!> @file diffusion_v.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: ! ------------ !> Diffusion term of the v-component !--------------------------------------------------------------------------------------------------! MODULE diffusion_v_mod PRIVATE PUBLIC diffusion_v INTERFACE diffusion_v MODULE PROCEDURE diffusion_v MODULE PROCEDURE diffusion_v_ij END INTERFACE diffusion_v CONTAINS !--------------------------------------------------------------------------------------------------! ! Description: ! ------------ !> Call for all grid points !--------------------------------------------------------------------------------------------------! SUBROUTINE diffusion_v USE arrays_3d, & ONLY: ddzu, ddzw, drho_air, km, rho_air_zw, tend, u, v, w USE control_parameters, & ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes USE grid_variables, & ONLY: ddx, ddy, ddy2 USE indices, & ONLY: nxl, nxr, nyn, nysv, nzb, nzt, topo_flags USE kinds USE surface_mod, & ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, surf_usm_v IMPLICIT NONE INTEGER(iwp) :: i !< running index x direction INTEGER(iwp) :: j !< running index y direction INTEGER(iwp) :: k !< running index z direction INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall INTEGER(iwp) :: m !< running index surface elements INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint REAL(wp) :: flag !< flag to mask topography grid points REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto yv-zw grid REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto yv-zw grid REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface !$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k, l, m) & !$ACC PRIVATE(surf_e, surf_s, flag, kmxm, kmxp, kmzm, kmzp) & !$ACC PRIVATE(mask_bottom, mask_east, mask_west, mask_top) & !$ACC PRESENT(topo_flags, km) & !$ACC PRESENT(u, v, w) & !$ACC PRESENT(ddzu, ddzw, drho_air, rho_air_zw) & !$ACC PRESENT(surf_def_h(0:2), surf_def_v(2:3)) & !$ACC PRESENT(surf_lsm_h(0:1), surf_lsm_v(2:3)) & !$ACC PRESENT(surf_usm_h(0:1), surf_usm_v(2:3)) & !$ACC PRESENT(tend) DO i = nxl, nxr DO j = nysv, nyn ! !-- Compute horizontal diffusion DO k = nzb+1, nzt ! !-- Predetermine flag to mask topography and wall-bounded grid points. !-- It is sufficient to masked only east- and west-facing surfaces, which need special !-- treatment for the v-component. flag = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i), 2 ) ) mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i+1), 2 ) ) mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i-1), 2 ) ) ! !-- Interpolate eddy diffusivities on staggered gridpoints kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) tend(k,j,i) = tend(k,j,i) + ( & mask_east * kmxp * ( & ( v(k,j,i+1) - v(k,j,i) ) * ddx & + ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & ) & - mask_west * kmxm * ( & ( v(k,j,i) - v(k,j,i-1) ) * ddx & + ( u(k,j,i) - u(k,j-1,i) ) * ddy & ) & ) * ddx * flag & + 2.0_wp * ( & km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & ) * ddy2 * flag ENDDO ! !-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3) surfaces. Note, !-- in the the flat case, loops won't be entered as start_index > end_index. Furtermore, !-- note, no vertical natural surfaces so far. !-- Default-type surfaces DO l = 2, 3 surf_s = surf_def_v(l)%start_index(j,i) surf_e = surf_def_v(l)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_v(l)%k(m) tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx ENDDO ENDDO ! !-- Natural-type surfaces DO l = 2, 3 surf_s = surf_lsm_v(l)%start_index(j,i) surf_e = surf_lsm_v(l)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_v(l)%k(m) tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx ENDDO ENDDO ! !-- Urban-type surfaces DO l = 2, 3 surf_s = surf_usm_v(l)%start_index(j,i) surf_e = surf_usm_v(l)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_v(l)%k(m) tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx ENDDO ENDDO ! !-- Compute vertical diffusion. In case of simulating a surface layer, respective grid !-- diffusive fluxes are masked (flag 10) within this loop, and added further below, else, !-- simple gradient approach is applied. Model top is also mask if top-momentum flux is !-- given. DO k = nzb+1, nzt ! !-- Determine flags to mask topography below and above. Flag 2 is used to mask !-- topography in general, while flag 8 implies also information about !-- use_surface_fluxes. Flag 9 is used to control momentum flux at model top. mask_bottom = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k-1,j,i), 8 ) ) mask_top = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k+1,j,i), 8 ) ) * & MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k+1,j,i), 9 ) ) flag = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i), 2 ) ) ! !