| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| subroutine y_solve |
| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c this function performs the solution of the approximate factorization |
| c step in the y-direction for all five matrix components |
| c simultaneously. The Thomas algorithm is employed to solve the |
| c systems for the y-lines. Boundary conditions are non-periodic |
| c--------------------------------------------------------------------- |
| |
| include 'header.h' |
| |
| integer i, j, k, j1, j2, m |
| double precision ru1, fac1, fac2 |
| |
| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| if (timeron) call timer_start(t_ysolve) |
| do k = 1, grid_points(3)-2 |
| |
| call lhsinitj(ny2+1, nx2) |
| |
| c--------------------------------------------------------------------- |
| c Computes the left hand side for the three y-factors |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c first fill the lhs for the u-eigenvalue |
| c--------------------------------------------------------------------- |
| |
| do i = 1, grid_points(1)-2 |
| do j = 0, grid_points(2)-1 |
| ru1 = c3c4*rho_i(i,j,k) |
| cv(j) = vs(i,j,k) |
| rhoq(j) = dmax1( dy3 + con43 * ru1, |
| > dy5 + c1c5*ru1, |
| > dymax + ru1, |
| > dy1) |
| end do |
| |
| do j = 1, grid_points(2)-2 |
| lhs(1,i,j) = 0.0d0 |
| lhs(2,i,j) = -dtty2 * cv(j-1) - dtty1 * rhoq(j-1) |
| lhs(3,i,j) = 1.0 + c2dtty1 * rhoq(j) |
| lhs(4,i,j) = dtty2 * cv(j+1) - dtty1 * rhoq(j+1) |
| lhs(5,i,j) = 0.0d0 |
| end do |
| end do |
| |
| c--------------------------------------------------------------------- |
| c add fourth order dissipation |
| c--------------------------------------------------------------------- |
| |
| do i = 1, grid_points(1)-2 |
| j = 1 |
| lhs(3,i,j) = lhs(3,i,j) + comz5 |
| lhs(4,i,j) = lhs(4,i,j) - comz4 |
| lhs(5,i,j) = lhs(5,i,j) + comz1 |
| |
| lhs(2,i,j+1) = lhs(2,i,j+1) - comz4 |
| lhs(3,i,j+1) = lhs(3,i,j+1) + comz6 |
| lhs(4,i,j+1) = lhs(4,i,j+1) - comz4 |
| lhs(5,i,j+1) = lhs(5,i,j+1) + comz1 |
| end do |
| |
| do j=3, grid_points(2)-4 |
| do i = 1, grid_points(1)-2 |
| |
| lhs(1,i,j) = lhs(1,i,j) + comz1 |
| lhs(2,i,j) = lhs(2,i,j) - comz4 |
| lhs(3,i,j) = lhs(3,i,j) + comz6 |
| lhs(4,i,j) = lhs(4,i,j) - comz4 |
| lhs(5,i,j) = lhs(5,i,j) + comz1 |
| end do |
| end do |
| |
| do i = 1, grid_points(1)-2 |
| j = grid_points(2)-3 |
| lhs(1,i,j) = lhs(1,i,j) + comz1 |
| lhs(2,i,j) = lhs(2,i,j) - comz4 |
| lhs(3,i,j) = lhs(3,i,j) + comz6 |
| lhs(4,i,j) = lhs(4,i,j) - comz4 |
| |
| lhs(1,i,j+1) = lhs(1,i,j+1) + comz1 |
| lhs(2,i,j+1) = lhs(2,i,j+1) - comz4 |
| lhs(3,i,j+1) = lhs(3,i,j+1) + comz5 |
| end do |
| |
| c--------------------------------------------------------------------- |
| c subsequently, do the other two factors |
| c--------------------------------------------------------------------- |
| do j = 1, grid_points(2)-2 |
| do i = 1, grid_points(1)-2 |
| lhsp(1,i,j) = lhs(1,i,j) |
| lhsp(2,i,j) = lhs(2,i,j) - |
| > dtty2 * speed(i,j-1,k) |
| lhsp(3,i,j) = lhs(3,i,j) |
| lhsp(4,i,j) = lhs(4,i,j) + |
| > dtty2 * speed(i,j+1,k) |
| lhsp(5,i,j) = lhs(5,i,j) |
| lhsm(1,i,j) = lhs(1,i,j) |
