| 1 | MODULE diffusion_v_mod |
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| 2 | |
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| 3 | !--------------------------------------------------------------------------------! |
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| 4 | ! This file is part of PALM. |
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| 5 | ! |
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| 6 | ! PALM is free software: you can redistribute it and/or modify it under the terms |
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| 7 | ! of the GNU General Public License as published by the Free Software Foundation, |
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| 8 | ! either version 3 of the License, or (at your option) any later version. |
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| 9 | ! |
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| 10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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| 11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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| 12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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| 13 | ! |
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| 14 | ! You should have received a copy of the GNU General Public License along with |
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| 15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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| 16 | ! |
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| 17 | ! Copyright 1997-2012 Leibniz University Hannover |
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| 18 | !--------------------------------------------------------------------------------! |
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| 19 | ! |
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| 20 | ! Current revisions: |
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| 21 | ! ----------------- |
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| 22 | ! |
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| 23 | ! |
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| 24 | ! Former revisions: |
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| 25 | ! ----------------- |
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| 26 | ! $Id: diffusion_v.f90 1037 2012-10-22 14:10:22Z hoffmann $ |
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| 27 | ! |
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| 28 | ! 1036 2012-10-22 13:43:42Z raasch |
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| 29 | ! code put under GPL (PALM 3.9) |
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| 30 | ! |
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| 31 | ! 1015 2012-09-27 09:23:24Z raasch |
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| 32 | ! accelerator version (*_acc) added |
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| 33 | ! |
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| 34 | ! 1001 2012-09-13 14:08:46Z raasch |
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| 35 | ! arrays comunicated by module instead of parameter list |
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| 36 | ! |
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| 37 | ! 978 2012-08-09 08:28:32Z fricke |
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| 38 | ! outflow damping layer removed |
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| 39 | ! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp |
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| 40 | ! |
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| 41 | ! 667 2010-12-23 12:06:00Z suehring/gryschka |
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| 42 | ! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng |
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| 43 | ! |
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| 44 | ! 366 2009-08-25 08:06:27Z raasch |
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| 45 | ! bc_lr replaced by bc_lr_cyc |
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| 46 | ! |
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| 47 | ! 106 2007-08-16 14:30:26Z raasch |
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| 48 | ! Momentumflux at top (vswst) included as boundary condition, |
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| 49 | ! j loop is starting from nysv (needed for non-cyclic boundary conditions) |
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| 50 | ! |
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| 51 | ! 75 2007-03-22 09:54:05Z raasch |
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| 52 | ! Wall functions now include diabatic conditions, call of routine wall_fluxes, |
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| 53 | ! z0 removed from argument list, vynp eliminated |
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| 54 | ! |
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| 55 | ! 20 2007-02-26 00:12:32Z raasch |
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| 56 | ! Bugfix: ddzw dimensioned 1:nzt"+1" |
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| 57 | ! |
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| 58 | ! RCS Log replace by Id keyword, revision history cleaned up |
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| 59 | ! |
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| 60 | ! Revision 1.15 2006/02/23 10:36:00 raasch |
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| 61 | ! nzb_2d replaced by nzb_v_outer in horizontal diffusion and by nzb_v_inner |
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| 62 | ! or nzb_diff_v, respectively, in vertical diffusion, |
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| 63 | ! wall functions added for north and south walls, +z0 in argument list, |
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| 64 | ! terms containing w(k-1,..) are removed from the Prandtl-layer equation |
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| 65 | ! because they cause errors at the edges of topography |
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| 66 | ! WARNING: loops containing the MAX function are still not properly vectorized! |
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| 67 | ! |
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| 68 | ! Revision 1.1 1997/09/12 06:24:01 raasch |
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| 69 | ! Initial revision |
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| 70 | ! |
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| 71 | ! |
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| 72 | ! Description: |
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| 73 | ! ------------ |
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| 74 | ! Diffusion term of the v-component |
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| 75 | !------------------------------------------------------------------------------! |
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| 76 | |
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| 77 | USE wall_fluxes_mod |
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| 78 | |
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| 79 | PRIVATE |
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| 80 | PUBLIC diffusion_v, diffusion_v_acc |
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| 81 | |
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| 82 | INTERFACE diffusion_v |
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| 83 | MODULE PROCEDURE diffusion_v |
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| 84 | MODULE PROCEDURE diffusion_v_ij |
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| 85 | END INTERFACE diffusion_v |
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| 86 | |
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| 87 | INTERFACE diffusion_v_acc |
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| 88 | MODULE PROCEDURE diffusion_v_acc |
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| 89 | END INTERFACE diffusion_v_acc |
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| 90 | |
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| 91 | CONTAINS |
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| 92 | |
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| 93 | |
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| 94 | !------------------------------------------------------------------------------! |
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| 95 | ! Call for all grid points |
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| 96 | !------------------------------------------------------------------------------! |
