| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| subroutine x_solve |
| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c |
| c Performs line solves in X direction by first factoring |
| c the block-tridiagonal matrix into an upper triangular matrix, |
| c and then performing back substitution to solve for the unknow |
| c vectors of each line. |
| c |
| c Make sure we treat elements zero to cell_size in the direction |
| c of the sweep. |
| c |
| c--------------------------------------------------------------------- |
| |
| include 'header.h' |
| include 'work_lhs_vec.h' |
| |
| integer i,j,k,m,n,isize |
| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| if (timeron) call timer_start(t_xsolve) |
| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c This function computes the left hand side in the xi-direction |
| c--------------------------------------------------------------------- |
| |
| isize = grid_points(1)-1 |
| |
| c--------------------------------------------------------------------- |
| c determine a (labeled f) and n jacobians |
| c--------------------------------------------------------------------- |
| !$omp parallel do default(shared) shared(isize) |
| !$omp& private(i,j,k,m,n) |
| do k = 1, grid_points(3)-2 |
| do j = 1, grid_points(2)-2 |
| do i = 0, isize |
| |
| tmp1 = rho_i(i,j,k) |
| tmp2 = tmp1 * tmp1 |
| tmp3 = tmp1 * tmp2 |
| c--------------------------------------------------------------------- |
| c |
| c--------------------------------------------------------------------- |
| fjac(1,1,i,j) = 0.0d+00 |
| fjac(1,2,i,j) = 1.0d+00 |
| fjac(1,3,i,j) = 0.0d+00 |
| fjac(1,4,i,j) = 0.0d+00 |
| fjac(1,5,i,j) = 0.0d+00 |
| |
| fjac(2,1,i,j) = -(u(2,i,j,k) * tmp2 * |
| > u(2,i,j,k)) |
| > + c2 * qs(i,j,k) |
| fjac(2,2,i,j) = ( 2.0d+00 - c2 ) |
| > * ( u(2,i,j,k) / u(1,i,j,k) ) |
| fjac(2,3,i,j) = - c2 * ( u(3,i,j,k) * tmp1 ) |
| fjac(2,4,i,j) = - c2 * ( u(4,i,j,k) * tmp1 ) |
| fjac(2,5,i,j) = c2 |
| |
| fjac(3,1,i,j) = - ( u(2,i,j,k)*u(3,i,j,k) ) * tmp2 |
| fjac(3,2,i,j) = u(3,i,j,k) * tmp1 |
| fjac(3,3,i,j) = u(2,i,j,k) * tmp1 |
| fjac(3,4,i,j) = 0.0d+00 |
| fjac(3,5,i,j) = 0.0d+00 |
| |
| fjac(4,1,i,j) = - ( u(2,i,j,k)*u(4,i,j,k) ) * tmp2 |
| fjac(4,2,i,j) = u(4,i,j,k) * tmp1 |
| fjac(4,3,i,j) = 0.0d+00 |
| fjac(4,4,i,j) = u(2,i,j,k) * tmp1 |
| fjac(4,5,i,j) = 0.0d+00 |
| |
| fjac(5,1,i,j) = ( c2 * 2.0d0 * square(i,j,k) |
| > - c1 * u(5,i,j,k) ) |
| > * ( u(2,i,j,k) * tmp2 ) |
| fjac(5,2,i,j) = c1 * u(5,i,j,k) * tmp1 |
| > - c2 |
| > * ( u(2,i,j,k)*u(2,i,j,k) * tmp2 |
| > + qs(i,j,k) ) |
| fjac(5,3,i,j) = - c2 * ( u(3,i,j,k)*u(2,i,j,k) ) |
| > * tmp2 |
| fjac(5,4,i,j) = - c2 * ( u(4,i,j,k)*u(2,i,j,k) ) |
| > * tmp2 |
| fjac(5,5,i,j) = c1 * ( u(2,i,j,k) * tmp1 ) |
| |
| njac(1,1,i,j) = 0.0d+00 |
| njac(1,2,i,j) = 0.0d+00 |
