MODULE diffusion_v_mod !------------------------------------------------------------------------------! ! Current revisions: ! ----------------- ! ! ! Former revisions: ! ----------------- ! $Id: diffusion_v.f90 484 2010-02-05 07:36:54Z maronga $ ! ! 366 2009-08-25 08:06:27Z raasch ! bc_lr replaced by bc_lr_cyc ! ! 106 2007-08-16 14:30:26Z raasch ! Momentumflux at top (vswst) included as boundary condition, ! j loop is starting from nysv (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, vynp 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 10:36:00 raasch ! nzb_2d replaced by nzb_v_outer in horizontal diffusion and by nzb_v_inner ! or nzb_diff_v, 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 06:24:01 raasch ! Initial revision ! ! ! Description: ! ------------ ! Diffusion term of the v-component !------------------------------------------------------------------------------! 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 !------------------------------------------------------------------------------! ! Call for all grid points !------------------------------------------------------------------------------! SUBROUTINE diffusion_v( ddzu, ddzw, km, km_damp_x, tend, u, v, vsws, & vswst, w ) USE control_parameters USE grid_variables USE indices IMPLICIT NONE INTEGER :: i, j, k REAL :: kmxm_x, kmxm_y, kmxp_x, kmxp_y, kmzm, kmzp REAL :: ddzu(1:nzt+1), ddzw(1:nzt+1), km_damp_x(nxl-1:nxr+1) REAL :: tend(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) REAL, DIMENSION(:,:), POINTER :: vsws, vswst REAL, DIMENSION(:,:,:), POINTER :: km, u, v, w REAL, 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, 1.0, 0.0, 0.0, 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_x = 0.25 * & ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) kmxm_x = 0.25 * & ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) kmxp_y = kmxp_x kmxm_y = kmxm_x ! !-- Increase diffusion at the outflow boundary in case of !-- non-cyclic lateral boundaries. Damping is only needed for !-- velocity components parallel to the outflow boundary in !-- the direction normal to the outflow boundary. IF ( .NOT. bc_lr_cyc ) THEN kmxp_x = MAX( kmxp_x, km_damp_x(i) ) kmxm_x = MAX( kmxm_x, km_damp_x(i) ) ENDIF tend(k,j,i) = tend(k,j,i) & & + ( kmxp_x * ( v(k,j,i+1) - v(k,j,i) ) * ddx & & + kmxp_y * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & & - kmxm_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx & & - kmxm_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy & & ) * ddx & & + 2.0 * ( & & 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 ) THEN DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i) kmxp_x = 0.25 * & ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) kmxm_x = 0.25 * & ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) kmxp_y = kmxp_x kmxm_y = kmxm_x ! !-- Increase diffusion at the outflow boundary in case of !-- non-cyclic lateral boundaries. Damping is only needed for !-- velocity components parallel to the outflow boundary in !-- the direction normal to the outflow boundary. IF ( .NOT. bc_lr_cyc ) THEN kmxp_x = MAX( kmxp_x, km_damp_x(i) ) kmxm_x = MAX( kmxm_x, km_damp_x(i) ) ENDIF tend(k,j,i) = tend(k,j,i) & + 2.0 * ( & 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_x * ( v(k,j,i+1) - v(k,j,i) ) * ddx & + kmxp_y * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & ) & - fxm(j,i) * ( & kmxm_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx & + kmxm_y * ( 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 * & ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) kmzm = 0.25 * & ( 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 & & ) & & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & & ) & & ) * 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_v_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-1,i)+km(k+1,j-1,i) ) kmzm = 0.25 * & ( 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 * ( w(k,j,i) - w(k,j-1,i) ) * ddy & & ) * ddzw(k) & & + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & & + vsws(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-1,i)+km(k+1,j-1,i) ) kmzm = 0.25 * & ( 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) & & - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & & ) * ddzw(k) & & + ( -vswst(j,i) & & - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & & ) * ddzw(k) ENDIF ENDDO ENDDO END SUBROUTINE diffusion_v !------------------------------------------------------------------------------! ! Call for grid point i,j !------------------------------------------------------------------------------! SUBROUTINE diffusion_v_ij( i, j, ddzu, ddzw, km, km_damp_x, tend, u, v, & vsws, vswst, w ) USE control_parameters USE grid_variables USE indices IMPLICIT NONE INTEGER :: i, j, k REAL :: kmxm_x, kmxm_y, kmxp_x, kmxp_y, kmzm, kmzp REAL :: ddzu(1:nzt+1), ddzw(1:nzt+1), km_damp_x(nxl-1:nxr+1) REAL :: tend(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) REAL, DIMENSION(nzb:nzt+1) :: vsus REAL, DIMENSION(:,:), POINTER :: vsws, vswst REAL, DIMENSION(:,:,:), POINTER :: km, u, v, w ! !-- Compute horizontal diffusion DO k = nzb_v_outer(j,i)+1, nzt ! !-- Interpolate eddy diffusivities on staggered gridpoints kmxp_x = 0.25 * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) kmxm_x = 0.25 * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) kmxp_y = kmxp_x kmxm_y = kmxm_x ! !-- Increase diffusion at the outflow boundary in case of non-cyclic !-- lateral boundaries. Damping is only needed for velocity components !-- parallel to the outflow boundary in the direction normal to the !-- outflow boundary. IF ( .NOT. bc_lr_cyc ) THEN kmxp_x = MAX( kmxp_x, km_damp_x(i) ) kmxm_x = MAX( kmxm_x, km_damp_x(i) ) ENDIF tend(k,j,i) = tend(k,j,i) & & + ( kmxp_x * ( v(k,j,i+1) - v(k,j,i) ) * ddx & & + kmxp_y * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & & - kmxm_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx & & - kmxm_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy & & ) * ddx & & + 2.0 * ( & & 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 ) 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, 1.0, 0.0, 0.0 ) DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i) kmxp_x = 0.25 * & ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) kmxm_x = 0.25 * & ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) kmxp_y = kmxp_x kmxm_y = kmxm_x ! !-- Increase diffusion at the outflow boundary in case of !-- non-cyclic lateral boundaries. Damping is only needed for !-- velocity components parallel to the outflow boundary in !-- the direction normal to the outflow boundary. IF ( .NOT. bc_lr_cyc ) THEN kmxp_x = MAX( kmxp_x, km_damp_x(i) ) kmxm_x = MAX( kmxm_x, km_damp_x(i) ) ENDIF tend(k,j,i) = tend(k,j,i) & + 2.0 * ( & 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_x * ( v(k,j,i+1) - v(k,j,i) ) * ddx & + kmxp_y * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & ) & - fxm(j,i) * ( & kmxm_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx & + kmxm_y * ( 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 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) kmzm = 0.25 * ( 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 & & ) & & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & & ) & & ) * 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_v_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-1,i)+km(k+1,j-1,i) ) kmzm = 0.25 * ( 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 * ( w(k,j,i) - w(k,j-1,i) ) * ddy & & ) * ddzw(k) & & + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & & + vsws(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-1,i)+km(k+1,j-1,i) ) kmzm = 0.25 * & ( 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) & & - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & & ) * ddzw(k) & & + ( -vswst(j,i) & & - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & & ) * ddzw(k) ENDIF END SUBROUTINE diffusion_v_ij END MODULE diffusion_v_mod