| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| subroutine x_solve |
| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c this function performs the solution of the approximate factorization |
| c step in the x-direction for all five matrix components |
| c simultaneously. The Thomas algorithm is employed to solve the |
| c systems for the x-lines. Boundary conditions are non-periodic |
| c--------------------------------------------------------------------- |
| |
| include 'header.h' |
| |
| integer i, j, k, i1, i2, m |
| double precision ru1, fac1, fac2 |
| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| if (timeron) call timer_start(t_xsolve) |
| do k = 1, nz2 |
| |
| call lhsinit(nx2+1, ny2) |
| |
| c--------------------------------------------------------------------- |
| c Computes the left hand side for the three x-factors |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c first fill the lhs for the u-eigenvalue |
| c--------------------------------------------------------------------- |
| do j = 1, ny2 |
| do i = 0, grid_points(1)-1 |
| ru1 = c3c4*rho_i(i,j,k) |
| cv(i) = us(i,j,k) |
| rhon(i) = dmax1(dx2+con43*ru1, |
| > dx5+c1c5*ru1, |
| > dxmax+ru1, |
| > dx1) |
| end do |
| |
| do i = 1, nx2 |
| lhs(1,i,j) = 0.0d0 |
| lhs(2,i,j) = - dttx2 * cv(i-1) - dttx1 * rhon(i-1) |
| lhs(3,i,j) = 1.0d0 + c2dttx1 * rhon(i) |
| lhs(4,i,j) = dttx2 * cv(i+1) - dttx1 * rhon(i+1) |
| lhs(5,i,j) = 0.0d0 |
| end do |
| end do |
| |
| c--------------------------------------------------------------------- |
| c add fourth order dissipation |
| c--------------------------------------------------------------------- |
| |
| do j = 1, ny2 |
| i = 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+1,j) = lhs(2,i+1,j) - comz4 |
| lhs(3,i+1,j) = lhs(3,i+1,j) + comz6 |
| lhs(4,i+1,j) = lhs(4,i+1,j) - comz4 |
| lhs(5,i+1,j) = lhs(5,i+1,j) + comz1 |
| end do |
| |
| do j = 1, ny2 |
| do i=3, grid_points(1)-4 |
| 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 j = 1, ny2 |
| i = grid_points(1)-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+1,j) = lhs(1,i+1,j) + comz1 |
| lhs(2,i+1,j) = lhs(2,i+1,j) - comz4 |
| lhs(3,i+1,j) = lhs(3,i+1,j) + comz5 |
| end do |
| |
| c--------------------------------------------------------------------- |
| c subsequently, fill the other factors (u+c), (u-c) by adding to |
| c the first |
| c--------------------------------------------------------------------- |
| do j = 1, ny2 |
| do i = 1, nx2 |
| lhsp(1,i,j) = lhs(1,i,j) |
| lhsp(2,i,j) = lhs(2,i,j) - |
| > dttx2 * speed(i-1,j,k) |
| lhsp(3,i,j) = lhs(3,i,j) |
| lhsp(4,i,j) = lhs(4,i,j) + |
| > dttx2 * speed(i+1,j,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) + |
| > dttx2 * speed(i-1,j,k) |
| lhsm(3,i,j) = lhs(3,i,j) |
| lhsm(4,i,j) = lhs(4,i,j) - |
| > dttx2 * speed(i+1,j,k) |
| lhsm(5,i,j) = lhs(5,i,j) |
| end do |
| end do |
| |
| c--------------------------------------------------------------------- |
| c FORWARD ELIMINATION |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c perform the Thomas algorithm; first, FORWARD ELIMINATION |
| c--------------------------------------------------------------------- |
| |
| do j = 1, ny2 |
| do i = 0, grid_points(1)-3 |
| i1 = i + 1 |
| i2 = i + 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,i1,j) = lhs(3,i1,j) - |
| > lhs(2,i1,j)*lhs(4,i,j) |
| lhs(4,i1,j) = lhs(4,i1,j) - |
| > lhs(2,i1,j)*lhs(5,i,j) |
| do m = 1, 3 |
| rhs(m,i1,j,k) = rhs(m,i1,j,k) - |
| > lhs(2,i1,j)*rhs(m,i,j,k) |
| end do |
| lhs(2,i2,j) = lhs(2,i2,j) - |
| > lhs(1,i2,j)*lhs(4,i,j) |
| lhs(3,i2,j) = lhs(3,i2,j) - |
| > lhs(1,i2,j)*lhs(5,i,j) |
| do m = 1, 3 |
| rhs(m,i2,j,k) = rhs(m,i2,j,k) - |
| > lhs(1,i2,j)*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--------------------------------------------------------------------- |
| |
| do j = 1, ny2 |
| i = grid_points(1)-2 |
| i1 = grid_points(1)-1 |
| 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,i1,j) = lhs(3,i1,j) - |
| > lhs(2,i1,j)*lhs(4,i,j) |
