!> @file sor.f90 !--------------------------------------------------------------------------------------------------! ! This file is part of the PALM model system. ! ! PALM is free software: you can redistribute it and/or modify it under the terms of the GNU General ! Public License as published by the Free Software Foundation, either version 3 of the License, or ! (at your option) any later version. ! ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the ! implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General ! Public License for more details. ! ! You should have received a copy of the GNU General Public License along with PALM. If not, see ! . ! ! Copyright 1997-2021 Leibniz Universitaet Hannover !--------------------------------------------------------------------------------------------------! ! ! ! Description: ! ------------ !> Solve the Poisson-equation with the SOR-Red/Black-scheme. !--------------------------------------------------------------------------------------------------! SUBROUTINE sor( d, ddzu, ddzw, p ) USE arrays_3d, & ONLY: rho_air, & rho_air_zw USE control_parameters, & ONLY: bc_dirichlet_l, & bc_dirichlet_n, & bc_dirichlet_r, & bc_dirichlet_s, & bc_lr_cyc, & bc_ns_cyc, & bc_radiation_l, & bc_radiation_n, & bc_radiation_r, & bc_radiation_s, & ibc_p_b, & ibc_p_t, & n_sor, & omega_sor USE exchange_horiz_mod, & ONLY: exchange_horiz USE grid_variables, & ONLY: ddx2, & ddy2 USE indices, & ONLY: nbgp, & nxl, & nxlg, & nxr, & nxrg, & nyn, & nyng, & nys, & nysg, & nz, & nzb, & nzt USE kinds IMPLICIT NONE INTEGER(iwp) :: i !< INTEGER(iwp) :: j !< INTEGER(iwp) :: k !< INTEGER(iwp) :: n !< INTEGER(iwp) :: nxl1 !< INTEGER(iwp) :: nxl2 !< INTEGER(iwp) :: nys1 !< INTEGER(iwp) :: nys2 !< REAL(wp) :: ddzu(1:nz+1) !< REAL(wp) :: ddzw(1:nzt+1) !< REAL(wp) :: d(nzb+1:nzt,nys:nyn,nxl:nxr) !< REAL(wp) :: p(nzb:nzt+1,nysg:nyng,nxlg:nxrg) !< REAL(wp), DIMENSION(:), ALLOCATABLE :: f1 !< REAL(wp), DIMENSION(:), ALLOCATABLE :: f2 !< REAL(wp), DIMENSION(:), ALLOCATABLE :: f3 !< ALLOCATE( f1(1:nz), f2(1:nz), f3(1:nz) ) ! !-- Compute pre-factors. DO k = 1, nz f2(k) = ddzu(k+1) * ddzw(k) * rho_air_zw(k) f3(k) = ddzu(k) * ddzw(k) * rho_air_zw(k-1) f1(k) = 2.0_wp * ( ddx2 + ddy2 ) * rho_air(k) + f2(k) + f3(k) ENDDO ! !-- Limits for RED- and BLACK-part. IF ( MOD( nxl , 2 ) == 0 ) THEN nxl1 = nxl nxl2 = nxl + 1 ELSE nxl1 = nxl + 1 nxl2 = nxl ENDIF IF ( MOD( nys , 2 ) == 0 ) THEN nys1 = nys nys2 = nys + 1 ELSE nys1 = nys + 1 nys2 = nys ENDIF DO n = 1, n_sor ! !