| njac(1,3,i,j) = 0.0d+00 |
| njac(1,4,i,j) = 0.0d+00 |
| njac(1,5,i,j) = 0.0d+00 |
| |
| njac(2,1,i,j) = - con43 * c3c4 * tmp2 * u(2,i,j,k) |
| njac(2,2,i,j) = con43 * c3c4 * tmp1 |
| njac(2,3,i,j) = 0.0d+00 |
| njac(2,4,i,j) = 0.0d+00 |
| njac(2,5,i,j) = 0.0d+00 |
| |
| njac(3,1,i,j) = - c3c4 * tmp2 * u(3,i,j,k) |
| njac(3,2,i,j) = 0.0d+00 |
| njac(3,3,i,j) = c3c4 * tmp1 |
| njac(3,4,i,j) = 0.0d+00 |
| njac(3,5,i,j) = 0.0d+00 |
| |
| njac(4,1,i,j) = - c3c4 * tmp2 * u(4,i,j,k) |
| njac(4,2,i,j) = 0.0d+00 |
| njac(4,3,i,j) = 0.0d+00 |
| njac(4,4,i,j) = c3c4 * tmp1 |
| njac(4,5,i,j) = 0.0d+00 |
| |
| njac(5,1,i,j) = - ( con43 * c3c4 |
| > - c1345 ) * tmp3 * (u(2,i,j,k)**2) |
| > - ( c3c4 - c1345 ) * tmp3 * (u(3,i,j,k)**2) |
| > - ( c3c4 - c1345 ) * tmp3 * (u(4,i,j,k)**2) |
| > - c1345 * tmp2 * u(5,i,j,k) |
| |
| njac(5,2,i,j) = ( con43 * c3c4 |
| > - c1345 ) * tmp2 * u(2,i,j,k) |
| njac(5,3,i,j) = ( c3c4 - c1345 ) * tmp2 * u(3,i,j,k) |
| njac(5,4,i,j) = ( c3c4 - c1345 ) * tmp2 * u(4,i,j,k) |
| njac(5,5,i,j) = ( c1345 ) * tmp1 |
| |
| enddo |
| enddo |
| |
| c--------------------------------------------------------------------- |
| c zero the left hand side for starters |
| c set diagonal values to 1. This is overkill, but convenient |
| c--------------------------------------------------------------------- |
| do j = 1, grid_points(2)-2 |
| do m = 1, 5 |
| do n = 1, 5 |
| lhs(m,n,aa,0,j) = 0.0d0 |
| lhs(m,n,bb,0,j) = 0.0d0 |
| lhs(m,n,cc,0,j) = 0.0d0 |
| lhs(m,n,aa,isize,j) = 0.0d0 |
| lhs(m,n,bb,isize,j) = 0.0d0 |
| lhs(m,n,cc,isize,j) = 0.0d0 |
| end do |
| lhs(m,m,bb,0,j) = 1.0d0 |
| lhs(m,m,bb,isize,j) = 1.0d0 |
| end do |
| enddo |
| |
| c--------------------------------------------------------------------- |
| c now jacobians set, so form left hand side in x direction |
| c--------------------------------------------------------------------- |
| do j = 1, grid_points(2)-2 |
| do i = 1, isize-1 |
| |
| tmp1 = dt * tx1 |
| tmp2 = dt * tx2 |
| |
| lhs(1,1,aa,i,j) = - tmp2 * fjac(1,1,i-1,j) |
| > - tmp1 * njac(1,1,i-1,j) |
| > - tmp1 * dx1 |
| lhs(1,2,aa,i,j) = - tmp2 * fjac(1,2,i-1,j) |
| > - tmp1 * njac(1,2,i-1,j) |
| lhs(1,3,aa,i,j) = - tmp2 * fjac(1,3,i-1,j) |
| > - tmp1 * njac(1,3,i-1,j) |
| lhs(1,4,aa,i,j) = - tmp2 * fjac(1,4,i-1,j) |
| > - tmp1 * njac(1,4,i-1,j) |
| lhs(1,5,aa,i,j) = - tmp2 * fjac(1,5,i-1,j) |
| > - tmp1 * njac(1,5,i-1,j) |
| |
| lhs(2,1,aa,i,j) = - tmp2 * fjac(2,1,i-1,j) |
| > - tmp1 * njac(2,1,i-1,j) |
| lhs(2,2,aa,i,j) = - tmp2 * fjac(2,2,i-1,j) |
| > - tmp1 * njac(2,2,i-1,j) |
| > - tmp1 * dx2 |
| lhs(2,3,aa,i,j) = - tmp2 * fjac(2,3,i-1,j) |
| > - tmp1 * njac(2,3,i-1,j) |
| lhs(2,4,aa,i,j) = - tmp2 * fjac(2,4,i-1,j) |
| > - tmp1 * njac(2,4,i-1,j) |
| lhs(2,5,aa,i,j) = - tmp2 * fjac(2,5,i-1,j) |
| > - tmp1 * njac(2,5,i-1,j) |
| |