| lhs(4,i1,j) = lhs(4,i1,j) - |
| > lhs(2,i1,j)*lhs(5,i,j) |
| do m = 1, 3 |
| rhs(m,i1,j,k) = rhs(m,i1,j,k) - |
| > lhs(2,i1,j)*rhs(m,i,j,k) |
| end do |
| c--------------------------------------------------------------------- |
| c scale the last row immediately |
| c--------------------------------------------------------------------- |
| fac2 = 1.d0/lhs(3,i1,j) |
| do m = 1, 3 |
| rhs(m,i1,j,k) = fac2*rhs(m,i1,j,k) |
| end do |
| end do |
| |
| c--------------------------------------------------------------------- |
| c do the u+c and the u-c factors |
| c--------------------------------------------------------------------- |
| |
| do j = 1, ny2 |
| do i = 0, grid_points(1)-3 |
| i1 = i + 1 |
| i2 = i + 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,i1,j) = lhsp(3,i1,j) - |
| > lhsp(2,i1,j)*lhsp(4,i,j) |
| lhsp(4,i1,j) = lhsp(4,i1,j) - |
| > lhsp(2,i1,j)*lhsp(5,i,j) |
| rhs(m,i1,j,k) = rhs(m,i1,j,k) - |
| > lhsp(2,i1,j)*rhs(m,i,j,k) |
| lhsp(2,i2,j) = lhsp(2,i2,j) - |
| > lhsp(1,i2,j)*lhsp(4,i,j) |
| lhsp(3,i2,j) = lhsp(3,i2,j) - |
| > lhsp(1,i2,j)*lhsp(5,i,j) |
| rhs(m,i2,j,k) = rhs(m,i2,j,k) - |
| > lhsp(1,i2,j)*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,i1,j) = lhsm(3,i1,j) - |
| > lhsm(2,i1,j)*lhsm(4,i,j) |
| lhsm(4,i1,j) = lhsm(4,i1,j) - |
| > lhsm(2,i1,j)*lhsm(5,i,j) |
| rhs(m,i1,j,k) = rhs(m,i1,j,k) - |
| > lhsm(2,i1,j)*rhs(m,i,j,k) |
| lhsm(2,i2,j) = lhsm(2,i2,j) - |
| > lhsm(1,i2,j)*lhsm(4,i,j) |
| lhsm(3,i2,j) = lhsm(3,i2,j) - |
| > lhsm(1,i2,j)*lhsm(5,i,j) |
| rhs(m,i2,j,k) = rhs(m,i2,j,k) - |
| > lhsm(1,i2,j)*rhs(m,i,j,k) |
| end do |
| end do |
| |
| c--------------------------------------------------------------------- |
| c And again the last two rows separately |
| c--------------------------------------------------------------------- |
| do j = 1, ny2 |
| i = grid_points(1)-2 |
| i1 = grid_points(1)-1 |
| 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,i1,j) = lhsp(3,i1,j) - |
| > lhsp(2,i1,j)*lhsp(4,i,j) |
| lhsp(4,i1,j) = lhsp(4,i1,j) - |
| > lhsp(2,i1,j)*lhsp(5,i,j) |
| rhs(m,i1,j,k) = rhs(m,i1,j,k) - |
| > lhsp(2,i1,j)*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,i1,j) = lhsm(3,i1,j) - |
| > lhsm(2,i1,j)*lhsm(4,i,j) |
| lhsm(4,i1,j) = lhsm(4,i1,j) - |
| > lhsm(2,i1,j)*lhsm(5,i,j) |
| rhs(m,i1,j,k) = rhs(m,i1,j,k) - |
| > lhsm(2,i1,j)*rhs(m,i,j,k) |
| c--------------------------------------------------------------------- |
| c Scale the last row immediately |
| c--------------------------------------------------------------------- |
| rhs(4,i1,j,k) = rhs(4,i1,j,k)/lhsp(3,i1,j) |
| rhs(5,i1,j,k) = rhs(5,i1,j,k)/lhsm(3,i1,j) |
| end do |
| |
| |
| c--------------------------------------------------------------------- |
| c BACKSUBSTITUTION |
| c--------------------------------------------------------------------- |
| |
| |
| do j = 1, ny2 |
| i = grid_points(1)-2 |
| i1 = grid_points(1)-1 |
| do m = 1, 3 |
| rhs(m,i,j,k) = rhs(m,i,j,k) - |
| > lhs(4,i,j)*rhs(m,i1,j,k) |
| end do |
| |
| rhs(4,i,j,k) = rhs(4,i,j,k) - |
| > lhsp(4,i,j)*rhs(4,i1,j,k) |
| rhs(5,i,j,k) = rhs(5,i,j,k) - |
| > lhsm(4,i,j)*rhs(5,i1,j,k) |
| end do |
| |
| c--------------------------------------------------------------------- |
| c The first three factors |
| c--------------------------------------------------------------------- |
| do j = 1, ny2 |
| do i = grid_points(1)-3, 0, -1 |
| i1 = i + 1 |
| i2 = i + 2 |
| do m = 1, 3 |
| rhs(m,i,j,k) = rhs(m,i,j,k) - |
| > lhs(4,i,j)*rhs(m,i1,j,k) - |
| > lhs(5,i,j)*rhs(m,i2,j,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,i1,j,k) - |
| > lhsp(5,i,j)*rhs(4,i2,j,k) |
| rhs(5,i,j,k) = rhs(5,i,j,k) - |
| > lhsm(4,i,j)*rhs(5,i1,j,k) - |
| > lhsm(5,i,j)*rhs(5,i2,j,k) |
| end do |
| end do |
| end do |
| if (timeron) call timer_stop(t_xsolve) |
| |
| c--------------------------------------------------------------------- |
| c Do the block-diagonal inversion |
| c--------------------------------------------------------------------- |
| call ninvr |
| |
| return |
| end |
| |
| |
| |
| |
| |
| |
| |
