MODULE diffusion_u_mod !--------------------------------------------------------------------------------! ! 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 1997-2012 Leibniz University Hannover !--------------------------------------------------------------------------------! ! ! Current revisions: ! ----------------- ! ! ! Former revisions: ! ----------------- ! $Id: diffusion_u.f90 1132 2013-04-12 14:35:30Z hoffmann $ ! ! 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 ! kmym_x/_y and kmyp_x/_y change to kmym and kmyp ! ! 667 2010-12-23 12:06:00Z suehring/gryschka ! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng ! ! 366 2009-08-25 08:06:27Z raasch ! bc_ns replaced by bc_ns_cyc ! ! 106 2007-08-16 14:30:26Z raasch ! Momentumflux at top (uswst) included as boundary condition, ! i loop is starting from nxlu (needed for non-cyclic boundary conditions) ! ! 75 2007-03-22 09:54:05Z raasch ! Wall functions now include diabatic conditions, call of routine wall_fluxes, ! z0 removed from argument list, uxrp eliminated ! ! 20 2007-02-26 00:12:32Z raasch ! Bugfix: ddzw dimensioned 1:nzt"+1" ! ! RCS Log replace by Id keyword, revision history cleaned up ! ! Revision 1.15 2006/02/23 10:35:35 raasch ! nzb_2d replaced by nzb_u_outer in horizontal diffusion and by nzb_u_inner ! or nzb_diff_u, respectively, in vertical diffusion, ! wall functions added for north and south walls, +z0 in argument list, ! terms containing w(k-1,..) are removed from the Prandtl-layer equation ! because they cause errors at the edges of topography ! WARNING: loops containing the MAX function are still not properly vectorized! ! ! Revision 1.1 1997/09/12 06:23:51 raasch ! Initial revision ! ! ! Description: ! ------------ ! Diffusion term of the u-component ! To do: additional damping (needed for non-cyclic bc) causes bad vectorization ! and slows down the speed on NEC about 5-10% !------------------------------------------------------------------------------! USE wall_fluxes_mod PRIVATE PUBLIC diffusion_u, diffusion_u_acc INTERFACE diffusion_u MODULE PROCEDURE diffusion_u MODULE PROCEDURE diffusion_u_ij END INTERFACE diffusion_u INTERFACE diffusion_u_acc MODULE PROCEDURE diffusion_u_acc END INTERFACE diffusion_u_acc CONTAINS !------------------------------------------------------------------------------! ! Call for all grid points !------------------------------------------------------------------------------! SUBROUTINE diffusion_u USE arrays_3d USE control_parameters USE grid_variables USE indices IMPLICIT NONE INTEGER :: i, j, k REAL :: kmym, kmyp, kmzm, kmzp REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs ! !-- First calculate horizontal momentum flux u'v' at vertical walls, !-- if neccessary IF ( topography /= 'flat' ) THEN CALL wall_fluxes( usvs, 1.0, 0.0, 0.0, 0.0, nzb_u_inner, & nzb_u_outer, wall_u ) ENDIF DO i = nxlu, nxr DO j = nys, nyn ! !-- Compute horizontal diffusion DO k = nzb_u_outer(j,i)+1, nzt ! !-- Interpolate eddy diffusivities on staggered gridpoints kmyp = 0.25 * & ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) kmym = 0.25 * & ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) tend(k,j,i) = tend(k,j,i) & & + 2.0 * ( & & km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & & - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & & ) * ddx2 & & + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & & + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & & - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & & - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & & ) * ddy ENDDO ! !-- Wall functions at the north and south walls, respectively IF ( wall_u(j,i) /= 0.0 ) THEN DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i) kmyp = 0.25 * & ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) kmym = 0.25 * & ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) tend(k,j,i) = tend(k,j,i) & + 2.0 * ( & km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & ) * ddx2 & + ( fyp(j,i) * ( & kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & ) & - fym(j,i) * ( & kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & + kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & ) & + wall_u(j,i) * usvs(k,j,i) & ) * ddy ENDDO ENDIF ! !-- Compute vertical diffusion. In case of simulating a Prandtl layer, !-- index k starts at nzb_u_inner+2. DO k = nzb_diff_u(j,i), nzt_diff ! !