-- Interpolate eddy diffusivities on staggered gridpoints kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) tend(k,j,i) = tend(k,j,i) & & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & & ) * rho_air_zw(k) * mask_top & & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & & ) * rho_air_zw(k-1) * mask_bottom & & ) * ddzw(k) * drho_air(k) * flag ENDDO ! !-- Vertical diffusion at the first grid point above the surface, if the momentum flux at !-- the bottom is given by the Prandtl law or if it is prescribed by the user. !-- Difference quotient of the momentum flux is not formed over half of the grid spacing !-- (2.0*ddzw(k)) any more, since the comparison with other (LES) models showed that the !-- values of the momentum flux becomes too large in this case. IF ( use_surface_fluxes ) THEN ! !-- Default-type surfaces, upward-facing surf_s = surf_def_h(0)%start_index(j,i) surf_e = surf_def_h(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_h(0)%k(m) tend(k,j,i) = tend(k,j,i) & + ( - ( - surf_def_h(0)%vsws(m) ) ) * ddzw(k) * drho_air(k) ENDDO ! !-- Default-type surfaces, dowward-facing surf_s = surf_def_h(1)%start_index(j,i) surf_e = surf_def_h(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_h(1)%k(m) tend(k,j,i) = tend(k,j,i) & + ( - surf_def_h(1)%vsws(m) ) * ddzw(k) * drho_air(k) ENDDO ! !-- Natural-type surfaces, upward-facing surf_s = surf_lsm_h(0)%start_index(j,i) surf_e = surf_lsm_h(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_h(0)%k(m) tend(k,j,i) = tend(k,j,i) & + ( - ( - surf_lsm_h(0)%vsws(m) ) ) * ddzw(k) * drho_air(k) ENDDO ! !-- Natural-type surfaces, downward-facing surf_s = surf_lsm_h(1)%start_index(j,i) surf_e = surf_lsm_h(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_h(1)%k(m) tend(k,j,i) = tend(k,j,i) & + ( - surf_lsm_h(1)%vsws(m) ) * ddzw(k) * drho_air(k) ENDDO ! !-- Urban-type surfaces, upward-facing surf_s = surf_usm_h(0)%start_index(j,i) surf_e = surf_usm_h(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_h(0)%k(m) tend(k,j,i) = tend(k,j,i) & + ( - ( - surf_usm_h(0)%vsws(m) ) ) * ddzw(k) * drho_air(k) ENDDO ! !-- Urban-type surfaces, downward-facing surf_s = surf_usm_h(1)%start_index(j,i) surf_e = surf_usm_h(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_h(1)%k(m) tend(k,j,i) = tend(k,j,i) & + ( - surf_usm_h(1)%vsws(m) ) * ddzw(k) * drho_air(k) ENDDO ENDIF ! !-- Add momentum flux at model top IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN surf_s = surf_def_h(2)%start_index(j,i) surf_e = surf_def_h(2)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_h(2)%k(m) tend(k,j,i) = tend(k,j,i) & + ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k) ENDDO ENDIF ENDDO ENDDO END SUBROUTINE diffusion_v !--------------------------------------------------------------------------------------------------! ! Description: ! ------------ !> Call for grid point i,j !--------------------------------------------------------------------------------------------------! SUBROUTINE diffusion_v_ij( i, j ) USE arrays_3d, & ONLY: ddzu, ddzw, drho_air, km, tend, u, v, w, rho_air_zw USE control_parameters, & ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes USE grid_variables, & ONLY: ddx, ddy, ddy2 USE indices, & ONLY: nzb, nzt, topo_flags USE kinds USE surface_mod, & ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, surf_usm_v IMPLICIT NONE INTEGER(iwp) :: i !< running index x direction INTEGER(iwp) :: j !< running index y direction INTEGER(iwp) :: k !< running index z direction INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall INTEGER(iwp) :: m !< running index surface elements INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint REAL(wp) :: flag !< flag to mask topography grid points REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface ! !-- Compute horizontal diffusion DO k = nzb+1, nzt ! !-- Predetermine flag to mask topography and wall-bounded grid points. !-- It is sufficient to masked only east- and west-facing surfaces, which need special !-- treatment for the v-component. flag = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i), 2 ) ) mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i+1), 2 ) ) mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i-1), 2 ) ) ! !-- Interpolate eddy diffusivities on staggered gridpoints kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) tend(k,j,i) = tend(k,j,i) + ( & mask_east * kmxp * ( & ( v(k,j,i+1) - v(k,j,i) ) * ddx & + ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & ) & - mask_west * kmxm * ( & ( v(k,j,i) - v(k,j,i-1) ) * ddx & + ( u(k,j,i) - u(k,j-1,i) ) * ddy & ) & ) * ddx * flag & + 2.0_wp * ( & km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & ) * ddy2 * flag ENDDO ! !