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2D_BWR_benchmark.f90
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! XYGeo.f90
!
! FUNCTIONS:
! XYGeo - Entry point of console application.
!
!****************************************************************************
!
! PROGRAM: XYGeo
!
! PURPOSE: Entry point for the console application.
!
!****************************************************************************
module DATA_STRUCTURE
implicit none
private i, N
integer :: i
integer, parameter :: SN = 8
integer, parameter :: N = SN*(SN+2)/2
integer, parameter :: SPECIFIED_BOUND = 1
integer, parameter :: REFLECTIVE_BOUND = 2
! angular type, with quadrature set
type :: angular_type
real(8) :: mu
real(8) :: eta
real(8) :: omega
endtype
! mesh type
type :: mesh_type
real(8) :: flux ! angular flux
real(8) :: x
real(8) :: y
real(8) :: sigma_t ! total macro-xs
real(8) :: sigma_s11 ! scatter macro-xs
real(8) :: sigma_s12
real(8) :: sigma_s21
real(8) :: sigma_s22
real(8) :: sigma_f ! fission macro-xs
real(8) :: Xf ! fission spectrum
real(8) :: scatter_source ! scattering source term
real(8) :: external_source ! external source term
real(8) :: fission_source ! fission source term
real(8) :: total_source ! total source term
endtype
! group constant type
type :: group_xs
real(8) :: sigma_t
real(8) :: sigma_s11
real(8) :: sigma_s12
real(8) :: sigma_s21
real(8) :: sigma_s22
real(8) :: sigma_f
real(8) :: external_source
endtype
! initialize the angular parameter
type(angular_type), dimension(N) :: angular
! 1. mu<0, eta<0
data angular(1)%mu / -0.2182179 /
data angular(2)%mu / -0.5773503 /
data angular(3)%mu / -0.7867958 /
data angular(4)%mu / -0.9511897 /
data angular(5)%mu / -0.2182179 /
data angular(6)%mu / -0.5773503 /
data angular(7)%mu / -0.7867958 /
data angular(8)%mu / -0.2182179 /
data angular(9)%mu / -0.5773503 /
data angular(10)%mu / -0.2182179 /
data angular(1)%eta / -0.9511897 /
data angular(2)%eta / -0.7867958 /
data angular(3)%eta / -0.5773503 /
data angular(4)%eta / -0.2182179 /
data angular(5)%eta / -0.7867958 /
data angular(6)%eta / -0.5773503 /
data angular(7)%eta / -0.2182179 /
data angular(8)%eta / -0.5773503 /
data angular(9)%eta / -0.2182179 /
data angular(10)%eta/ -0.2182179 /
! 2. mu>0, eta<0
data angular(11)%mu / 0.2182179 /
data angular(12)%mu / 0.5773503 /
data angular(13)%mu / 0.7867958 /
data angular(14)%mu / 0.9511897 /
data angular(15)%mu / 0.2182179 /
data angular(16)%mu / 0.5773503 /
data angular(17)%mu / 0.7867958 /
data angular(18)%mu / 0.2182179 /
data angular(19)%mu / 0.5773503 /
data angular(20)%mu / 0.2182179 /
data angular(11)%eta / -0.9511897 /
data angular(12)%eta / -0.7867958 /
data angular(13)%eta / -0.5773503 /
data angular(14)%eta / -0.2182179 /
data angular(15)%eta / -0.7867958 /
data angular(16)%eta / -0.5773503 /
data angular(17)%eta / -0.2182179 /
data angular(18)%eta / -0.5773503 /
data angular(19)%eta / -0.2182179 /
data angular(20)%eta / -0.2182179 /
! 3. mu<0, eta>0
data angular(21)%mu / -0.2182179 /
data angular(22)%mu / -0.5773503 /
data angular(23)%mu / -0.7867958 /
data angular(24)%mu / -0.9511897 /
data angular(25)%mu / -0.2182179 /
data angular(26)%mu / -0.5773503 /
data angular(27)%mu / -0.7867958 /
data angular(28)%mu / -0.2182179 /
data angular(29)%mu / -0.5773503 /
data angular(30)%mu / -0.2182179 /
data angular(21)%eta / 0.9511897 /
data angular(22)%eta / 0.7867958 /
data angular(23)%eta / 0.5773503 /