-- Interpolate eddy diffusivities on staggered gridpoints kmzp = 0.25 * & ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) kmzm = 0.25 * & ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) tend(k,j,i) = tend(k,j,i) & & + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & & + ( w(k,j,i) - w(k,j,i-1) ) * ddx & & ) & & - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & & + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & & ) & & ) * ddzw(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) modell 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_u_inner(j,i)+1 ! !-- Interpolate eddy diffusivities on staggered gridpoints kmzp = 0.25 * & ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) kmzm = 0.25 * & ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) tend(k,j,i) = tend(k,j,i) & & + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx & & ) * ddzw(k) & & + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & & + usws(j,i) & & ) * ddzw(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 kmzp = 0.25 * & ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) kmzm = 0.25 * & ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) tend(k,j,i) = tend(k,j,i) & & - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & & ) * ddzw(k) & & + ( -uswst(j,i) & & - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & & ) * ddzw(k) ENDIF ENDDO ENDDO END SUBROUTINE diffusion_u !------------------------------------------------------------------------------! ! Call for all grid points - accelerator version !------------------------------------------------------------------------------! SUBROUTINE diffusion_u_acc USE arrays_3d USE control_parameters USE grid_variables USE indices IMPLICIT NONE INTEGER :: i, j, k REAL :: kmym, kmyp, kmzm, kmzp !$acc declare create ( usvs ) REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs ! !-- First calculate horizontal momentum flux u'v' at vertical walls, !-- if neccessary IF ( topography /= 'flat' ) THEN CALL wall_fluxes_acc( usvs, 1.0, 0.0, 0.0, 0.0, nzb_u_inner, & nzb_u_outer, wall_u ) ENDIF !$acc kernels present ( u, v, w, km, tend, usws, uswst ) & !$acc present ( ddzu, ddzw, fym, fyp, wall_u ) & !$acc present ( nzb_u_inner, nzb_u_outer, nzb_diff_u ) !$acc loop DO i = i_left, i_right DO j = j_south, j_north ! !-- Compute horizontal diffusion !$acc loop vector(32) DO k = 1, nzt IF ( k > nzb_u_outer(j,i) ) THEN ! !-- Interpolate eddy diffusivities on staggered gridpoints kmyp = 0.25 * & ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) kmym = 0.25 * & ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) tend(k,j,i) = tend(k,j,i) & & + 2.0 * ( & & km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & & - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & & ) * ddx2 & & + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & & + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & & - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & & - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & & ) * ddy ENDIF ENDDO ! !-- Wall functions at the north and south walls, respectively !$acc loop vector(32) DO k = 1, nzt IF( k > nzb_u_inner(j,i) .AND. k <= nzb_u_outer(j,i) .AND. & wall_u(j,i) /= 0.0 ) THEN kmyp = 0.25 * & ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) kmym = 0.25 * & ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) tend(k,j,i) = tend(k,j,i) & + 2.0 * ( & km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & ) * ddx2 & + ( fyp(j,i) * ( & kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & ) & - fym(j,i) * ( & kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & + kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & ) & + wall_u(j,i) * usvs(k,j,i) & ) * ddy ENDIF ENDDO ! !-- Compute vertical diffusion. In case of simulating a Prandtl layer, !-- index k starts at nzb_u_inner+2. !$acc loop vector(32) DO k = 1, nzt_diff IF ( k >= nzb_diff_u(j,i) ) THEN ! !-- Interpolate eddy diffusivities on staggered gridpoints kmzp = 0.25 * & ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) kmzm = 0.25 * & ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) tend(k,j,i) = tend(k,j,i) & & + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1)& & + ( w(k,j,i) - w(k,j,i-1) ) * ddx & & ) & & - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k)& & + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & & ) & & ) * ddzw(k) ENDIF ENDDO ENDDO 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) modell 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 !