)=S3DS2*P(3)-AUX*P(1)
P(8)=3.*S3DS2*P(9)-AUX*P(7)
P(14)=P(14)-AUX*P(13)
*
350 CONTINUE
*----
* COMPUTE REMAINING PROBABILITIES
*----
P(4)=P(4)-4.*SQRT3*P(3)+8.*P(1)
P(5)=P(5)+AUX*P(3)
P(6)=(S2S3*P(5)+8.*(-SQRT3*P(3)+P(1))-P(4))*2./9.
P(10)=P(10)-4.*SQRT2*P(8)-8.*P(7)
P(11)=P(11)+AUX*P(9)
P(12)=(8.*(P(7)-SQRT3*P(9))-S2S3*P(11)-P(10))*2./9.
P(15)=P(15)-4.*SQRT2*P(14)-8.*P(13)
P(3)=-P(3)
P(5)=-P(5)
P(9)=-P(9)
P(11)=-P(11)
*----
* TRANSMISSION MATRIX
*----
DO 59 I=1,18
DO 58 J=1,18
IB=IROT(J,I)
IF(IB.LT.0) THEN
PSS(I,J)=-REAL(P(-IB))
ELSEIF(IB.GT.0) THEN
PSS(I,J)=REAL(P(IB))
ELSE
PSS(I,J)=0.
ENDIF
58 CONTINUE
59 CONTINUE
*----
* LEAKAGE PRABABILITIES MATRIX
*----
PIS(3)=0.
K=3
DO 56 I=1,5
K=K+3
PIS(K-2)=PIS(1)
PIS(K-1)=PIS(2)
PIS(K)=0.
56 CONTINUE
*
RETURN
END
|