data angular(24)%eta / 0.2182179 /
data angular(25)%eta / 0.7867958 /
data angular(26)%eta / 0.5773503 /
data angular(27)%eta / 0.2182179 /
data angular(28)%eta / 0.5773503 /
data angular(29)%eta / 0.2182179 /
data angular(30)%eta / 0.2182179 /
! 4. mu>0, eta>0
data angular(31)%mu / 0.2182179 /
data angular(32)%mu / 0.5773503 /
data angular(33)%mu / 0.7867958 /
data angular(34)%mu / 0.9511897 /
data angular(35)%mu / 0.2182179 /
data angular(36)%mu / 0.5773503 /
data angular(37)%mu / 0.7867958 /
data angular(38)%mu / 0.2182179 /
data angular(39)%mu / 0.5773503 /
data angular(40)%mu / 0.2182179 /
data angular(31)%eta / 0.9511897 /
data angular(32)%eta / 0.7867958 /
data angular(33)%eta / 0.5773503 /
data angular(34)%eta / 0.2182179 /
data angular(35)%eta / 0.7867958 /
data angular(36)%eta / 0.5773503 /
data angular(37)%eta / 0.2182179 /
data angular(38)%eta / 0.5773503 /
data angular(39)%eta / 0.2182179 /
data angular(40)%eta / 0.2182179 /
! omega
data angular(1)%omega / 0.1209877 /
data angular(2)%omega / 0.0907407 /
data angular(3)%omega / 0.0907407 /
data angular(4)%omega / 0.1209877 /
data angular(5)%omega / 0.0907407 /
data angular(6)%omega / 0.0925926 /
data angular(7)%omega / 0.0907407 /
data angular(8)%omega / 0.0907407 /
data angular(9)%omega / 0.0907407 /
data angular(10)%omega / 0.1209877 /
data angular(11)%omega / 0.1209877 /
data angular(12)%omega / 0.0907407 /
data angular(13)%omega / 0.0907407 /
data angular(14)%omega / 0.1209877 /
data angular(15)%omega / 0.0907407 /
data angular(16)%omega / 0.0925926 /
data angular(17)%omega / 0.0907407 /
data angular(18)%omega / 0.0907407 /
data angular(19)%omega / 0.0907407 /
data angular(20)%omega / 0.1209877 /
data angular(21)%omega / 0.1209877 /
data angular(22)%omega / 0.0907407 /
data angular(23)%omega / 0.0907407 /
data angular(24)%omega / 0.1209877 /
data angular(25)%omega / 0.0907407 /
data angular(26)%omega / 0.0925926 /
data angular(27)%omega / 0.0907407 /
data angular(28)%omega / 0.0907407 /
data angular(29)%omega / 0.0907407 /
data angular(30)%omega / 0.1209877 /
data angular(31)%omega / 0.1209877 /
data angular(32)%omega / 0.0907407 /
data angular(33)%omega / 0.0907407 /
data angular(34)%omega / 0.1209877 /
data angular(35)%omega / 0.0907407 /
data angular(36)%omega / 0.0925926 /
data angular(37)%omega / 0.0907407 /
data angular(38)%omega / 0.0907407 /
data angular(39)%omega / 0.0907407 /
data angular(40)%omega / 0.1209877 /
endmodule
! mesh module
module MESHER
use DATA_STRUCTURE
implicit none
contains
! generate the grid
subroutine Generate_grid(mesh_group, len_x, len_y)
implicit none
type(mesh_type),dimension(:,:,:,:),intent(inout)::mesh_group
real(8), intent(in) :: len_x
real(8), intent(in) :: len_y
integer :: x_cnt
integer :: y_cnt
integer :: angular_cnt
integer :: energy_cnt
integer :: i, j, k, g
real(8) :: dx, dy
energy_cnt = size(mesh_group, 1)
angular_cnt = size(mesh_group, 2)
x_cnt = size(mesh_group, 3)
y_cnt = size(mesh_group, 4)
dx = len_x / (x_cnt-1)
dy = len_y / (y_cnt-1)
do g=1, energy_cnt
do k=1, angular_cnt
do j=1, y_cnt
do i=1, x_cnt
mesh_group(g,k,i,j)%x = (i-1)*dx
mesh_group(g,k,i,j)%y = (j-1)*dy
mesh_group(g,k,i,j)%flux = 0.d0
mesh_group(g,k,i,j)%sigma_t = 0.d0
mesh_group(g,k,i,j)%sigma_s11 = 0.d0
mesh_group(g,k,i,j)%sigma_s12 = 0.d0
mesh_group(g,k,i,j)%sigma_s21 = 0.d0
mesh_group(g,k,i,j)%sigma_s22 = 0.d0
mesh_group(g,k,i,j)%sigma_f = 0.d0
mesh_group(g,k,i,j)%Xf = 0.d0