$acc loop DO i = i_left, i_right !$acc loop vector(32) DO j = j_south, j_north k = nzb_u_inner(j,i)+1 ! !-- Interpolate eddy diffusivities on staggered gridpoints kmzp = 0.25 * & ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) kmzm = 0.25 * & ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) tend(k,j,i) = tend(k,j,i) & & + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx & & ) * ddzw(k) & & + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & & + usws(j,i) & & ) * ddzw(k) ENDDO ENDDO 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 !$acc loop DO i = i_left, i_right !$acc loop vector(32) DO j = j_south, j_north ! !-- Interpolate eddy diffusivities on staggered gridpoints kmzp = 0.25 * & ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) kmzm = 0.25 * & ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) tend(k,j,i) = tend(k,j,i) & & - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & & ) * ddzw(k) & & + ( -uswst(j,i) & & - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & & ) * ddzw(k) ENDDO ENDDO ENDIF !$acc end kernels END SUBROUTINE diffusion_u_acc !------------------------------------------------------------------------------! ! Call for grid point i,j !------------------------------------------------------------------------------! SUBROUTINE diffusion_u_ij( i, j ) USE arrays_3d USE control_parameters USE grid_variables USE indices IMPLICIT NONE INTEGER :: i, j, k REAL :: kmym, kmyp, kmzm, kmzp REAL, DIMENSION(nzb:nzt+1) :: usvs ! !-- Compute horizontal diffusion DO k = nzb_u_outer(j,i)+1, nzt ! !-- Interpolate eddy diffusivities on staggered gridpoints kmyp = 0.25 * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) kmym = 0.25 * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) tend(k,j,i) = tend(k,j,i) & & + 2.0 * ( & & km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & & - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & & ) * ddx2 & & + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & & + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & & - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & & - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & & ) * ddy ENDDO ! !-- Wall functions at the north and south walls, respectively IF ( wall_u(j,i) .NE. 0.0 ) THEN ! !-- Calculate the horizontal momentum flux u'v' CALL wall_fluxes( i, j, nzb_u_inner(j,i)+1, nzb_u_outer(j,i), & usvs, 1.0, 0.0, 0.0, 0.0 ) DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i) kmyp = 0.25 * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) kmym = 0.25 * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) tend(k,j,i) = tend(k,j,i) & + 2.0 * ( & km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & ) * ddx2 & + ( fyp(j,i) * ( & kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & ) & - fym(j,i) * ( & kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & + kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & ) & + wall_u(j,i) * usvs(k) & ) * ddy ENDDO ENDIF ! !-- Compute vertical diffusion. In case of simulating a Prandtl layer, !-- index k starts at nzb_u_inner+2. DO k = nzb_diff_u(j,i), nzt_diff ! !-- Interpolate eddy diffusivities on staggered gridpoints kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) tend(k,j,i) = tend(k,j,i) & & + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & & + ( w(k,j,i) - w(k,j,i-1) ) * ddx & & ) & & - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & & + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & & ) & & ) * ddzw(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) modell 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_u_inner(j,i)+1 ! !-- Interpolate eddy diffusivities on staggered gridpoints kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) tend(k,j,i) = tend(k,j,i) & & + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx & & ) * ddzw(k) & & + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & & + usws(j,i) & & ) * ddzw(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 kmzp = 0.25 * & ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) kmzm = 0.25 * & ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) tend(k,j,i) = tend(k,j,i) & & - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & & ) * ddzw(k) & & + ( -uswst(j,i) & & - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & & ) * ddzw(k) ENDIF END SUBROUTINE diffusion_u_ij END MODULE diffusion_u_mod