initialize.f
9.65 KB
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c---------------------------------------------------------------------
c---------------------------------------------------------------------
subroutine initialize
c---------------------------------------------------------------------
c---------------------------------------------------------------------
c---------------------------------------------------------------------
c This subroutine initializes the field variable u using
c tri-linear transfinite interpolation of the boundary values
c---------------------------------------------------------------------
include 'header.h'
integer c, i, j, k, m, ii, jj, kk, ix, iy, iz
double precision xi, eta, zeta, Pface(5,3,2), Pxi, Peta,
> Pzeta, temp(5)
c---------------------------------------------------------------------
c Later (in compute_rhs) we compute 1/u for every element. A few of
c the corner elements are not used, but it convenient (and faster)
c to compute the whole thing with a simple loop. Make sure those
c values are nonzero by initializing the whole thing here.
c---------------------------------------------------------------------
do c = 1, ncells
do kk = -1, KMAX
do jj = -1, JMAX
do ii = -1, IMAX
do m = 1, 5
u(m, ii, jj, kk, c) = 1.0
end do
end do
end do
end do
end do
c---------------------------------------------------------------------
c---------------------------------------------------------------------
c first store the "interpolated" values everywhere on the grid
c---------------------------------------------------------------------
do c=1, ncells
kk = 0
do k = cell_low(3,c), cell_high(3,c)
zeta = dble(k) * dnzm1
jj = 0
do j = cell_low(2,c), cell_high(2,c)
eta = dble(j) * dnym1
ii = 0
do i = cell_low(1,c), cell_high(1,c)
xi = dble(i) * dnxm1
do ix = 1, 2
call exact_solution(dble(ix-1), eta, zeta,
> Pface(1,1,ix))
enddo
do iy = 1, 2
call exact_solution(xi, dble(iy-1) , zeta,
> Pface(1,2,iy))
enddo
do iz = 1, 2
call exact_solution(xi, eta, dble(iz-1),
> Pface(1,3,iz))
enddo
do m = 1, 5
Pxi = xi * Pface(m,1,2) +
> (1.0d0-xi) * Pface(m,1,1)
Peta = eta * Pface(m,2,2) +
> (1.0d0-eta) * Pface(m,2,1)
Pzeta = zeta * Pface(m,3,2) +
> (1.0d0-zeta) * Pface(m,3,1)
u(m,ii,jj,kk,c) = Pxi + Peta + Pzeta -
> Pxi*Peta - Pxi*Pzeta - Peta*Pzeta +
> Pxi*Peta*Pzeta
enddo
ii = ii + 1
enddo
jj = jj + 1
enddo
kk = kk+1
enddo
enddo
c---------------------------------------------------------------------
c now store the exact values on the boundaries
c---------------------------------------------------------------------
c---------------------------------------------------------------------
c west face
c---------------------------------------------------------------------
c = slice(1,1)
ii = 0
xi = 0.0d0
kk = 0
do k = cell_low(3,c), cell_high(3,c)
zeta = dble(k) * dnzm1
jj = 0
do j = cell_low(2,c), cell_high(2,c)
eta = dble(j) * dnym1
call exact_solution(xi, eta, zeta, temp)
do m = 1, 5
u(m,ii,jj,kk,c) = temp(m)
enddo
jj = jj + 1
enddo
kk = kk + 1
enddo
c---------------------------------------------------------------------
c east face
c---------------------------------------------------------------------
c = slice(1,ncells)
ii = cell_size(1,c)-1
xi = 1.0d0
kk = 0
do k = cell_low(3,c), cell_high(3,c)
zeta = dble(k) * dnzm1
jj = 0
do j = cell_low(2,c), cell_high(2,c)
eta = dble(j) * dnym1
call exact_solution(xi, eta, zeta, temp)
do m = 1, 5
u(m,ii,jj,kk,c) = temp(m)
enddo
jj = jj + 1
enddo
kk = kk + 1
enddo
c---------------------------------------------------------------------
c south face
