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*DECK XDRH13
SUBROUTINE XDRH13 (IR1,NMILG,NG,NSMAX,IQUAD,FRTM,NS,IDIL,MIXGR,
1 RS,FRACT,SIGMA,SIGMS,P1I,P1DI,P1KI,SIGA1)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Calculation of the reduced collision probabilities for the She-Liu-Shi
* double heterogeneity model (part 1).
*
*Copyright:
* Copyright (C) 2019 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): R. Chambon
*
*Parameters: input
* IR1 number of elementary mixtures in the domain.
* NMILG number of composite mixtures in the domain.
* NG number of different kind of micro structures. A kind of
* micro structure is characterized by the radius of its
* micro volumes. All the micro volumes of the same kind
* should own the same nuclear properties in a given macro
* volume.
* NSMAX maximum number of volumes (tubes or shells) in each kind of
* micro structure.
* IQUAD quadrature parameter for the treatment of the micro volumes.
* if IQUAD < 0, lines with regular interval are applied.
* FRTM minimum volume fraction of the grain in the representative
* volume for She-Liu-Shi models.
* NS number of volumes in each kind of micro structure.
* IDIL elementary mixture indices in the diluent of the composite
* mixtures.
* MIXGR elementary mixture indices in the micro structures.
* RS radius of the micro volumes.
* FRACT volumic fractions of the micro volumes.
*
*Parameters: input/output
* SIGMA total macroscopic cross sections in each mixture of the
* composite geometry.
* SIGMS scattering macroscopic cross sections in each mixture of the
* composite geometry.
*
*Parameters: output
* P1I non collision probability in subvolume with 1 grain type.
* P1KI escape probability from layer k in subvolume
* with 1 grain type.
* P1DI escape probability from matrix in subvolume
* with 1 grain type.
* SIGA1 output cross sections.
*
*Reference:
* D. She, Z. Liu, and L. Shi, An Equivalent Homogenization Method for
* Treating the Stochastic Media, Nucl. Sci. Eng., 185, 351-360 (2018)
*
*-----------------------------------------------------------------------
*
IMPLICIT NONE
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER IR1,NMILG,NG,NSMAX,IQUAD,NS(NG),IDIL(NMILG),
1 MIXGR(NSMAX,NG,NMILG)
REAL FRTM,RS(NSMAX+1,NG),FRACT(NG,IR1+NMILG),SIGMA(0:IR1+NMILG),
1 SIGMS(0:IR1+NMILG),P1I(NG,NMILG),P1DI(NG,NMILG),
2 P1KI(NSMAX,NG,NMILG),SIGA1(NG,NMILG)
*----
* LOCAL VARIABLES
*----
INTEGER NR,IBM,J,K,N,M,MIL,NSMAX2
REAL DILF,DX,DXFACT,DRMIN,X,EP,EPI1,EPI2,LM,LGAR,SIGMA1,SIGMS1,
> FRT,RMAX,SIGT,XI,FRTT
DOUBLE PRECISION P1,P1D
REAL RGAR(NSMAX+2),LR(NSMAX+1)
*----
* ALLOCATABLE ARRAYS
*----
REAL, ALLOCATABLE, DIMENSION(:) :: SIG
DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:) :: P1K
*----
* SCRATCH STORAGE ALLOCATION
*----
NSMAX2=NSMAX+NG
ALLOCATE(SIG(NSMAX2),P1K(NSMAX2))
*----
* COMPUTE THE EQUIVALENT TOTAL AND SCATTERING CROSS SECTIONS
* IN COMPOSITE REGIONS
*----
DXFACT=100.0
IF(IQUAD.LT.0) DXFACT=REAL(-IQUAD)
DO 180 IBM=1,NMILG
MIL=IR1+IBM
SIGT=SIGMA(IDIL(IBM))
DILF=1.0
SIGMA(IR1+IBM)=0.0
SIGMS(IR1+IBM)=0.0
DO 10 J=1,NG
DILF=DILF-FRACT(J,MIL)
10 CONTINUE
DO 130 J=1,NG
FRT=FRACT(J,MIL)
IF(FRT.LE.0.00001) GO TO 130
NR=NS(J)
DRMIN=RS(NS(J)+1,J)
RGAR(1)=0.0
DO 15 K=2,NS(J)+1
DRMIN=MIN(DRMIN,RS(K,J)-RS(K-1,J))
RGAR(K)=RS(K,J)
15 CONTINUE
DO 20 K=1,NS(J)
P1K(K)=0.0D0
SIG(K)=SIGMA(MIXGR(K,J,IBM))
20 CONTINUE
FRTT=1.0-DILF
* FRT too small -> additional ring of matrix
IF((1.0-DILF).LT.FRTM) THEN
NR=NR+1
RGAR(NR+1)=RGAR(NR)*(FRTM/FRT)**(1.0/3.0)
SIG(NR)=SIGT
FRTT=FRTM
ENDIF
RMAX=RGAR(NR+1)
LGAR=4.0/3.0*RMAX/FRTT
P1=0.0D0
P1D=0.0D0
DX=DRMIN/DXFACT
XI=-0.5
K=1
* integral over radius to compute collision prob.