| lhs(3,1,aa,i,j) = - tmp2 * fjac(3,1,i-1,j) |
| > - tmp1 * njac(3,1,i-1,j) |
| lhs(3,2,aa,i,j) = - tmp2 * fjac(3,2,i-1,j) |
| > - tmp1 * njac(3,2,i-1,j) |
| lhs(3,3,aa,i,j) = - tmp2 * fjac(3,3,i-1,j) |
| > - tmp1 * njac(3,3,i-1,j) |
| > - tmp1 * dx3 |
| lhs(3,4,aa,i,j) = - tmp2 * fjac(3,4,i-1,j) |
| > - tmp1 * njac(3,4,i-1,j) |
| lhs(3,5,aa,i,j) = - tmp2 * fjac(3,5,i-1,j) |
| > - tmp1 * njac(3,5,i-1,j) |
| |
| lhs(4,1,aa,i,j) = - tmp2 * fjac(4,1,i-1,j) |
| > - tmp1 * njac(4,1,i-1,j) |
| lhs(4,2,aa,i,j) = - tmp2 * fjac(4,2,i-1,j) |
| > - tmp1 * njac(4,2,i-1,j) |
| lhs(4,3,aa,i,j) = - tmp2 * fjac(4,3,i-1,j) |
| > - tmp1 * njac(4,3,i-1,j) |
| lhs(4,4,aa,i,j) = - tmp2 * fjac(4,4,i-1,j) |
| > - tmp1 * njac(4,4,i-1,j) |
| > - tmp1 * dx4 |
| lhs(4,5,aa,i,j) = - tmp2 * fjac(4,5,i-1,j) |
| > - tmp1 * njac(4,5,i-1,j) |
| |
| lhs(5,1,aa,i,j) = - tmp2 * fjac(5,1,i-1,j) |
| > - tmp1 * njac(5,1,i-1,j) |
| lhs(5,2,aa,i,j) = - tmp2 * fjac(5,2,i-1,j) |
| > - tmp1 * njac(5,2,i-1,j) |
| lhs(5,3,aa,i,j) = - tmp2 * fjac(5,3,i-1,j) |
| > - tmp1 * njac(5,3,i-1,j) |
| lhs(5,4,aa,i,j) = - tmp2 * fjac(5,4,i-1,j) |
| > - tmp1 * njac(5,4,i-1,j) |
| lhs(5,5,aa,i,j) = - tmp2 * fjac(5,5,i-1,j) |
| > - tmp1 * njac(5,5,i-1,j) |
| > - tmp1 * dx5 |
| |
| lhs(1,1,bb,i,j) = 1.0d+00 |
| > + tmp1 * 2.0d+00 * njac(1,1,i,j) |
| > + tmp1 * 2.0d+00 * dx1 |
| lhs(1,2,bb,i,j) = tmp1 * 2.0d+00 * njac(1,2,i,j) |
| lhs(1,3,bb,i,j) = tmp1 * 2.0d+00 * njac(1,3,i,j) |
| lhs(1,4,bb,i,j) = tmp1 * 2.0d+00 * njac(1,4,i,j) |
| lhs(1,5,bb,i,j) = tmp1 * 2.0d+00 * njac(1,5,i,j) |
| |
| lhs(2,1,bb,i,j) = tmp1 * 2.0d+00 * njac(2,1,i,j) |
| lhs(2,2,bb,i,j) = 1.0d+00 |
| > + tmp1 * 2.0d+00 * njac(2,2,i,j) |
| > + tmp1 * 2.0d+00 * dx2 |
| lhs(2,3,bb,i,j) = tmp1 * 2.0d+00 * njac(2,3,i,j) |
| lhs(2,4,bb,i,j) = tmp1 * 2.0d+00 * njac(2,4,i,j) |
| lhs(2,5,bb,i,j) = tmp1 * 2.0d+00 * njac(2,5,i,j) |
| |
| lhs(3,1,bb,i,j) = tmp1 * 2.0d+00 * njac(3,1,i,j) |
| lhs(3,2,bb,i,j) = tmp1 * 2.0d+00 * njac(3,2,i,j) |
| lhs(3,3,bb,i,j) = 1.0d+00 |
| > + tmp1 * 2.0d+00 * njac(3,3,i,j) |
| > + tmp1 * 2.0d+00 * dx3 |
| lhs(3,4,bb,i,j) = tmp1 * 2.0d+00 * njac(3,4,i,j) |
| lhs(3,5,bb,i,j) = tmp1 * 2.0d+00 * njac(3,5,i,j) |
| |
| lhs(4,1,bb,i,j) = tmp1 * 2.0d+00 * njac(4,1,i,j) |
| lhs(4,2,bb,i,j) = tmp1 * 2.0d+00 * njac(4,2,i,j) |
| lhs(4,3,bb,i,j) = tmp1 * 2.0d+00 * njac(4,3,i,j) |
| lhs(4,4,bb,i,j) = 1.0d+00 |
| > + tmp1 * 2.0d+00 * njac(4,4,i,j) |
| > + tmp1 * 2.0d+00 * dx4 |
| lhs(4,5,bb,i,j) = tmp1 * 2.0d+00 * njac(4,5,i,j) |
| |
| lhs(5,1,bb,i,j) = tmp1 * 2.0d+00 * njac(5,1,i,j) |
| lhs(5,2,bb,i,j) = tmp1 * 2.0d+00 * njac(5,2,i,j) |
| lhs(5,3,bb,i,j) = tmp1 * 2.0d+00 * njac(5,3,i,j) |
| lhs(5,4,bb,i,j) = tmp1 * 2.0d+00 * njac(5,4,i,j) |
| lhs(5,5,bb,i,j) = 1.0d+00 |
| > + tmp1 * 2.0d+00 * njac(5,5,i,j) |
| > + tmp1 * 2.0d+00 * dx5 |
| |