| lhsm(2,i,j) = lhs(2,i,j) + |
| > dtty2 * speed(i,j-1,k) |
| lhsm(3,i,j) = lhs(3,i,j) |
| lhsm(4,i,j) = lhs(4,i,j) - |
| > dtty2 * speed(i,j+1,k) |
| lhsm(5,i,j) = lhs(5,i,j) |
| end do |
| end do |
| |
| |
| c--------------------------------------------------------------------- |
| c FORWARD ELIMINATION |
| c--------------------------------------------------------------------- |
| |
| do j = 0, grid_points(2)-3 |
| j1 = j + 1 |
| j2 = j + 2 |
| do i = 1, grid_points(1)-2 |
| fac1 = 1.d0/lhs(3,i,j) |
| lhs(4,i,j) = fac1*lhs(4,i,j) |
| lhs(5,i,j) = fac1*lhs(5,i,j) |
| do m = 1, 3 |
| rhs(m,i,j,k) = fac1*rhs(m,i,j,k) |
| end do |
| lhs(3,i,j1) = lhs(3,i,j1) - |
| > lhs(2,i,j1)*lhs(4,i,j) |
| lhs(4,i,j1) = lhs(4,i,j1) - |
| > lhs(2,i,j1)*lhs(5,i,j) |
| do m = 1, 3 |
| rhs(m,i,j1,k) = rhs(m,i,j1,k) - |
| > lhs(2,i,j1)*rhs(m,i,j,k) |
| end do |
| lhs(2,i,j2) = lhs(2,i,j2) - |
| > lhs(1,i,j2)*lhs(4,i,j) |
| lhs(3,i,j2) = lhs(3,i,j2) - |
| > lhs(1,i,j2)*lhs(5,i,j) |
| do m = 1, 3 |
| rhs(m,i,j2,k) = rhs(m,i,j2,k) - |
| > lhs(1,i,j2)*rhs(m,i,j,k) |
| end do |
| end do |
| end do |
| |
| c--------------------------------------------------------------------- |
| c The last two rows in this grid block are a bit different, |
| c since they do not have two more rows available for the |
| c elimination of off-diagonal entries |
| c--------------------------------------------------------------------- |
| |
| j = grid_points(2)-2 |
| j1 = grid_points(2)-1 |
| do i = 1, grid_points(1)-2 |
| fac1 = 1.d0/lhs(3,i,j) |
| lhs(4,i,j) = fac1*lhs(4,i,j) |
| lhs(5,i,j) = fac1*lhs(5,i,j) |
| do m = 1, 3 |
| rhs(m,i,j,k) = fac1*rhs(m,i,j,k) |
| end do |
| lhs(3,i,j1) = lhs(3,i,j1) - |
| > lhs(2,i,j1)*lhs(4,i,j) |
| lhs(4,i,j1) = lhs(4,i,j1) - |
| > lhs(2,i,j1)*lhs(5,i,j) |
| do m = 1, 3 |
| rhs(m,i,j1,k) = rhs(m,i,j1,k) - |
| > lhs(2,i,j1)*rhs(m,i,j,k) |
| end do |
| c--------------------------------------------------------------------- |
| c scale the last row immediately |
| c--------------------------------------------------------------------- |
| fac2 = 1.d0/lhs(3,i,j1) |
| do m = 1, 3 |
| rhs(m,i,j1,k) = fac2*rhs(m,i,j1,k) |
| end do |
| end do |
| |
| c--------------------------------------------------------------------- |
| c do the u+c and the u-c factors |
| c--------------------------------------------------------------------- |
| do j = 0, grid_points(2)-3 |
| j1 = j + 1 |
| j2 = j + 2 |
| do i = 1, grid_points(1)-2 |
| m = 4 |
| fac1 = 1.d0/lhsp(3,i,j) |
| lhsp(4,i,j) = fac1*lhsp(4,i,j) |
| lhsp(5,i,j) = fac1*lhsp(5,i,j) |
| rhs(m,i,j,k) = fac1*rhs(m,i,j,k) |
| lhsp(3,i,j1) = lhsp(3,i,j1) - |
| > lhsp(2,i,j1)*lhsp(4,i,j) |
| lhsp(4,i,j1) = lhsp(4,i,j1) - |
| > lhsp(2,i,j1)*lhsp(5,i,j) |
| rhs(m,i,j1,k) = rhs(m,i,j1,k) - |
| > lhsp(2,i,j1)*rhs(m,i,j,k) |
| lhsp(2,i,j2) = lhsp(2,i,j2) - |
| > lhsp(1,i,j2)*lhsp(4,i,j) |
| lhsp(3,i,j2) = lhsp(3,i,j2) - |
| > lhsp(1,i,j2)*lhsp(5,i,j) |
| rhs(m,i,j2,k) = rhs(m,i,j2,k) - |
| > lhsp(1,i,j2)*rhs(m,i,j,k) |
| m = 5 |
| fac1 = 1.d0/lhsm(3,i,j) |
| lhsm(4,i,j) = fac1*lhsm(4,i,j) |
| lhsm(5,i,j) = fac1*lhsm(5,i,j) |
| rhs(m,i,j,k) = fac1*rhs(m,i,j,k) |
