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subroutine NSSANM1(nel,ng,nmix,iqfr,qfr,mat,xxx,keff,diff,sigr,chi,sigf,scat,fd,savg)
!
!-----------------------------------------------------------------------
!
!Purpose:
! Compute the ANM volume fluxes and boundary fluxes and currents using
! a solution of one- and two-node relations in Cartesian 1D geometry.
!
!Copyright:
! Copyright (C) 2022 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
! nel number of nodes in the nodal calculation.
! ng number of energy groups.
! nmix number of material mixtures in the nodal calculation.
! iqfr node-ordered physical albedo indices.
! qfr albedo function information.
! mat material mixture index in eacn node.
! xxx Cartesian coordinates along the X axis.
! keff effective multiplication facctor.
! diff diffusion coefficients
! sigr removal cross sections.
! chi fission spectra.
! sigf nu times fission cross section.
! scat scattering cross section.
! fd discontinuity factors
! savg nodal fluxes.
!
!Parameters: output
! savg boundary fluxes and currents.
!
!-----------------------------------------------------------------------
!
!----
! subroutine arguments
!----
integer,intent(in) :: nel,ng,nmix,iqfr(6,nel),mat(nel)
real,intent(in) :: qfr(6,nel,ng),xxx(nel+1),keff,diff(nmix,ng),sigr(nmix,ng), &
& chi(nmix,ng),sigf(nmix,ng),scat(nmix,ng,ng),fd(nmix,2,ng,ng)
real, dimension(4*nel+1,ng),intent(inout) :: savg
!----
! allocatable arrays
!----
real, allocatable, dimension(:) :: work1,work2,work4,work5
real, allocatable, dimension(:,:) :: A,B,Lambda,work3
real(kind=8), allocatable, dimension(:,:,:) :: Lx,Rx
!----
! scratch storage allocation
!----
allocate(A(ng,ng+1),B(ng,ng),Lambda(ng,ng))
allocate(work1(ng),work2(ng),work3(ng,ng),work4(ng),work5(ng))
allocate(Lx(ng,2*ng,nel),Rx(ng,2*ng,nel))
!
! compute nodal coefficients
do iel=1,nel
ibm=mat(iel)
if(ibm == 0) cycle
work1(:ng)=diff(ibm,:ng)
work2(:ng)=sigr(ibm,:ng)
work3(:ng,:ng)=scat(ibm,:ng,:ng)
work4(:ng)=chi(ibm,:ng)
work5(:ng)=sigf(ibm,:ng)
delx=xxx(iel+1)-xxx(iel)
call NSSLR1(keff,ng,delx,work1,work2,work3,work4,work5, &
& Lx(1,1,iel),Rx(1,1,iel))
enddo
!----
! compute boundary currents
! left one-node relation
!----
A(:ng,:ng+1)=0.0
if((iqfr(1,1) > 0).or.(iqfr(1,1) == -1)) then
! physical albedo
Lambda(:ng,:ng)=0.0
do ig=1,ng
Lambda(ig,ig)=qfr(1,1,ig)
enddo
A(:ng,:ng)=real(matmul(Lambda(:ng,:ng),Lx(:ng,ng+1:2*ng,1)),4)
B(:ng,:ng)=real(matmul(Lambda(:ng,:ng),Lx(:ng,:ng,1)),4)
do ig=1,ng
A(ig,ig)=1.0+A(ig,ig)
enddo
A(:ng,ng+1)=-matmul(B(:ng,:ng),savg(1,:ng))
else if(iqfr(1,1) == -2) then
! zero net current
do ig=1,ng
A(ig,ig)=1.0
enddo
else if(iqfr(1,1) == -3) then
! zero flux
A(:ng,:ng)=real(Lx(:ng,ng+1:2*ng,1),4)
A(:ng,ng+1)=real(-matmul(Lx(:ng,:ng,1),savg(1,:ng)),4)
else
call XABORT('NSSANM1: illegal left boundary condition.')
endif
call ALSB(ng,1,A,ier,ng)
if(ier /= 0) call XABORT('NSSANM1: singular matrix.(1)')
savg(3*nel+1,:ng)=A(:ng,ng+1)
! two-node relations
do i=2,nel
A(:ng,:ng)=real(matmul(fd(mat(i-1),2,:ng,:ng),Rx(:ng,ng+1:2*ng,i-1))- &
& matmul(fd(mat(i),1,:ng,:ng),Lx(:ng,ng+1:2*ng,i)),4)
A(:ng,ng+1)=-real(matmul(matmul(fd(mat(i-1),2,:ng,:ng),Rx(:ng,:ng,i-1)),savg(i-1,:ng))- &
& matmul(matmul(fd(mat(i),1,:ng,:ng),Lx(:ng,:ng,i)),savg(i,:ng)),4)
call ALSB(ng,1,A,ier,ng)
if(ier /= 0) call XABORT('NSSANM1: singular matrix.(2)')
savg(3*nel+i,:ng)=A(:ng,ng+1)
enddo
! right one-node relation
if((iqfr(2,nel) > 0).or.(iqfr(2,nel) == -1)) then
! physical albedo
Lambda(:ng,:ng)=0.0
do ig=1,ng
Lambda(ig,ig)=qfr(2,nel,ig)
enddo
A(:ng,:ng)=real(matmul(Lambda(:ng,:ng),Rx(:ng,ng+1:2*ng,nel)),4)
B(:ng,:ng)=real(matmul(Lambda(:ng,:ng),Rx(:ng,:ng,nel)),4)
do ig=1,ng
A(ig,ig)=-1.0+A(ig,ig)
enddo
A(:ng,ng+1)=-matmul(B(:ng,:ng),savg(nel,:ng))
else if(iqfr(2,nel) == -2) then
! zero net current
do ig=1,ng
A(2*nel*ng+ig,2*nel*ng+ig)=1.0
enddo
else if(iqfr(2,nel) == -3) then
! zero flux
A(:ng,:ng)=real(Rx(:ng,ng+1:2*ng,nel),4)
A(:ng,ng+1)=real(-matmul(Rx(:ng,:ng,nel),savg(nel,:ng)),4)
else
call XABORT('NSSANM1: illegal right boundary condition.')
endif
call ALSB(ng,1,A,ier,ng)
if(ier /= 0) call XABORT('NSSANM1: singular matrix.(3)')
savg(4*nel+1,:ng)=A(:ng,ng+1)
!----
! compute boundary fluxes
!----
do i=1,nel
savg(nel+i,:ng)=real(matmul(Lx(:ng,:ng,i),savg(i,:ng))+ &
& matmul(Lx(:ng,ng+1:2*ng,i),savg(3*nel+i,:ng)),4)
savg(2*nel+i,:ng)=real(matmul(Rx(:ng,:ng,i),savg(i,:ng))+ &
& matmul(Rx(:ng,ng+1:2*ng,i),savg(3*nel+i+1,:ng)),4)
enddo
!----
! scratch storage deallocation
!----
deallocate(Rx,Lx)
deallocate(work5,work4,work3,work2,work1)
deallocate(Lambda,B,A)
end subroutine NSSANM1
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