!> @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 1997-2018 Leibniz Universitaet Hannover !------------------------------------------------------------------------------! ! ! Current revisions: ! ----------------- ! ! ! Former revisions: ! ----------------- ! $Id: diffusion_v.f90 3547 2018-11-21 13:21:24Z knoop $ ! variables documented ! ! 3241 2018-09-12 15:02:00Z raasch ! unused variables removed ! ! 2718 2018-01-02 08:49:38Z maronga ! Corrected "Former revisions" section ! ! 2696 2017-12-14 17:12:51Z kanani ! Change in file header (GPL part) ! ! 2638 2017-11-23 12:44:23Z raasch ! bugfix for constant top momentumflux ! ! 2233 2017-05-30 18:08:54Z suehring ! ! 2232 2017-05-30 17:47:52Z suehring ! Adjustments to new topography and surface concept ! ! 2118 2017-01-17 16:38:49Z raasch ! OpenACC version of subroutine removed ! ! 2037 2016-10-26 11:15:40Z knoop ! Anelastic approximation implemented ! ! 2000 2016-08-20 18:09:15Z knoop ! Forced header and separation lines into 80 columns ! ! 1873 2016-04-18 14:50:06Z maronga ! Module renamed (removed _mod) ! ! 1850 2016-04-08 13:29:27Z maronga ! Module renamed ! ! 1740 2016-01-13 08:19:40Z raasch ! unnecessary calculations of kmzm and kmzp in wall bounded parts removed ! ! 1682 2015-10-07 23:56:08Z knoop ! Code annotations made doxygen readable ! ! 1340 2014-03-25 19:45:13Z kanani ! REAL constants defined as wp-kind ! ! 1320 2014-03-20 08:40:49Z raasch ! ONLY-attribute added to USE-statements, ! kind-parameters added to all INTEGER and REAL declaration statements, ! kinds are defined in new module kinds, ! revision history before 2012 removed, ! comment fields (!:) to be used for variable explanations added to ! all variable declaration statements ! ! 1257 2013-11-08 15:18:40Z raasch ! openacc loop and loop vector clauses removed, declare create moved after ! the FORTRAN declaration statement ! ! 1128 2013-04-12 06:19:32Z raasch ! loop index bounds in accelerator version replaced by i_left, i_right, j_south, ! j_north ! ! 1036 2012-10-22 13:43:42Z raasch ! code put under GPL (PALM 3.9) ! ! 1015 2012-09-27 09:23:24Z raasch ! accelerator version (*_acc) added ! ! 1001 2012-09-13 14:08:46Z raasch ! arrays comunicated by module instead of parameter list ! ! 978 2012-08-09 08:28:32Z fricke ! outflow damping layer removed ! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp ! ! Revision 1.1 1997/09/12 06:24:01 raasch ! Initial revision ! ! ! 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, km, tend, u, v, w, drho_air, 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: nxl, nxr, nyn, nysv, nzb, nzt, wall_flags_0 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 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( wall_flags_0(k,j,i), 2 ) ) mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) ) mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(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( wall_flags_0(k-1,j,i), 8 ) ) mask_top = MERGE( 1.0_wp, 0.0_wp, & BTEST( wall_flags_0(k+1,j,i), 8 ) ) * & MERGE( 1.0_wp, 0.0_wp, & BTEST( wall_flags_0(k+1,j,i), 9 ) ) flag = MERGE( 1.0_wp, 0.0_wp, & BTEST( wall_flags_0(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%start_index(j,i) surf_e = surf_lsm_h%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_h%k(m) tend(k,j,i) = tend(k,j,i) & + ( - ( - surf_lsm_h%vsws(m) ) & ) * ddzw(k) * drho_air(k) ENDDO ! !-- Urban-type surfaces, upward-facing surf_s = surf_usm_h%start_index(j,i) surf_e = surf_usm_h%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_h%k(m) tend(k,j,i) = tend(k,j,i) & + ( - ( - surf_usm_h%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, km, tend, u, v, w, drho_air, 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, wall_flags_0 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( wall_flags_0(k,j,i), 2 ) ) mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) ) mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(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( wall_flags_0(k-1,j,i), 8 ) ) mask_top = MERGE( 1.0_wp, 0.0_wp, & BTEST( wall_flags_0(k+1,j,i), 8 ) ) * & MERGE( 1.0_wp, 0.0_wp, & BTEST( wall_flags_0(k+1,j,i), 9 ) ) flag = MERGE( 1.0_wp, 0.0_wp, & BTEST( wall_flags_0(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%start_index(j,i) surf_e = surf_lsm_h%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_h%k(m) tend(k,j,i) = tend(k,j,i) & + ( - ( - surf_lsm_h%vsws(m) ) & ) * ddzw(k) * drho_air(k) ENDDO ! !-- Urban-type surfaces, upward-facing surf_s = surf_usm_h%start_index(j,i) surf_e = surf_usm_h%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_h%k(m) tend(k,j,i) = tend(k,j,i) & + ( - ( - surf_usm_h%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