mesh_group(g,k,i,j)%scatter_source = 0.d0
mesh_group(g,k,i,j)%external_source = 0.d0
mesh_group(g,k,i,j)%fission_source = 0.d0
mesh_group(g,k,i,j)%total_source = 0.d0
enddo
enddo
enddo
enddo
return
endsubroutine
endmodule
! solver module
module SOLVER
use DATA_STRUCTURE
use MESHER
implicit none
! set the maxxium iteration
integer, parameter :: MAX_ITER = 1E4
! set the convergence standard
real(8), parameter :: errno = 1.d-6
contains
! initialize the field
subroutine Initialize(mesh_group, value)
implicit none
type(mesh_type), dimension(:,:,:,:),intent(inout)::mesh_group
real(8),intent(in) :: value
integer :: i, j, k, g
integer :: x_cnt, y_cnt, angular_cnt, energy_cnt
energy_cnt = size(mesh_group, 1)
angular_cnt = size(mesh_group, 2)
x_cnt = size(mesh_group,3)
y_cnt = size(mesh_group,4)
do g=1, energy_cnt
do k=1, angular_cnt
do j=1, y_cnt
do i=1, x_cnt
mesh_group(g,k,i,j)%flux = value
enddo
enddo
enddo
enddo
return
endsubroutine
! initialize the macro-xs
subroutine MacroXS(mesh_group)
implicit none
type(mesh_type),dimension(:,:,:,:),intent(inout) :: mesh_group
integer :: i,j,k,g
integer :: x_cnt, y_cnt, angular_cnt, energy_cnt
energy_cnt = size(mesh_group, 1)
angular_cnt = size(mesh_group, 2)
x_cnt = size(mesh_group, 3)
y_cnt = size(mesh_group, 4)
do g=1, energy_cnt
do k=1, angular_cnt
do j=1, y_cnt
do i=1, x_cnt
if((mod(i,2).eq.0) .and. (mod(j,2).eq.0)) then
! Fast group
if(g .eq. 1) then
! region 1
if((mesh_group(g,k,i,j)%x.GT.1.5d0 .and. mesh_group(g,k,i,j)%x.LT.7.9d0) &
.and.(mesh_group(g,k,i,j)%y.GT.1.0d0 .and. mesh_group(g,k,i,j)%y.LT.7.4d0))then
mesh_group(g,k,i,j)%sigma_t = 1.96647d-1
mesh_group(g,k,i,j)%sigma_s11 = 1.780d-1
mesh_group(g,k,i,j)%sigma_s12 = 1.002d-2
mesh_group(g,k,i,j)%sigma_f = 6.203d-3
mesh_group(g,k,i,j)%Xf = 1.0d0
mesh_group(g,k,i,j)%external_source = 0.d0
! region 2
else
mesh_group(g,k,i,j)%sigma_t = 2.22064d-1
mesh_group(g,k,i,j)%sigma_s11 = 1.995d-1
mesh_group(g,k,i,j)%sigma_s12 = 2.188d-2
mesh_group(g,k,i,j)%sigma_f = 0.d0
mesh_group(g,k,i,j)%Xf = 1.0d0
mesh_group(g,k,i,j)%external_source = 0.d0
endif
endif
! Thermal group
if(g .eq. 2) then
! region 1
if((mesh_group(g,k,i,j)%x.GT.1.5d0 .and. mesh_group(g,k,i,j)%x.LT.7.9d0) &
.and.(mesh_group(g,k,i,j)%y.GT.1.0d0 .and. mesh_group(g,k,i,j)%y.LT.7.4d0))then
mesh_group(g,k,i,j)%sigma_t = 5.96159d-1
mesh_group(g,k,i,j)%sigma_s21 = 1.089d-3
mesh_group(g,k,i,j)%sigma_s22 = 5.255d-1
mesh_group(g,k,i,j)%sigma_f = 1.101d-1
mesh_group(g,k,i,j)%Xf = 0.d0
mesh_group(g,k,i,j)%external_source = 0.d0
! region 2
else
mesh_group(g,k,i,j)%sigma_t = 8.87874d-1
mesh_group(g,k,i,j)%sigma_s21 = 1.558d-3
mesh_group(g,k,i,j)%sigma_s22 = 8.783d-1
mesh_group(g,k,i,j)%sigma_f = 0.d0
mesh_group(g,k,i,j)%Xf = 0.d0
mesh_group(g,k,i,j)%external_source = 0.d0
endif
endif
endif
enddo
enddo
enddo
enddo
return
endsubroutine
! source term calculation, the fission source term need to think twice.
subroutine SourceTerm(mesh_group, keff)
implicit none
type(mesh_type), dimension(:,:,:,:), intent(inout) :: mesh_group
real(8), intent(in) :: keff
integer :: g, gg, k, kk, i, j
integer :: energy_cnt
integer :: angular_cnt
integer :: x_cnt, y_cnt
real(8), dimension(:), allocatable :: scalar_flux
energy_cnt = size(mesh_group, 1)
angular_cnt = size(mesh_group, 2)
x_cnt = size(mesh_group, 3)
y_cnt = size(mesh_group, 4)
! allocate the scalar_flux array
allocate(scalar_flux(energy_cnt))
! loop over the spatial, angular and energy parameter.