c---------------------------------------------------------------------
c = slice(2,1)
jj = 0
eta = 0.0d0
kk = 0
do k = cell_low(3,c), cell_high(3,c)
zeta = dble(k) * dnzm1
ii = 0
do i = cell_low(1,c), cell_high(1,c)
xi = dble(i) * dnxm1
call exact_solution(xi, eta, zeta, temp)
do m = 1, 5
u(m,ii,jj,kk,c) = temp(m)
enddo
ii = ii + 1
enddo
kk = kk + 1
enddo
c---------------------------------------------------------------------
c north face
c---------------------------------------------------------------------
c = slice(2,ncells)
jj = cell_size(2,c)-1
eta = 1.0d0
kk = 0
do k = cell_low(3,c), cell_high(3,c)
zeta = dble(k) * dnzm1
ii = 0
do i = cell_low(1,c), cell_high(1,c)
xi = dble(i) * dnxm1
call exact_solution(xi, eta, zeta, temp)
do m = 1, 5
u(m,ii,jj,kk,c) = temp(m)
enddo
ii = ii + 1
enddo
kk = kk + 1
enddo
c---------------------------------------------------------------------
c bottom face
c---------------------------------------------------------------------
c = slice(3,1)
kk = 0
zeta = 0.0d0
jj = 0
do j = cell_low(2,c), cell_high(2,c)
eta = dble(j) * dnym1
ii = 0
do i =cell_low(1,c), cell_high(1,c)
xi = dble(i) *dnxm1
call exact_solution(xi, eta, zeta, temp)
do m = 1, 5
u(m,ii,jj,kk,c) = temp(m)
enddo
ii = ii + 1
enddo
jj = jj + 1
enddo
c---------------------------------------------------------------------
c top face
c---------------------------------------------------------------------
c = slice(3,ncells)
kk = cell_size(3,c)-1
zeta = 1.0d0
jj = 0
do j = cell_low(2,c), cell_high(2,c)
eta = dble(j) * dnym1
ii = 0
do i =cell_low(1,c), cell_high(1,c)
xi = dble(i) * dnxm1
call exact_solution(xi, eta, zeta, temp)
do m = 1, 5
u(m,ii,jj,kk,c) = temp(m)
enddo
ii = ii + 1
enddo
jj = jj + 1
enddo
return
end
c---------------------------------------------------------------------
c---------------------------------------------------------------------
subroutine lhsinit
c---------------------------------------------------------------------
c---------------------------------------------------------------------
include 'header.h'
integer i, j, k, d, c, m, n
c---------------------------------------------------------------------
c loop over all cells
c---------------------------------------------------------------------
do c = 1, ncells
c---------------------------------------------------------------------
c first, initialize the start and end arrays
c---------------------------------------------------------------------
do d = 1, 3
if (cell_coord(d,c) .eq. 1) then
start(d,c) = 1
else
start(d,c) = 0
endif
if (cell_coord(d,c) .eq. ncells) then
end(d,c) = 1
else
end(d,c) = 0
endif
enddo
c---------------------------------------------------------------------
c zero the whole left hand side for starters
c---------------------------------------------------------------------
do k = 0, cell_size(3,c)-1
do j = 0, cell_size(2,c)-1
do i = 0, cell_size(1,c)-1
do m = 1,5
do n = 1, 5
lhsc(m,n,i,j,k,c) = 0.0d0
enddo
enddo
enddo
enddo
enddo
enddo
return
end
c---------------------------------------------------------------------
c---------------------------------------------------------------------
subroutine lhsabinit(lhsa, lhsb, size)
implicit none
integer size
double precision lhsa(5, 5, -1:size), lhsb(5, 5, -1:size)
integer i, m, n
c---------------------------------------------------------------------
c next, set all diagonal values to 1. This is overkill, but convenient
c---------------------------------------------------------------------
do i = 0, size
do m = 1, 5
do n = 1, 5
lhsa(m,n,i) = 0.0d0
lhsb(m,n,i) = 0.0d0
enddo
lhsb(m,m,i) = 1.0d0
enddo
enddo
return
end