-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3) surfaces. Note, in the !-- the flat case, loops won't be entered as start_index > end_index. Furtermore, note, no !-- vertical natural surfaces so far. !-- Default-type surfaces DO l = 2, 3 surf_s = surf_def_v(l)%start_index(j,i) surf_e = surf_def_v(l)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_v(l)%k(m) tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx ENDDO ENDDO ! !-- Natural-type surfaces DO l = 2, 3 surf_s = surf_lsm_v(l)%start_index(j,i) surf_e = surf_lsm_v(l)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_v(l)%k(m) tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx ENDDO ENDDO ! !-- Urban-type surfaces DO l = 2, 3 surf_s = surf_usm_v(l)%start_index(j,i) surf_e = surf_usm_v(l)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_v(l)%k(m) tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx ENDDO ENDDO ! !-- Compute vertical diffusion. In case of simulating a surface layer, respective grid diffusive !-- fluxes are masked (flag 8) within this loop, and added further below, else, simple gradient !-- approach is applied. Model top is also mask if top-momentum flux is given. DO k = nzb+1, nzt ! !-- Determine flags to mask topography below and above. Flag 2 is used to mask topography in !-- general, while flag 10 implies also information about use_surface_fluxes. Flag 9 is used !-- to control momentum flux at model top. mask_bottom = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k-1,j,i), 8 ) ) mask_top = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k+1,j,i), 8 ) ) * & MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k+1,j,i), 9 ) ) flag = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i), 2 ) ) ! !-- Interpolate eddy diffusivities on staggered gridpoints kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) tend(k,j,i) = tend(k,j,i) & & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & & ) * rho_air_zw(k) * mask_top & & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & & ) * rho_air_zw(k-1) * mask_bottom & & ) * ddzw(k) * drho_air(k) * flag ENDDO ! !-- Vertical diffusion at the first grid point above the surface, if the momentum flux at the !-- bottom is given by the Prandtl law or if it is prescribed by the user. !-- Difference quotient of the momentum flux is not formed over half of the grid spacing !-- (2.0*ddzw(k)) any more, since the comparison with other (LES) models showed that the values !-- of the momentum flux becomes too large in this case. IF ( use_surface_fluxes ) THEN ! !-- Default-type surfaces, upward-facing surf_s = surf_def_h(0)%start_index(j,i) surf_e = surf_def_h(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_h(0)%k(m) tend(k,j,i) = tend(k,j,i) + ( - ( - surf_def_h(0)%vsws(m) ) ) * ddzw(k) * drho_air(k) ENDDO ! !-- Default-type surfaces, dowward-facing surf_s = surf_def_h(1)%start_index(j,i) surf_e = surf_def_h(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_h(1)%k(m) tend(k,j,i) = tend(k,j,i) + ( - surf_def_h(1)%vsws(m) ) * ddzw(k) * drho_air(k) ENDDO ! !-- Natural-type surfaces, upward-facing surf_s = surf_lsm_h(0)%start_index(j,i) surf_e = surf_lsm_h(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_h(0)%k(m) tend(k,j,i) = tend(k,j,i) + ( - ( - surf_lsm_h(0)%vsws(m) ) ) * ddzw(k) * drho_air(k) ENDDO ! !-- Natural-type surfaces, downward-facing surf_s = surf_lsm_h(1)%start_index(j,i) surf_e = surf_lsm_h(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_h(1)%k(m) tend(k,j,i) = tend(k,j,i) + ( - surf_lsm_h(1)%vsws(m) ) * ddzw(k) * drho_air(k) ENDDO ! !-- Urban-type surfaces, upward-facing surf_s = surf_usm_h(0)%start_index(j,i) surf_e = surf_usm_h(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_h(0)%k(m) tend(k,j,i) = tend(k,j,i) + ( - ( - surf_usm_h(0)%vsws(m) ) ) * ddzw(k) * drho_air(k) ENDDO ! !-- Urban-type surfaces, downward-facing surf_s = surf_usm_h(1)%start_index(j,i) surf_e = surf_usm_h(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_h(1)%k(m) tend(k,j,i) = tend(k,j,i) + ( - surf_usm_h(1)%vsws(m) ) * ddzw(k) * drho_air(k) ENDDO ENDIF ! !-- Add momentum flux at model top IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN surf_s = surf_def_h(2)%start_index(j,i) surf_e = surf_def_h(2)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_h(2)%k(m) tend(k,j,i) = tend(k,j,i) + ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k) ENDDO ENDIF END SUBROUTINE diffusion_v_ij END MODULE diffusion_v_mod