-- RED-part DO i = nxl1, nxr, 2 DO j = nys2, nyn, 2 DO k = nzb+1, nzt p(k,j,i) = p(k,j,i) + omega_sor / f1(k) * ( & rho_air(k) * ddx2 * ( p(k,j,i+1) + p(k,j,i-1) ) + & rho_air(k) * ddy2 * ( p(k,j+1,i) + p(k,j-1,i) ) + & f2(k) * p(k+1,j,i) + & f3(k) * p(k-1,j,i) - & d(k,j,i) - & f1(k) * p(k,j,i) ) ENDDO ENDDO ENDDO DO i = nxl2, nxr, 2 DO j = nys1, nyn, 2 DO k = nzb+1, nzt p(k,j,i) = p(k,j,i) + omega_sor / f1(k) * ( & rho_air(k) * ddx2 * ( p(k,j,i+1) + p(k,j,i-1) ) + & rho_air(k) * ddy2 * ( p(k,j+1,i) + p(k,j-1,i) ) + & f2(k) * p(k+1,j,i) + & f3(k) * p(k-1,j,i) - & d(k,j,i) - & f1(k) * p(k,j,i) ) ENDDO ENDDO ENDDO ! !-- Exchange of boundary values for p. CALL exchange_horiz( p, nbgp ) ! !-- Horizontal (Neumann) boundary conditions in case of non-cyclic boundaries IF ( .NOT. bc_lr_cyc ) THEN IF ( bc_dirichlet_l .OR. bc_radiation_l ) p(:,:,nxl-1) = p(:,:,nxl) IF ( bc_dirichlet_r .OR. bc_radiation_r ) p(:,:,nxr+1) = p(:,:,nxr) ENDIF IF ( .NOT. bc_ns_cyc ) THEN IF ( bc_dirichlet_n .OR. bc_radiation_n ) p(:,nyn+1,:) = p(:,nyn,:) IF ( bc_dirichlet_s .OR. bc_radiation_s ) p(:,nys-1,:) = p(:,nys,:) ENDIF ! !-- BLACK-part DO i = nxl1, nxr, 2 DO j = nys1, nyn, 2 DO k = nzb+1, nzt p(k,j,i) = p(k,j,i) + omega_sor / f1(k) * ( & rho_air(k) * ddx2 * ( p(k,j,i+1) + p(k,j,i-1) ) + & rho_air(k) * ddy2 * ( p(k,j+1,i) + p(k,j-1,i) ) + & f2(k) * p(k+1,j,i) + & f3(k) * p(k-1,j,i) - & d(k,j,i) - & f1(k) * p(k,j,i) ) ENDDO ENDDO ENDDO DO i = nxl2, nxr, 2 DO j = nys2, nyn, 2 DO k = nzb+1, nzt p(k,j,i) = p(k,j,i) + omega_sor / f1(k) * ( & rho_air(k) * ddx2 * ( p(k,j,i+1) + p(k,j,i-1) ) + & rho_air(k) * ddy2 * ( p(k,j+1,i) + p(k,j-1,i) ) + & f2(k) * p(k+1,j,i) + & f3(k) * p(k-1,j,i) - & d(k,j,i) - & f1(k) * p(k,j,i) ) ENDDO ENDDO ENDDO ! !-- Exchange of boundary values for p. CALL exchange_horiz( p, nbgp ) ! !-- Boundary conditions top/bottom. !-- Bottom boundary IF ( ibc_p_b == 1 ) THEN ! Neumann p(nzb,:,:) = p(nzb+1,:,:) ELSE ! Dirichlet p(nzb,:,:) = 0.0_wp ENDIF ! !-- Top boundary IF ( ibc_p_t == 1 ) THEN ! Neumann p(nzt+1,:,:) = p(nzt,:,:) ELSE ! Dirichlet p(nzt+1,:,:) = 0.0_wp ENDIF ! !-- Horizontal (Neumann) boundary conditions in case of non-cyclic boundaries IF ( .NOT. bc_lr_cyc ) THEN IF ( bc_dirichlet_l .OR. bc_radiation_l ) p(:,:,nxl-1) = p(:,:,nxl) IF ( bc_dirichlet_r .OR. bc_radiation_r ) p(:,:,nxr+1) = p(:,:,nxr) ENDIF IF ( .NOT. bc_ns_cyc ) THEN IF ( bc_dirichlet_n .OR. bc_radiation_n ) p(:,nyn+1,:) = p(:,nyn,:) IF ( bc_dirichlet_s .OR. bc_radiation_s ) p(:,nys-1,:) = p(:,nys,:) ENDIF ENDDO DEALLOCATE( f1, f2, f3 ) END SUBROUTINE sor