do g=1, energy_cnt
do k=1, angular_cnt
do j=1, y_cnt
do i=1, x_cnt
scalar_flux = 0.d0
if((mod(i,2).eq.0) .and. (mod(j,2).eq.0)) then
do gg=1, energy_cnt
do kk=1, angular_cnt
scalar_flux(gg) = scalar_flux(gg) &
+0.25d0*mesh_group(gg,kk,i,j)%flux*angular(kk)%omega
enddo
enddo
! scattering source term
if(g .eq. 1) then
mesh_group(g,k,i,j)%scatter_source = mesh_group(1,k,i,j)%sigma_s11*scalar_flux(1) &
+mesh_group(2,k,i,j)%sigma_s21*scalar_flux(2)
else
mesh_group(g,k,i,j)%scatter_source = mesh_group(1,k,i,j)%sigma_s12*scalar_flux(1) &
+mesh_group(2,k,i,j)%sigma_s22*scalar_flux(2)
endif
! fission source term
if(g .eq. 1) then
mesh_group(g,k,i,j)%fission_source = mesh_group(1,k,i,j)%sigma_f*scalar_flux(1) &
*mesh_group(1,k,i,j)%Xf &
+mesh_group(2,k,i,j)%sigma_f*scalar_flux(2) &
*mesh_group(1,k,i,j)%Xf
! in this case, the thermal group does not have the fission source term.
else
mesh_group(g,k,i,j)%fission_source = 0.d0
endif
! total source term
mesh_group(g,k,i,j)%total_source = mesh_group(g,k,i,j)%scatter_source &
+mesh_group(g,k,i,j)%external_source &
+mesh_group(g,k,i,j)%fission_source/keff
endif
enddo
enddo
enddo
enddo
! release the allocated memory
deallocate(scalar_flux)
return
end subroutine
! solve the first direction
! mu<0, eta<0
subroutine SolveFirstDirection(mesh_group, boundary_type, boundary_angular_flux)
implicit none
type(mesh_type),dimension(:,:,:,:),intent(inout) :: mesh_group
integer, intent(in) :: boundary_type
real(8), intent(in) :: boundary_angular_flux
integer :: i, j, k, g, kk
integer :: x_cnt, y_cnt
integer :: angular_cnt
integer :: energy_cnt
real(8) :: nume
real(8) :: deno
real(8) :: dx
real(8) :: dy
energy_cnt = size(mesh_group, 1)
angular_cnt = size(mesh_group, 2)
x_cnt = size(mesh_group, 3)
y_cnt = size(mesh_group, 4)
do g=1, energy_cnt
do k=1, angular_cnt
if((angular(k)%mu.LT.0.d0) .and. (angular(k)%eta.LT.0.d0)) then
do j=y_cnt, 1, -1
do i=x_cnt, 1, -1
if(j .eq. y_cnt) then
! specified boundary
if(boundary_type .eq. SPECIFIED_BOUND) then
mesh_group(g,k,i,j)%flux = boundary_angular_flux
endif
! reflective boundary
if(boundary_type .eq. REFLECTIVE_BOUND) then
do kk=1, angular_cnt ! Y reflective, only eta is opposite number
if(angular(kk)%mu .eq. angular(k)%mu) then
if(angular(kk)%eta .eq. -angular(k)%eta) then
mesh_group(g,k,i,j)%flux = mesh_group(g,kk,i,j)%flux
endif
endif
enddo
endif
cycle
endif
if(i .eq. x_cnt) then
! specified boundary
if(boundary_type .eq. SPECIFIED_BOUND) then
mesh_group(g,k,i,j)%flux = boundary_angular_flux
endif
! reflective boundary
if(boundary_type .eq. REFLECTIVE_BOUND) then
do kk=1, angular_cnt ! X reflective, only mu is opposite number
if(angular(kk)%mu .eq. -angular(k)%mu)then
if(angular(kk)%eta .eq. angular(k)%eta) then
mesh_group(g,k,i,j)%flux = mesh_group(g,kk,i,j)%flux
endif
endif
enddo
endif
cycle
endif
if(mod(j,2).eq.0) then
if(mod(i,2).eq.0) then
dx = mesh_group(g,k,i+1,j)%x - mesh_group(g,k,i-1,j)%x
dy = mesh_group(g,k,i,j+1)%y - mesh_group(g,k,i,j-1)%y
nume = mesh_group(g,k,i,j)%total_source*dx*dy &
-2.d0*angular(k)%mu*mesh_group(g,k,i+1,j)%flux*dy &
-2.d0*angular(k)%eta*mesh_group(g,k,i,j+1)%flux*dx
deno = mesh_group(g,k,i,j)%sigma_t*dx*dy &
-2.d0*angular(k)%mu*dy &
-2.d0*angular(k)%eta*dx
mesh_group(g,k,i,j)%flux = nume / deno
! exterpolate the flux, diamond difference
mesh_group(g,k,i,j-1)%flux = 2.d0*mesh_group(g,k,i,j)%flux - mesh_group(g,k,i,j+1)%flux