| lhs(1,1,cc,i,j) = tmp2 * fjac(1,1,i+1,j) |
| > - tmp1 * njac(1,1,i+1,j) |
| > - tmp1 * dx1 |
| lhs(1,2,cc,i,j) = tmp2 * fjac(1,2,i+1,j) |
| > - tmp1 * njac(1,2,i+1,j) |
| lhs(1,3,cc,i,j) = tmp2 * fjac(1,3,i+1,j) |
| > - tmp1 * njac(1,3,i+1,j) |
| lhs(1,4,cc,i,j) = tmp2 * fjac(1,4,i+1,j) |
| > - tmp1 * njac(1,4,i+1,j) |
| lhs(1,5,cc,i,j) = tmp2 * fjac(1,5,i+1,j) |
| > - tmp1 * njac(1,5,i+1,j) |
| |
| lhs(2,1,cc,i,j) = tmp2 * fjac(2,1,i+1,j) |
| > - tmp1 * njac(2,1,i+1,j) |
| lhs(2,2,cc,i,j) = tmp2 * fjac(2,2,i+1,j) |
| > - tmp1 * njac(2,2,i+1,j) |
| > - tmp1 * dx2 |
| lhs(2,3,cc,i,j) = tmp2 * fjac(2,3,i+1,j) |
| > - tmp1 * njac(2,3,i+1,j) |
| lhs(2,4,cc,i,j) = tmp2 * fjac(2,4,i+1,j) |
| > - tmp1 * njac(2,4,i+1,j) |
| lhs(2,5,cc,i,j) = tmp2 * fjac(2,5,i+1,j) |
| > - tmp1 * njac(2,5,i+1,j) |
| |
| lhs(3,1,cc,i,j) = tmp2 * fjac(3,1,i+1,j) |
| > - tmp1 * njac(3,1,i+1,j) |
| lhs(3,2,cc,i,j) = tmp2 * fjac(3,2,i+1,j) |
| > - tmp1 * njac(3,2,i+1,j) |
| lhs(3,3,cc,i,j) = tmp2 * fjac(3,3,i+1,j) |
| > - tmp1 * njac(3,3,i+1,j) |
| > - tmp1 * dx3 |
| lhs(3,4,cc,i,j) = tmp2 * fjac(3,4,i+1,j) |
| > - tmp1 * njac(3,4,i+1,j) |
| lhs(3,5,cc,i,j) = tmp2 * fjac(3,5,i+1,j) |
| > - tmp1 * njac(3,5,i+1,j) |
| |
| lhs(4,1,cc,i,j) = tmp2 * fjac(4,1,i+1,j) |
| > - tmp1 * njac(4,1,i+1,j) |
| lhs(4,2,cc,i,j) = tmp2 * fjac(4,2,i+1,j) |
| > - tmp1 * njac(4,2,i+1,j) |
| lhs(4,3,cc,i,j) = tmp2 * fjac(4,3,i+1,j) |
| > - tmp1 * njac(4,3,i+1,j) |
| lhs(4,4,cc,i,j) = tmp2 * fjac(4,4,i+1,j) |
| > - tmp1 * njac(4,4,i+1,j) |
| > - tmp1 * dx4 |
| lhs(4,5,cc,i,j) = tmp2 * fjac(4,5,i+1,j) |
| > - tmp1 * njac(4,5,i+1,j) |
| |
| lhs(5,1,cc,i,j) = tmp2 * fjac(5,1,i+1,j) |
| > - tmp1 * njac(5,1,i+1,j) |
| lhs(5,2,cc,i,j) = tmp2 * fjac(5,2,i+1,j) |
| > - tmp1 * njac(5,2,i+1,j) |
| lhs(5,3,cc,i,j) = tmp2 * fjac(5,3,i+1,j) |
| > - tmp1 * njac(5,3,i+1,j) |
| lhs(5,4,cc,i,j) = tmp2 * fjac(5,4,i+1,j) |
| > - tmp1 * njac(5,4,i+1,j) |
| lhs(5,5,cc,i,j) = tmp2 * fjac(5,5,i+1,j) |
| > - tmp1 * njac(5,5,i+1,j) |
| > - tmp1 * dx5 |
| |
| enddo |
| enddo |
| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c performs guaussian elimination on this cell. |
| c |
| c assumes that unpacking routines for non-first cells |
| c preload C' and rhs' from previous cell. |
| c |
| c assumed send happens outside this routine, but that |
| c c'(IMAX) and rhs'(IMAX) will be sent to next cell |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c outer most do loops - sweeping in i direction |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c multiply c(0,j,k) by b_inverse and copy back to c |
| c multiply rhs(0) by b_inverse(0) and copy to rhs |
| c--------------------------------------------------------------------- |
| !dir$ ivdep |
| do j = 1, grid_points(2)-2 |
| call binvcrhs( lhs(1,1,bb,0,j), |
| > lhs(1,1,cc,0,j), |
| > rhs(1,0,j,k) ) |
