c--------------------------------------------------------------------- c--------------------------------------------------------------------- subroutine x_solve(rho_i, qs, square, u, rhs, nx, nxmax, ny, nz) 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 nx, nxmax, ny, nz double precision rho_i ( 0:nxmax-1,0:ny-1,0:nz-1), $ qs ( 0:nxmax-1,0:ny-1,0:nz-1), $ square( 0:nxmax-1,0:ny-1,0:nz-1), $ u (5,0:nxmax-1,0:ny-1,0:nz-1), $ rhs (5,0:nxmax-1,0:ny-1,0:nz-1) 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--------------------------------------------------------------------- !$OMP PARALLEL DEFAULT(SHARED) PRIVATE(n,m,i,j,k,isize) !$OMP& SHARED(dx5,dx4,dx3,dx2,dx1,tx2,tx1,dt,c1345,c3c4,con43,c1,c2, !$OMP& nx,ny,nz) isize = nx-1 c--------------------------------------------------------------------- c determine a (labeled f) and n jacobians c--------------------------------------------------------------------- !$OMP DO do k = 1, nz-2 do j = 1, ny-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.d0 fjac(1,2,i,j) = 1.d0 fjac(1,3,i,j) = 0.d0 fjac(1,4,i,j) = 0.d0 fjac(1,5,i,j) = 0.d0 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.d0 - 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.d0 fjac(3,5,i,j) = 0.d0 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.d0 fjac(4,4,i,j) = u(2,i,j,k) * tmp1 fjac(4,5,i,j) = 0.d0 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.d0 njac(1,2,i,j) = 0.d0 njac(1,3,i,j) = 0.d0 njac(1,4,i,j) = 0.d0 njac(1,5,i,j) = 0.d0 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.d0 njac(2,4,i,j) = 0.d0 njac(2,5,i,j) = 0.d0 njac(3,1,i,j) = - c3c4 * tmp2 * u(3,i,j,k) njac(3,2,i,j) = 0.d0 njac(3,3,i,j) = c3c4 * tmp1 njac(3,4,i,j) = 0.d0 njac(3,5,i,j) = 0.d0 njac(4,1,i,j) = - c3c4 * tmp2 * u(4,i,j,k) njac(4,2,i,j) = 0.d0 njac(4,3,i,j) = 0.d0 njac(4,4,i,j) = c3c4 * tmp1 njac(4,5,i,j) = 0.d0 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 whole left hand side for starters c--------------------------------------------------------------------- do j = 1, ny-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 enddo enddo c--------------------------------------------------------------------- c next, set all diagonal values to 1. This is overkill, but convenient c--------------------------------------------------------------------- do m = 1, 5 lhs(m,m,bb,0,j) = 1.0d0 lhs(m,m,bb,isize,j) = 1.0d0 enddo enddo c--------------------------------------------------------------------- c now jacobians set, so form left hand side in x direction c--------------------------------------------------------------------- do j = 1, ny-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.d0 > + tmp1 * 2.d0 * njac(1,1,i,j) > + tmp1 * 2.d0 * dx1 lhs(1,2,bb,i,j) = tmp1 * 2.d0 * njac(1,2,i,j) lhs(1,3,bb,i,j) = tmp1 * 2.d0 * njac(1,3,i,j) lhs(1,4,bb,i,j) = tmp1 * 2.d0 * njac(1,4,i,j) lhs(1,5,bb,i,j) = tmp1 * 2.d0 * njac(1,5,i,j) lhs(2,1,bb,i,j) = tmp1 * 2.d0 * njac(2,1,i,j) lhs(2,2,bb,i,j) = 1.d0 > + tmp1 * 2.d0 * njac(2,2,i,j) > + tmp1 * 2.d0 * dx2 lhs(2,3,bb,i,j) = tmp1 * 2.d0 * njac(2,3,i,j) lhs(2,4,bb,i,j) = tmp1 * 2.d0 * njac(2,4,i,j) lhs(2,5,bb,i,j) = tmp1 * 2.d0 * njac(2,5,i,j) lhs(3,1,bb,i,j) = tmp1 * 2.d0 * njac(3,1,i,j) lhs(3,2,bb,i,j) = tmp1 * 2.d0 * njac(3,2,i,j) lhs(3,3,bb,i,j) = 1.d0 > + tmp1 * 2.d0 * njac(3,3,i,j) > + tmp1 * 2.d0 * dx3 lhs(3,4,bb,i,j) = tmp1 * 2.d0 * njac(3,4,i,j) lhs(3,5,bb,i,j) = tmp1 * 2.d0 * njac(3,5,i,j) lhs(4,1,bb,i,j) = tmp1 * 2.d0 * njac(4,1,i,j) lhs(4,2,bb,i,j) = tmp1 * 2.d0 * njac(4,2,i,j) lhs(4,3,bb,i,j) = tmp1 * 2.d0 * njac(4,3,i,j) lhs(4,4,bb,i,j) = 1.d0 > + tmp1 * 2.d0 * njac(4,4,i,j) > + tmp1 * 2.d0 * dx4 lhs(4,5,bb,i,j) = tmp1 * 2.d0 * njac(4,5,i,j) lhs(5,1,bb,i,j) = tmp1 * 2.d0 * njac(5,1,i,j) lhs(5,2,bb,i,j) = tmp1 * 2.d0 * njac(5,2,i,j) lhs(5,3,bb,i,j) = tmp1 * 2.d0 * njac(5,3,i,j) lhs(5,4,bb,i,j) = tmp1 * 2.d0 * njac(5,4,i,j) lhs(5,5,bb,i,j) = 1.d0 > + tmp1 * 2.d0 * njac(5,5,i,j) > + tmp1 * 2.d0 * 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 gaussian 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, ny-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, ny-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, ny-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, ny-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 !$OMP END DO nowait !$OMP END PARALLEL if (timeron) call timer_stop(t_xsolve) return end