if(mesh_group(g,k,i,j-1)%flux .LT. 0.d0) then
mesh_group(g,k,i,j-1)%flux = 0.d0
endif
else
! exterpolate the flux, diamond difference
mesh_group(g,k,i,j)%flux = 2.d0*mesh_group(g,k,i+1,j)%flux - mesh_group(g,k,i+2,j)%flux
if(mesh_group(g,k,i,j)%flux .LT. 0.d0) then
mesh_group(g,k,i,j)%flux = 0.d0
endif
endif
endif
enddo
enddo
endif
enddo
enddo
return
endsubroutine
! solve the second direction
! mu>0, eta<0
subroutine SolveSecondDirection(mesh_group, boundary_type, boundary_angular_flux)
implicit none
type(mesh_type),dimension(:,:,:,:),intent(inout) :: mesh_group
integer, intent(in) :: boundary_type
real(8), intent(in) :: boundary_angular_flux
integer :: i, j, k, g, kk
integer :: x_cnt, y_cnt
integer :: angular_cnt
integer :: energy_cnt
real(8) :: nume
real(8) :: deno
real(8) :: dx
real(8) :: dy
energy_cnt = size(mesh_group, 1)
angular_cnt = size(mesh_group, 2)
x_cnt = size(mesh_group, 3)
y_cnt = size(mesh_group, 4)
do g=1, energy_cnt
do k=1, angular_cnt
if((angular(k)%mu.GT.0.d0) .and. (angular(k)%eta.LT.0.d0))then
do j=y_cnt, 1, -1
do i=1, x_cnt
if(j .eq. y_cnt)then
! specified boundary
if(boundary_type .eq. SPECIFIED_BOUND)then
mesh_group(g,k,i,j)%flux = boundary_angular_flux
endif
! reflective boundary
if(boundary_type .eq. REFLECTIVE_BOUND) then
do kk=1, angular_cnt
if(angular(kk)%mu .eq. angular(k)%mu)then
if(angular(kk)%eta .eq. -angular(k)%eta) then
mesh_group(g,k,i,j)%flux = mesh_group(g,kk,i,j)%flux
endif
endif
enddo
endif
cycle
endif
if(i .eq. 1)then
! specified boundary
if(boundary_type .eq. SPECIFIED_BOUND)then
mesh_group(g,k,i,j)%flux = boundary_angular_flux
endif
! reflective boundary
if(boundary_type .eq. REFLECTIVE_BOUND) then
do kk=1, angular_cnt
if(angular(kk)%mu .eq. -angular(k)%mu)then
if(angular(kk)%eta .eq. angular(k)%eta) then
mesh_group(g,k,i,j)%flux = mesh_group(g,kk,i,j)%flux
endif
endif
enddo
endif
cycle
endif
if(mod(j,2).eq.0)then
if(mod(i,2).eq.0)then
dx = mesh_group(g,k,i+1,j)%x - mesh_group(g,k,i-1,j)%x
dy = mesh_group(g,k,i,j+1)%y - mesh_group(g,k,i,j-1)%y
nume = mesh_group(g,k,i,j)%total_source*dx*dy &
+2.d0*angular(k)%mu*mesh_group(g,k,i-1,j)%flux*dy &
-2.d0*angular(k)%eta*mesh_group(g,k,i,j+1)%flux*dx
deno = mesh_group(g,k,i,j)%sigma_t*dx*dy + &
+2.d0*angular(k)%mu*dy &
-2.d0*angular(k)%eta*dx
mesh_group(g,k,i,j)%flux = nume/deno
! exterpolate the flux, diamond difference
mesh_group(g,k,i,j-1)%flux = 2.d0*mesh_group(g,k,i,j)%flux - mesh_group(g,k,i,j+1)%flux
if(mesh_group(g,k,i,j-1)%flux .LT. 0.d0)then
mesh_group(g,k,i,j-1)%flux = 0.d0
endif
else
! exterpolate the flux, diamond difference
mesh_group(g,k,i,j)%flux = 2.d0*mesh_group(g,k,i-1,j)%flux - mesh_group(g,k,i-2,j)%flux
if(mesh_group(g,k,i,j)%flux .LT. 0.d0)then
mesh_group(g,k,i,j)%flux= 0.d0
endif
endif
endif
enddo
enddo
endif
enddo
enddo
return
endsubroutine
! solve the third direction
! mu<0, eta>0
subroutine SolveThirdDirection(mesh_group, boundary_type, boundary_angular_flux)
implicit none
type(mesh_type),dimension(:,:,:,:),intent(inout) :: mesh_group
integer, intent(in) :: boundary_type
real(8), intent(in) :: boundary_angular_flux
integer :: i, j, k, g, kk
integer :: x_cnt, y_cnt
integer :: angular_cnt
integer :: energy_cnt
real(8) :: nume
real(8) :: deno
real(8) :: dx
real(8) :: dy
energy_cnt = size(mesh_group, 1)
angular_cnt = size(mesh_group, 2)
x_cnt = size(mesh_group, 3)
y_cnt = size(mesh_group, 4)
do g=1, energy_cnt