| enddo |
| |
| c--------------------------------------------------------------------- |
| c begin inner most do loop |
| c do all the elements of the cell unless last |
| c--------------------------------------------------------------------- |
| !dir$ ivdep |
| !dir$ interchange(i,j) |
| do j = 1, grid_points(2)-2 |
| do i=1,isize-1 |
| |
| c--------------------------------------------------------------------- |
| c rhs(i) = rhs(i) - A*rhs(i-1) |
| c--------------------------------------------------------------------- |
| call matvec_sub(lhs(1,1,aa,i,j), |
| > rhs(1,i-1,j,k),rhs(1,i,j,k)) |
| |
| c--------------------------------------------------------------------- |
| c B(i) = B(i) - C(i-1)*A(i) |
| c--------------------------------------------------------------------- |
| call matmul_sub(lhs(1,1,aa,i,j), |
| > lhs(1,1,cc,i-1,j), |
| > lhs(1,1,bb,i,j)) |
| |
| |
| c--------------------------------------------------------------------- |
| c multiply c(i,j,k) by b_inverse and copy back to c |
| c multiply rhs(1,j,k) by b_inverse(1,j,k) and copy to rhs |
| c--------------------------------------------------------------------- |
| call binvcrhs( lhs(1,1,bb,i,j), |
| > lhs(1,1,cc,i,j), |
| > rhs(1,i,j,k) ) |
| |
| enddo |
| enddo |
| |
| c--------------------------------------------------------------------- |
| c rhs(isize) = rhs(isize) - A*rhs(isize-1) |
| c--------------------------------------------------------------------- |
| !dir$ ivdep |
| do j = 1, grid_points(2)-2 |
| call matvec_sub(lhs(1,1,aa,isize,j), |
| > rhs(1,isize-1,j,k),rhs(1,isize,j,k)) |
| |
| c--------------------------------------------------------------------- |
| c B(isize) = B(isize) - C(isize-1)*A(isize) |
| c--------------------------------------------------------------------- |
| call matmul_sub(lhs(1,1,aa,isize,j), |
| > lhs(1,1,cc,isize-1,j), |
| > lhs(1,1,bb,isize,j)) |
| |
| c--------------------------------------------------------------------- |
| c multiply rhs() by b_inverse() and copy to rhs |
| c--------------------------------------------------------------------- |
| call binvrhs( lhs(1,1,bb,isize,j), |
| > rhs(1,isize,j,k) ) |
| enddo |
| |
| |
| c--------------------------------------------------------------------- |
| c back solve: if last cell, then generate U(isize)=rhs(isize) |
| c else assume U(isize) is loaded in un pack backsub_info |
| c so just use it |
| c after call u(istart) will be sent to next cell |
| c--------------------------------------------------------------------- |
| |
| do j = 1, grid_points(2)-2 |
| do i=isize-1,0,-1 |
| do m=1,BLOCK_SIZE |
| do n=1,BLOCK_SIZE |
| rhs(m,i,j,k) = rhs(m,i,j,k) |
| > - lhs(m,n,cc,i,j)*rhs(n,i+1,j,k) |
| enddo |
| enddo |
| enddo |
| enddo |
| |
| enddo |
| if (timeron) call timer_stop(t_xsolve) |
| |
| return |
| end |
| |
