!> @file diffusion_v.f90 !------------------------------------------------------------------------------! ! This file is part of PALM. ! ! 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 1997-2017 Leibniz Universitaet Hannover !------------------------------------------------------------------------------! ! ! Current revisions: ! ----------------- ! ! ! Former revisions: ! ----------------- ! $Id: diffusion_v.f90 2119 2017-01-17 16:51:50Z suehring $ ! ! 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 USE wall_fluxes_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, vsws, vswst, w, & drho_air, rho_air_zw USE control_parameters, & ONLY: constant_top_momentumflux, topography, use_surface_fluxes, & use_top_fluxes USE grid_variables, & ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v USE indices, & ONLY: nxl, nxr, nyn, nys, nysv, nzb, nzb_diff_v, nzb_v_inner, & nzb_v_outer, nzt, nzt_diff USE kinds IMPLICIT NONE INTEGER(iwp) :: i !< INTEGER(iwp) :: j !< INTEGER(iwp) :: k !< REAL(wp) :: kmxm !< REAL(wp) :: kmxp !< REAL(wp) :: kmzm !< REAL(wp) :: kmzp !< REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus !< ! !-- First calculate horizontal momentum flux v'u' at vertical walls, !-- if neccessary IF ( topography /= 'flat' ) THEN CALL wall_fluxes( vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp, nzb_v_inner, & nzb_v_outer, wall_v ) ENDIF DO i = nxl, nxr DO j = nysv, nyn ! !-- Compute horizontal diffusion DO k = nzb_v_outer(j,i)+1, nzt ! !-- 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) & & + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & & + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & & - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & & - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & & ) * ddx & & + 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 ENDDO ! !-- Wall functions at the left and right walls, respectively IF ( wall_v(j,i) /= 0.0_wp ) THEN DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i) 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) & + 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 & + ( fxp(j,i) * ( & kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & ) & - fxm(j,i) * ( & kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & + kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & ) & + wall_v(j,i) * vsus(k,j,i) & ) * ddx ENDDO ENDIF ! !-- Compute vertical diffusion. In case of simulating a Prandtl !-- layer, index k starts at nzb_v_inner+2. DO k = nzb_diff_v(j,i), nzt_diff ! !-- 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) & & - 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) & & ) * ddzw(k) * drho_air(k) 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. !-- The term containing w(k-1,..) (see above equation) is removed here !-- because the vertical velocity is assumed to be zero at the surface. IF ( use_surface_fluxes ) THEN k = nzb_v_inner(j,i)+1 ! !-- 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) ) 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) & & - ( -vsws(j,i) ) & & ) * ddzw(k) * drho_air(k) ENDIF ! !-- Vertical diffusion at the first gridpoint below the top boundary, !-- if the momentum flux at the top is prescribed by the user IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN k = nzt ! !-- Interpolate eddy diffusivities on staggered gridpoints 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) & & + ( ( -vswst(j,i) ) & & - 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) & & ) * ddzw(k) * drho_air(k) 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, vsws, vswst, 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, fxm, fxp, wall_v USE indices, & ONLY: nzb, nzb_diff_v, nzb_v_inner, nzb_v_outer, nzt, nzt_diff USE kinds IMPLICIT NONE INTEGER(iwp) :: i !< INTEGER(iwp) :: j !< INTEGER(iwp) :: k !< REAL(wp) :: kmxm !< REAL(wp) :: kmxp !< REAL(wp) :: kmzm !< REAL(wp) :: kmzp !< REAL(wp), DIMENSION(nzb:nzt+1) :: vsus !< ! !-- Compute horizontal diffusion DO k = nzb_v_outer(j,i)+1, nzt ! !-- 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) & & + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & & + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & & - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & & - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & & ) * ddx & & + 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 ENDDO ! !-- Wall functions at the left and right walls, respectively IF ( wall_v(j,i) /= 0.0_wp ) THEN ! !-- Calculate the horizontal momentum flux v'u' CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), & vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp ) DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i) 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) & + 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 & + ( fxp(j,i) * ( & kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & ) & - fxm(j,i) * ( & kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & + kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & ) & + wall_v(j,i) * vsus(k) & ) * ddx ENDDO ENDIF ! !-- Compute vertical diffusion. In case of simulating a Prandtl layer, !-- index k starts at nzb_v_inner+2. DO k = nzb_diff_v(j,i), nzt_diff ! !-- 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) & & - 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) & & ) * ddzw(k) * drho_air(k) 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. !-- The term containing w(k-1,..) (see above equation) is removed here !-- because the vertical velocity is assumed to be zero at the surface. IF ( use_surface_fluxes ) THEN k = nzb_v_inner(j,i)+1 ! !-- 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) ) 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) & & - ( -vsws(j,i) ) & & ) * ddzw(k) * drho_air(k) ENDIF ! !-- Vertical diffusion at the first gridpoint below the top boundary, !-- if the momentum flux at the top is prescribed by the user IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN k = nzt ! !-- Interpolate eddy diffusivities on staggered gridpoints 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) & & + ( ( -vswst(j,i) ) & & - 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) & & ) * ddzw(k) * drho_air(k) ENDIF END SUBROUTINE diffusion_v_ij END MODULE diffusion_v_mod