do k=1, angular_cnt
if((angular(k)%mu.LT.0.d0) .and. (angular(k)%eta.GT.0.d0))then
do j=1, y_cnt
do i=x_cnt, 1, -1
if(j .eq. 1) then
! specified boundary
if(boundary_type .eq. SPECIFIED_BOUND)then
mesh_group(g,k,i,j)%flux = boundary_angular_flux
endif
! reflective boundary
if(boundary_type .eq. REFLECTIVE_BOUND) then
do kk=1, angular_cnt
if(angular(kk)%mu .eq. angular(k)%mu)then
if(angular(kk)%eta .eq. -angular(k)%eta) then
mesh_group(g,k,i,j)%flux = mesh_group(g,kk,i,j)%flux
endif
endif
enddo
endif
cycle
endif
if(i .eq. x_cnt) then
! specified boundary
if(boundary_type .eq. SPECIFIED_BOUND)then
mesh_group(g,k,i,j)%flux = boundary_angular_flux
endif
! reflective boundary
if(boundary_type .eq. REFLECTIVE_BOUND) then
do kk=1, angular_cnt
if(angular(kk)%mu .eq. -angular(k)%mu)then
if(angular(kk)%eta .eq. angular(k)%eta) then
mesh_group(g,k,i,j)%flux = mesh_group(g,kk,i,j)%flux
endif
endif
enddo
endif
cycle
endif
if(mod(j,2).eq.0)then
if(mod(i,2).eq.0)then
dx = mesh_group(g,k,i+1,j)%x - mesh_group(g,k,i-1,j)%x
dy = mesh_group(g,k,i,j+1)%y - mesh_group(g,k,i,j-1)%y
nume = mesh_group(g,k,i,j)%total_source*dx*dy &
-2.d0*angular(k)%mu*mesh_group(g,k,i+1,j)%flux*dy &
+2.d0*angular(k)%eta*mesh_group(g,k,i,j-1)%flux*dx
deno = mesh_group(g,k,i,j)%sigma_t*dx*dy &
-2.d0*angular(k)%mu*dy &
+2.d0*angular(k)%eta*dx
mesh_group(g,k,i,j)%flux = nume / deno
! exterpolate the flux, diamond difference
mesh_group(g,k,i,j+1)%flux = 2.d0*mesh_group(g,k,i,j)%flux - mesh_group(g,k,i,j-1)%flux
if(mesh_group(g,k,i,j+1)%flux .LT. 0.d0)then
mesh_group(g,k,i,j+1)%flux = 0.d0
endif
else
mesh_group(g,k,i,j)%flux = 2.d0*mesh_group(g,k,i+1,j)%flux - mesh_group(g,k,i+2,j)%flux
if(mesh_group(g,k,i,j)%flux .LT. 0.d0)then
mesh_group(g,k,i,j)%flux = 0.d0
endif
endif
endif
enddo
enddo
endif
enddo
enddo
return
endsubroutine
! solve the fourth direction
! mu>0, eta>0
subroutine SolveFourthDirection(mesh_group, boundary_type, boundary_angular_flux)
implicit none
type(mesh_type),dimension(:,:,:,:),intent(inout) :: mesh_group
integer, intent(in) :: boundary_type
real(8), intent(in) :: boundary_angular_flux
integer :: i, j, k, g,kk
integer :: x_cnt, y_cnt
integer :: angular_cnt
integer :: energy_cnt
real(8) :: nume
real(8) :: deno
real(8) :: dx
real(8) :: dy
energy_cnt = size(mesh_group, 1)
angular_cnt = size(mesh_group, 2)
x_cnt = size(mesh_group, 3)
y_cnt = size(mesh_group, 4)
do g=1, energy_cnt
do k=1, angular_cnt
if((angular(k)%mu.GT.0.d0) .and. (angular(k)%eta.GT.0.d0))then
do j=1, y_cnt
do i=1, x_cnt
if(j .eq. 1) then
! specified boundary
if(boundary_type .eq. SPECIFIED_BOUND) then
mesh_group(g,k,i,j)%flux = boundary_angular_flux
endif
! reflective boundary
if(boundary_type .eq. REFLECTIVE_BOUND) then
do kk=1, angular_cnt
if(angular(kk)%mu .eq. angular(k)%mu)then
if(angular(kk)%eta .eq. -angular(k)%eta) then
mesh_group(g,k,i,j)%flux = mesh_group(g,kk,i,j)%flux
endif
endif
enddo
endif
cycle
endif
if(i .eq. 1) then
! specified boundary
if(boundary_type .eq. SPECIFIED_BOUND) then
mesh_group(g,k,i,j)%flux = boundary_angular_flux
endif
! reflective boundary
if(boundary_type .eq. REFLECTIVE_BOUND) then
do kk=1, angular_cnt
if(angular(kk)%mu .eq. -angular(k)%mu)then
if(angular(kk)%eta .eq. angular(k)%eta) then
mesh_group(g,k,i,j)%flux = mesh_group(g,kk,i,j)%flux
endif
endif
enddo
endif
cycle
endif
if(mod(j,2).eq.0)then
if(mod(i,2).eq.0)then
