| 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 i, j, k, m, 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 k = 0, grid_points(3)-1 |
| do j = 0, grid_points(2)-1 |
| do i = 0, grid_points(1)-1 |
| do m = 1, 5 |
| u(m,i,j,k) = 1.0 |
| end do |
| end do |
| end do |
| end do |
| c--------------------------------------------------------------------- |
| |
| |
| |
| c--------------------------------------------------------------------- |
| c first store the "interpolated" values everywhere on the grid |
| c--------------------------------------------------------------------- |
| |
| do k = 0, grid_points(3)-1 |
| zeta = dble(k) * dnzm1 |
| do j = 0, grid_points(2)-1 |
| eta = dble(j) * dnym1 |
| do i = 0, grid_points(1)-1 |
| 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,i,j,k) = Pxi + Peta + Pzeta - |
| > Pxi*Peta - Pxi*Pzeta - Peta*Pzeta + |
| > Pxi*Peta*Pzeta |
| |
| enddo |
| enddo |
| enddo |
| enddo |
| |
| c--------------------------------------------------------------------- |
| c now store the exact values on the boundaries |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c west face |
| c--------------------------------------------------------------------- |
| i = 0 |
| xi = 0.0d0 |
| do k = 0, grid_points(3)-1 |
| zeta = dble(k) * dnzm1 |
| do j = 0, grid_points(2)-1 |
| eta = dble(j) * dnym1 |
| call exact_solution(xi, eta, zeta, temp) |
| do m = 1, 5 |
| u(m,i,j,k) = temp(m) |
| enddo |
| enddo |
| enddo |
| |
| c--------------------------------------------------------------------- |
| c east face |
| c--------------------------------------------------------------------- |
| |
| i = grid_points(1)-1 |
| xi = 1.0d0 |
| do k = 0, grid_points(3)-1 |
| zeta = dble(k) * dnzm1 |
| do j = 0, grid_points(2)-1 |
| eta = dble(j) * dnym1 |
| call exact_solution(xi, eta, zeta, temp) |
| do m = 1, 5 |
| u(m,i,j,k) = temp(m) |
| enddo |
| enddo |
| enddo |
| |
| c--------------------------------------------------------------------- |
| c south face |
| c--------------------------------------------------------------------- |
| j = 0 |
| eta = 0.0d0 |
| do k = 0, grid_points(3)-1 |
| zeta = dble(k) * dnzm1 |
| do i = 0, grid_points(1)-1 |
| xi = dble(i) * dnxm1 |
| call exact_solution(xi, eta, zeta, temp) |
| do m = 1, 5 |
| u(m,i,j,k) = temp(m) |
| enddo |
| enddo |
| enddo |
| |
| |
| c--------------------------------------------------------------------- |
| c north face |
| c--------------------------------------------------------------------- |
| j = grid_points(2)-1 |
| eta = 1.0d0 |
| do k = 0, grid_points(3)-1 |
| zeta = dble(k) * dnzm1 |
| do i = 0, grid_points(1)-1 |
| xi = dble(i) * dnxm1 |
| call exact_solution(xi, eta, zeta, temp) |
| do m = 1, 5 |
| u(m,i,j,k) = temp(m) |
| enddo |
| enddo |
| enddo |
| |
| c--------------------------------------------------------------------- |
| c bottom face |
| c--------------------------------------------------------------------- |
| k = 0 |
| zeta = 0.0d0 |
| do j = 0, grid_points(2)-1 |
| eta = dble(j) * dnym1 |
| do i =0, grid_points(1)-1 |
| xi = dble(i) *dnxm1 |
| call exact_solution(xi, eta, zeta, temp) |
| do m = 1, 5 |
| u(m,i,j,k) = temp(m) |
| enddo |
| enddo |
| enddo |
| |
| c--------------------------------------------------------------------- |
| c top face |
| c--------------------------------------------------------------------- |
| k = grid_points(3)-1 |
| zeta = 1.0d0 |
| do j = 0, grid_points(2)-1 |
| eta = dble(j) * dnym1 |
| do i =0, grid_points(1)-1 |
| xi = dble(i) * dnxm1 |
| call exact_solution(xi, eta, zeta, temp) |
| do m = 1, 5 |
| u(m,i,j,k) = temp(m) |
| enddo |
| enddo |
| enddo |
| |
| return |
| end |
| |
| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| subroutine lhsinit(lhs, size) |
| implicit none |
| integer size |
| double precision lhs(5,5,3,0:size) |
| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| integer i, m, n |
| |
| i = size |
| c--------------------------------------------------------------------- |
| c zero the whole left hand side for starters |
| c--------------------------------------------------------------------- |
| do m = 1, 5 |
| do n = 1, 5 |
| lhs(m,n,1,0) = 0.0d0 |
| lhs(m,n,2,0) = 0.0d0 |
| lhs(m,n,3,0) = 0.0d0 |
| lhs(m,n,1,i) = 0.0d0 |
| lhs(m,n,2,i) = 0.0d0 |
| lhs(m,n,3,i) = 0.0d0 |
| enddo |
| enddo |
| |
| c--------------------------------------------------------------------- |
| c next, set all diagonal values to 1. This is overkill, but convenient |
| c--------------------------------------------------------------------- |
| do m = 1, 5 |
| lhs(m,m,2,0) = 1.0d0 |
| lhs(m,m,2,i) = 1.0d0 |
| enddo |
| |
| return |
| end |
| |
| |
| |