| lhsm(3,i,j1) = lhsm(3,i,j1) - |
| > lhsm(2,i,j1)*lhsm(4,i,j) |
| lhsm(4,i,j1) = lhsm(4,i,j1) - |
| > lhsm(2,i,j1)*lhsm(5,i,j) |
| rhs(m,i,j1,k) = rhs(m,i,j1,k) - |
| > lhsm(2,i,j1)*rhs(m,i,j,k) |
| lhsm(2,i,j2) = lhsm(2,i,j2) - |
| > lhsm(1,i,j2)*lhsm(4,i,j) |
| lhsm(3,i,j2) = lhsm(3,i,j2) - |
| > lhsm(1,i,j2)*lhsm(5,i,j) |
| rhs(m,i,j2,k) = rhs(m,i,j2,k) - |
| > lhsm(1,i,j2)*rhs(m,i,j,k) |
| end do |
| end do |
| |
| c--------------------------------------------------------------------- |
| c And again the last two rows separately |
| c--------------------------------------------------------------------- |
| j = grid_points(2)-2 |
| j1 = grid_points(2)-1 |
| do i = 1, grid_points(1)-2 |
| m = 4 |
| fac1 = 1.d0/lhsp(3,i,j) |
| lhsp(4,i,j) = fac1*lhsp(4,i,j) |
| lhsp(5,i,j) = fac1*lhsp(5,i,j) |
| rhs(m,i,j,k) = fac1*rhs(m,i,j,k) |
| lhsp(3,i,j1) = lhsp(3,i,j1) - |
| > lhsp(2,i,j1)*lhsp(4,i,j) |
| lhsp(4,i,j1) = lhsp(4,i,j1) - |
| > lhsp(2,i,j1)*lhsp(5,i,j) |
| rhs(m,i,j1,k) = rhs(m,i,j1,k) - |
| > lhsp(2,i,j1)*rhs(m,i,j,k) |
| m = 5 |
| fac1 = 1.d0/lhsm(3,i,j) |
| lhsm(4,i,j) = fac1*lhsm(4,i,j) |
| lhsm(5,i,j) = fac1*lhsm(5,i,j) |
| rhs(m,i,j,k) = fac1*rhs(m,i,j,k) |
| lhsm(3,i,j1) = lhsm(3,i,j1) - |
| > lhsm(2,i,j1)*lhsm(4,i,j) |
| lhsm(4,i,j1) = lhsm(4,i,j1) - |
| > lhsm(2,i,j1)*lhsm(5,i,j) |
| rhs(m,i,j1,k) = rhs(m,i,j1,k) - |
| > lhsm(2,i,j1)*rhs(m,i,j,k) |
| c--------------------------------------------------------------------- |
| c Scale the last row immediately |
| c--------------------------------------------------------------------- |
| rhs(4,i,j1,k) = rhs(4,i,j1,k)/lhsp(3,i,j1) |
| rhs(5,i,j1,k) = rhs(5,i,j1,k)/lhsm(3,i,j1) |
| end do |
| |
| |
| c--------------------------------------------------------------------- |
| c BACKSUBSTITUTION |
| c--------------------------------------------------------------------- |
| |
| j = grid_points(2)-2 |
| j1 = grid_points(2)-1 |
| do i = 1, grid_points(1)-2 |
| do m = 1, 3 |
| rhs(m,i,j,k) = rhs(m,i,j,k) - |
| > lhs(4,i,j)*rhs(m,i,j1,k) |
| end do |
| |
| rhs(4,i,j,k) = rhs(4,i,j,k) - |
| > lhsp(4,i,j)*rhs(4,i,j1,k) |
| rhs(5,i,j,k) = rhs(5,i,j,k) - |
| > lhsm(4,i,j)*rhs(5,i,j1,k) |
| end do |
| |
| c--------------------------------------------------------------------- |
| c The first three factors |
| c--------------------------------------------------------------------- |
| do j = grid_points(2)-3, 0, -1 |
| j1 = j + 1 |
| j2 = j + 2 |
| do i = 1, grid_points(1)-2 |
| do m = 1, 3 |
| rhs(m,i,j,k) = rhs(m,i,j,k) - |
| > lhs(4,i,j)*rhs(m,i,j1,k) - |
| > lhs(5,i,j)*rhs(m,i,j2,k) |
| end do |
| |
| c--------------------------------------------------------------------- |
| c And the remaining two |
| c--------------------------------------------------------------------- |
| rhs(4,i,j,k) = rhs(4,i,j,k) - |
| > lhsp(4,i,j)*rhs(4,i,j1,k) - |
| > lhsp(5,i,j)*rhs(4,i,j2,k) |
| rhs(5,i,j,k) = rhs(5,i,j,k) - |
| > lhsm(4,i,j)*rhs(5,i,j1,k) - |
| > lhsm(5,i,j)*rhs(5,i,j2,k) |
| end do |
| end do |
| end do |
| if (timeron) call timer_stop(t_ysolve) |
| |
| call pinvr |
| |
| return |
| end |
| |
| |
| |
| |
| |
| |
| |