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| 97 | SUBROUTINE diffusion_v |
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| 98 | |
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| 99 | USE arrays_3d |
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| 100 | USE control_parameters |
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| 101 | USE grid_variables |
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| 102 | USE indices |
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| 103 | |
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| 104 | IMPLICIT NONE |
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| 105 | |
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| 106 | INTEGER :: i, j, k |
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| 107 | REAL :: kmxm, kmxp, kmzm, kmzp |
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| 108 | |
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| 109 | REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus |
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| 110 | |
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| 111 | ! |
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| 112 | !-- First calculate horizontal momentum flux v'u' at vertical walls, |
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| 113 | !-- if neccessary |
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| 114 | IF ( topography /= 'flat' ) THEN |
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| 115 | CALL wall_fluxes( vsus, 0.0, 1.0, 0.0, 0.0, nzb_v_inner, & |
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| 116 | nzb_v_outer, wall_v ) |
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| 117 | ENDIF |
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| 118 | |
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| 119 | DO i = nxl, nxr |
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| 120 | DO j = nysv, nyn |
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| 121 | ! |
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| 122 | !-- Compute horizontal diffusion |
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| 123 | DO k = nzb_v_outer(j,i)+1, nzt |
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| 124 | ! |
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| 125 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 126 | kmxp = 0.25 * & |
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| 127 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 128 | kmxm = 0.25 * & |
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| 129 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 130 | |
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| 131 | tend(k,j,i) = tend(k,j,i) & |
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| 132 | & + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 133 | & + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 134 | & - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 135 | & - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 136 | & ) * ddx & |
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| 137 | & + 2.0 * ( & |
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| 138 | & km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 139 | & - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 140 | & ) * ddy2 |
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| 141 | ENDDO |
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| 142 | |
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| 143 | ! |
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| 144 | !-- Wall functions at the left and right walls, respectively |
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| 145 | IF ( wall_v(j,i) /= 0.0 ) THEN |
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| 146 | |
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| 147 | DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i) |
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| 148 | kmxp = 0.25 * & |
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| 149 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 150 | kmxm = 0.25 * & |
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| 151 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 152 | |
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| 153 | tend(k,j,i) = tend(k,j,i) & |
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| 154 | + 2.0 * ( & |
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| 155 | km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 156 | - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 157 | ) * ddy2 & |
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| 158 | + ( fxp(j,i) * ( & |
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| 159 | kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 160 | + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 161 | ) & |
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| 162 | - fxm(j,i) * ( & |
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| 163 | kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 164 | + kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 165 | ) & |
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| 166 | + wall_v(j,i) * vsus(k,j,i) & |
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| 167 | ) * ddx |
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| 168 | ENDDO |
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| 169 | ENDIF |
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| 170 | |
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| 171 | ! |
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| 172 | !-- Compute vertical diffusion. In case of simulating a Prandtl |
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| 173 | !-- layer, index k starts at nzb_v_inner+2. |
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| 174 | DO k = nzb_diff_v(j,i), nzt_diff |
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| 175 | ! |
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| 176 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 177 | kmzp = 0.25 * & |
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| 178 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 179 | kmzm = 0.25 * & |
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| 180 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 181 | |
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| 182 | tend(k,j,i) = tend(k,j,i) & |
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| 183 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 184 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 185 | & ) & |
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| 186 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 187 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 188 | & ) & |
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| 189 | & ) * ddzw(k) |
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| 190 | ENDDO |
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| 191 | |
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| 192 | ! |
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| 193 | !-- Vertical diffusion at the first grid point above the surface, |
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| 194 | !-- if the momentum flux at the bottom is given by the Prandtl law |
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| 195 | !-- or if it is prescribed by the user. |
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| 196 | !-- Difference quotient of the momentum flux is not formed over |
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| 197 | !-- half of the grid spacing (2.0*ddzw(k)) any more, since the |
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| 198 | !-- comparison with other (LES) modell showed that the values of |
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| 199 | !-- the momentum flux becomes too large in this case. |
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| 200 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 201 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 202 | IF ( use_surface_fluxes ) THEN |
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| 203 | k = nzb_v_inner(j,i)+1 |
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| 204 | ! |
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| 205 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 206 | kmzp = 0.25 * & |
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| 207 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 208 | kmzm = 0.25 * & |
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| 209 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 210 | |
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| 211 | tend(k,j,i) = tend(k,j,i) & |
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| 212 | & + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 213 | & ) * ddzw(k) & |