30 XI=XI+1.0
X=DX*XI
IF (X.GT.RGAR(K+1)) K=K+1
IF (K.GT.NR) GO TO 100
* Ref 1): Eq 13-17
* compute segment lengths
LM=LGAR/2.0
DO 40 N=1,NR
IF (N.LT.K) THEN
LR(N)=0.0D0
ELSEIF (N.EQ.K) THEN
LR(N)=(RGAR(N+1)**2.0 - X**2.0)**0.5
ELSE
LR(N)=(RGAR(N+1)**2.0 - X**2.0)**0.5
1 -(RGAR(N)**2.0 - X**2.0)**0.5
ENDIF
LM=LM-LR(N)
40 CONTINUE
* Ref 1): Eq 18-19
EP=2*SIGT*LM
DO 50 N=1,NR
EP=EP+2*LR(N)*SIG(N)
50 CONTINUE
P1=P1+X*DX*EXP(-EP)
DO 70 N=K,NR
EPI1=SIGT*LM
EPI2=SIGT*LM
DO 60 M=1,NR
IF (M.LT.N) THEN
EPI2=EPI2+2*LR(M)*SIG(M)
ELSEIF (M.EQ.N) THEN
EPI2=EPI2+LR(M)*SIG(M)
ELSE
EPI1=EPI1+LR(M)*SIG(M)
EPI2=EPI2+LR(M)*SIG(M)
ENDIF
60 CONTINUE
* bug
IF(N.GT.NSMAX2) CALL XABORT('XDRH13: NSMAX OVERFLOW.')
P1K(N)=P1K(N)+X*DX*(EXP(-EPI1)+EXP(-EPI2))*
1 (1.0D0-EXP(-LR(N)*SIG(N)))
70 CONTINUE
GO TO 30
100 CONTINUE
P1=P1*2/RMAX**2.0
P1I(J,IBM)=REAL(P1)
P1D=1.0D0-P1
DO 110 K=1,NS(J)
P1K(K)=P1K(K)*2/RMAX**2.0
P1KI(K,J,IBM)=REAL(P1K(K))
* collision prob. conservation, Ref 1): Eq 4
P1D=P1D-P1K(K)
110 CONTINUE
P1DI(J,IBM)=REAL(P1D)
* Ref 1): Eq 5
SIGMA1=REAL(-LOG(P1)/LGAR)
SIGA1(J,IBM)=SIGMA1
SIGMS1=REAL(P1D/(1.0-P1)*SIGMA1/SIGT*SIGMS(IDIL(IBM)))
DO 120 K=1,NS(J)
SIGMS1=REAL(SIGMS1+P1K(K)/(1.0-P1)*SIGMA1/SIG(K)*
1 SIGMS(MIXGR(K,J,IBM)))
120 CONTINUE
* Ref 1): Eq 26
SIGMA(IR1+IBM)=SIGMA(IR1+IBM)+SIGMA1*FRT/(1-DILF)
SIGMS(IR1+IBM)=SIGMS(IR1+IBM)+SIGMS1*FRT/(1-DILF)
130 CONTINUE
180 CONTINUE
*----
* SCRATCH STORAGE DEALLOCATION
*----
DEALLOCATE(P1K,SIG)
RETURN
END
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