dx = mesh_group(g,k,i+1,j)%x - mesh_group(g,k,i-1,j)%x
dy = mesh_group(g,k,i,j+1)%y - mesh_group(g,k,i,j-1)%y
nume = mesh_group(g,k,i,j)%total_source*dx*dy &
+2.d0*angular(k)%mu*mesh_group(g,k,i-1,j)%flux*dy &
+2.d0*angular(k)%eta*mesh_group(g,k,i,j-1)%flux*dx
deno = mesh_group(g,k,i,j)%sigma_t*dx*dy &
+2.d0*angular(k)%mu*dy &
+2.d0*angular(k)%eta*dx
mesh_group(g,k,i,j)%flux = nume/deno
! exterpolate the flux, diamond difference
mesh_group(g,k,i,j+1)%flux = 2.d0*mesh_group(g,k,i,j)%flux - mesh_group(g,k,i,j-1)%flux
if(mesh_group(g,k,i,j+1)%flux .LT. 0.d0)then
mesh_group(g,k,i,j+1)%flux = 0.d0
endif
else
mesh_group(g,k,i,j)%flux = 2.d0*mesh_group(g,k,i-1,j)%flux - mesh_group(g,k,i-2,j)%flux
if(mesh_group(g,k,i,j)%flux .LT. 0.d0)then
mesh_group(g,k,i,j)%flux = 0.d0
endif
endif
endif
enddo
enddo
endif
enddo
enddo
return
endsubroutine
! Solve the k-eigenvalue
subroutine EigenValue(mesh_group, old_mesh_group, keff)
implicit none
type(mesh_type), dimension(:,:,:,:), intent(inout) :: mesh_group
type(mesh_type), dimension(:,:,:,:), intent(inout) :: old_mesh_group
real(8), intent(inout) :: keff
integer :: g, k, i, j
integer :: energy_cnt
integer :: angular_cnt
integer :: x_cnt, y_cnt
real(8) :: sum_fission_source
real(8) :: old_sum_fission_source
energy_cnt = size(mesh_group, 1)
angular_cnt = size(mesh_group, 2)
x_cnt = size(mesh_group, 3)
y_cnt = size(mesh_group, 4)
sum_fission_source = 0.d0
old_sum_fission_source = 0.d0
! loop over the spatial, angular and energy parameter.
do g=1, energy_cnt
do k=1, angular_cnt
do j=1, y_cnt
do i=1, x_cnt
if((mod(i,2).eq.0) .and. (mod(j,2).eq.0)) then
sum_fission_source = sum_fission_source + mesh_group(g,k,i,j)%fission_source
old_sum_fission_source = old_sum_fission_source + old_mesh_group(g,k,i,j)%fission_source
endif
enddo
enddo
enddo
enddo
keff = keff*sum_fission_source/old_sum_fission_source
return
end subroutine
! Power Iteration Method
subroutine PowerIteration(mesh_group, old_mesh_group, len_x, len_y, keff_guess)
implicit none
type(mesh_type), dimension(:,:,:,:), intent(inout) :: mesh_group
type(mesh_type), dimension(:,:,:,:), intent(inout) :: old_mesh_group
real(8), intent(in) :: len_x
real(8), intent(in) :: len_y
real(8), intent(in) :: keff_guess
integer :: g,k,i,j,gg,kk
integer :: iter
integer :: energy_cnt
integer :: angular_cnt
integer :: x_cnt
integer :: y_cnt
real(8) :: keff, old_keff
real(8) :: residual = 0.d0
real(8), intrinsic :: sqrt
energy_cnt = size(mesh_group, 1)
angular_cnt = size(mesh_group, 2)
x_cnt = size(mesh_group, 3)
y_cnt = size(mesh_group, 4)
! mesher
call Generate_grid(mesh_group, len_x, len_y)
! initialize the macroscopic cross section
call MacroXS(mesh_group)
! initialize the field
keff = keff_guess
call Initialize(mesh_group, 1.d0)
call SourceTerm(mesh_group, keff)
old_mesh_group = mesh_group
old_keff = keff + 1.d0
do iter=1, MAX_ITER
! calculate the source term
call SourceTerm(mesh_group,keff)
! calculate the neutron angular flux field, vaccum boundary
call SolveFirstDirection(mesh_group, REFLECTIVE_BOUND, -1.d0)
call SolveSecondDirection(mesh_group, REFLECTIVE_BOUND, -1.d0)
call SolveThirdDirection(mesh_group, REFLECTIVE_BOUND, -1.d0)
call SolveFourthDirection(mesh_group, REFLECTIVE_BOUND, -1.d0)
! check out the keff convergence
call EigenValue(mesh_group, old_mesh_group, keff)
residual = abs(old_keff - keff)
if(residual .LT. errno) then
write(*,*) "The keff has converged!"
