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*DECK XHX2D0
SUBROUTINE XHX2D0 (NGPT,ZGAUS,WGAUS,COTE,SIGT,TRONC,PII,PIS,PSS)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Compute DP0 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).
*
*Comments:
* Faces identification for hexagon
* side 4
* xxxxxxxx
* x x
* side 5 x x side 3
* x x
* x x
* x x
* side 6 x x side 2
* x x
* xxxxxxxx
* side 1
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER NGPT
REAL ZGAUS(NGPT),WGAUS(NGPT),COTE,SIGT,TRONC,PII,PIS(6),
+ PSS(6,6)
*----
* 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(6,6)
DOUBLE PRECISION P(3),PIS10
*----
* 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, 1, 2, 3, 2, 1,
+ 1, 0, 1, 2, 3, 2,
+ 2, 1, 0, 1, 2, 3,
+ 3, 2, 1, 0, 1, 2,
+ 2, 3, 2, 1, 0, 1,
+ 1, 2, 3, 2, 1, 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(3)=0.
P(2)=0.
P(1)=0.
*----
* COMPUTE CORDE =4*V*SIGMA/S=SQRT(3)*COTE*SIGMA (AVERAGE CORDE)
*----
CORDE=SQRT3*COTE*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)
COSA=SQRT3*COSFI-SINFI
AUX=SQRT3*SINFI
SINA=AUX+COSFI
SINB=COSFI-AUX
*----
* 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(3)=P(3)+WEIGHT*SINB*FKI3(1)
P(2)=P(2)+WEIGHT*COSFI*SINA*(FKI4(IAUX1)-FKI4(1))
GO TO 30
*
25 WEIGHT=WGAUS(I)
P(2)=P(2)+WEIGHT*COSFI*SINA*FKI4(IAUX1)
30 P(1)=P(1)+WEIGHT*SINFI*COSA*(BI4(0)-FKI4(IAUX2))
50 CONTINUE
*----
* NORMALIZATION
*----
X1=1./(3.*CORDE)
P(1)=X1*P(1)
P(2)=X1*P(2)
P(3)=P(3)/3.
PIS10=(1.-2.*(P(1)+P(2))-P(3))/(6.*CORDE)
PII=(1.-6.*REAL(PIS10))/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)
AUX1=AUX*(2.5*ALOG3-4.*ALOG2)-.5
AUX2=5.*SQRT3-9.-2.*ALOG3+.5*ALOGX
P(2)=SQRT3-1.5+TAU0*AUX1-TAU02*AUX2/3.
AUX0=2.*AUX0
AUX1=AUX*(.5*ALOG3-ALOG2)
P(3)=AUX0-8.*(1./6.+AUX1)*TAU0-4.*TAU02*(AUX0-.5*ALOG3)
PII=COTE*SQRT3*(4.*SQRT3-8.-2.*ALOGX+10.*ALOG3)/12.
PIS10=(1.-SIGT*PII)/6.
*
350 CONTINUE
*----
* TRANSMISSION MATRIX
*----
DO 59 I=1,6
DO 58 J=1,6
IB=IROT(J,I)
IF(IB.GT.0) THEN
PSS(I,J)=REAL(P(IB))
ELSE
PSS(I,J)=0.
ENDIF
58 CONTINUE
59 CONTINUE
*----
* LEAKAGE PRABABILITIES MATRIX
*----
DO 56 I=1,6
PIS(I)=REAL(PIS10)
56 CONTINUE
*
RETURN
END
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