write(*,*) "keff = ", keff
exit
endif
write(*, "(A15,I3,A15,G15.7,A20,G15.7)") "Iteration=", iter, &
"Residual=", residual, &
"K-eigenvalue=", keff
old_mesh_group = mesh_group
old_keff = keff
enddo
if(iter .GT. MAX_ITER)then
write(*,*) " Diverge...."
endif
return
endsubroutine
endmodule
module POSTPROCESS
use DATA_STRUCTURE
use MESHER
use SOLVER
implicit none
contains
! Check out the negative angular flux
subroutine CheckNegativeFlux(mesh_group)
implicit none
type(mesh_type), dimension(:,:,:,:), intent(in) :: mesh_group
integer :: g,k,i,j
integer :: energy_cnt
integer :: angular_cnt
integer :: x_cnt
integer :: y_cnt
integer :: flag
energy_cnt = size(mesh_group, 1)
angular_cnt = size(mesh_group, 2)
x_cnt = size(mesh_group, 3)
y_cnt = size(mesh_group, 4)
flag = 1
do g=1, energy_cnt
do k=1, angular_cnt
do j=1, y_cnt
do i=1, x_cnt
if(mesh_group(g,k,i,j)%flux .LT. 0.d0)then
if(abs(mesh_group(g,k,i,j)%flux) .GT. 1.d-8)then
write(*,*)mesh_group(g,k,i,j)%flux
flag = 0
endif
endif
enddo
enddo
enddo
enddo
if(flag .eq. 0)then
write(*,*)"Negative angular flux..."
else
write(*,*)"Check negative angular flux has passed successfully..."
endif
return
endsubroutine
! Export the scalar flux data
subroutine ExportScalarFlux(mesh_group)
implicit none
type(mesh_type), dimension(:,:,:,:), intent(in) :: mesh_group
integer :: g,k,i,j, kk
integer :: energy_cnt, angular_cnt
integer :: x_cnt, y_cnt
real(8) :: scalar_flux = 0.d0
integer :: group1_fileid = 20
integer :: group2_fileid = 21
character(len=20) :: group1_filename = "FastGroup.dat"
character(len=20) :: group2_filename = "ThermalGroup.dat"
energy_cnt = size(mesh_group, 1)
angular_cnt = size(mesh_group, 2)
x_cnt = size(mesh_group, 3)
y_cnt = size(mesh_group, 4)
! open the file
open(unit=group1_fileid, file=group1_filename)
open(unit=group2_fileid, file=group2_filename)
! export the fast group scalar flux data
do j=y_cnt, 1, -1
do i=1, x_cnt
scalar_flux = 0.d0
if((mod(i,2).eq.0) .and. (mod(j,2).eq.0))then
do k=1, angular_cnt
scalar_flux = scalar_flux + 0.25d0*mesh_group(1,k,i,j)%flux*angular(k)%omega
enddo
write(group1_fileid,"(F12.6\)") scalar_flux
endif
enddo
write(group1_fileid,*)
enddo
! export the thermal group scalar flux data
do j=y_cnt, 1, -1
do i=1, x_cnt
scalar_flux = 0.d0
if((mod(i,2).eq.0) .and. (mod(j,2).eq.0))then
do k=1, angular_cnt
scalar_flux = scalar_flux + 0.25d0*mesh_group(2,k,i,j)%flux*angular(k)%omega
enddo
write(group2_fileid,"(F12.6\)") scalar_flux
endif
enddo
write(group2_fileid,*)
enddo
close(group1_fileid)
close(group2_fileid)
return
endsubroutine
endmodule
program main
use DATA_STRUCTURE
use MESHER
use SOLVER
use POSTPROCESS
implicit none
type(mesh_type), dimension(:,:,:,:), allocatable :: mesh_group
type(mesh_type), dimension(:,:,:,:), allocatable :: old_mesh_group
real(8) :: len_x = 8.9d0
real(8) :: len_y = 8.9d0
integer :: x_cnt = 200
integer :: y_cnt = 200
allocate(mesh_group(2, SN*(SN+2)/2, 2*x_cnt+1, 2*y_cnt+1))
allocate(old_mesh_group(2, SN*(SN+2)/2, 2*x_cnt+1, 2*y_cnt+1))
call PowerIteration(mesh_group, old_mesh_group, len_x, len_y, 1.d0)
call CheckNegativeFlux(mesh_group)
call ExportScalarFlux(mesh_group)
deallocate(mesh_group)
deallocate(old_mesh_group)
endprogram