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| 214 | & + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 215 | & + vsws(j,i) & |
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| 216 | & ) * ddzw(k) |
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| 217 | ENDIF |
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| 218 | |
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| 219 | ! |
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| 220 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
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| 221 | !-- if the momentum flux at the top is prescribed by the user |
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| 222 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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| 223 | k = nzt |
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| 224 | ! |
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| 225 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 226 | kmzp = 0.25 * & |
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| 227 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 228 | kmzm = 0.25 * & |
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| 229 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 230 | |
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| 231 | tend(k,j,i) = tend(k,j,i) & |
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| 232 | & - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 233 | & ) * ddzw(k) & |
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| 234 | & + ( -vswst(j,i) & |
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| 235 | & - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 236 | & ) * ddzw(k) |
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| 237 | ENDIF |
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| 238 | |
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| 239 | ENDDO |
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| 240 | ENDDO |
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| 241 | |
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| 242 | END SUBROUTINE diffusion_v |
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| 243 | |
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| 244 | |
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| 245 | !------------------------------------------------------------------------------! |
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| 246 | ! Call for all grid points - accelerator version |
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| 247 | !------------------------------------------------------------------------------! |
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| 248 | SUBROUTINE diffusion_v_acc |
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| 249 | |
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| 250 | USE arrays_3d |
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| 251 | USE control_parameters |
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| 252 | USE grid_variables |
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| 253 | USE indices |
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| 254 | |
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| 255 | IMPLICIT NONE |
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| 256 | |
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| 257 | INTEGER :: i, j, k |
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| 258 | REAL :: kmxm, kmxp, kmzm, kmzp |
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| 259 | |
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| 260 | !$acc declare create ( vsus ) |
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| 261 | REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus |
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| 262 | |
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| 263 | ! |
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| 264 | !-- First calculate horizontal momentum flux v'u' at vertical walls, |
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| 265 | !-- if neccessary |
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| 266 | IF ( topography /= 'flat' ) THEN |
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| 267 | CALL wall_fluxes_acc( vsus, 0.0, 1.0, 0.0, 0.0, nzb_v_inner, & |
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| 268 | nzb_v_outer, wall_v ) |
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| 269 | ENDIF |
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| 270 | |
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| 271 | !$acc kernels present ( u, v, w, km, tend, vsws, vswst ) & |
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| 272 | !$acc present ( ddzu, ddzw, fxm, fxp, wall_v ) & |
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| 273 | !$acc present ( nzb_v_inner, nzb_v_outer, nzb_diff_v ) |
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| 274 | !$acc loop |
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| 275 | DO i = nxl, nxr |
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| 276 | DO j = nysv, nyn |
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| 277 | ! |
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| 278 | !-- Compute horizontal diffusion |
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| 279 | !$acc loop vector(32) |
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| 280 | DO k = 1, nzt |
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| 281 | IF ( k > nzb_v_outer(j,i) ) THEN |
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| 282 | ! |
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| 283 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 284 | kmxp = 0.25 * & |
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| 285 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 286 | kmxm = 0.25 * & |
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| 287 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 288 | |
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| 289 | tend(k,j,i) = tend(k,j,i) & |
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| 290 | & + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 291 | & + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 292 | & - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 293 | & - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 294 | & ) * ddx & |
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| 295 | & + 2.0 * ( & |
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| 296 | & km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 297 | & - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 298 | & ) * ddy2 |
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| 299 | ENDIF |
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| 300 | ENDDO |
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| 301 | |
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| 302 | ! |
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| 303 | !-- Wall functions at the left and right walls, respectively |
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| 304 | !$acc loop vector(32) |
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| 305 | DO k = 1, nzt |
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| 306 | IF( k > nzb_v_inner(j,i) .AND. k <= nzb_v_outer(j,i) .AND. & |
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| 307 | wall_v(j,i) /= 0.0 ) THEN |
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| 308 | |
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| 309 | kmxp = 0.25 * & |
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| 310 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 311 | kmxm = 0.25 * & |
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| 312 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 313 | |
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| 314 | tend(k,j,i) = tend(k,j,i) & |
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| 315 | + 2.0 * ( & |
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| 316 | km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 317 | - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 318 | ) * ddy2 & |
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| 319 | + ( fxp(j,i) * ( & |
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| 320 | kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 321 | + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 322 | ) & |
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| 323 | - fxm(j,i) * ( & |
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| 324 | kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 325 | + kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 326 | ) & |
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| 327 | + wall_v(j,i) * vsus(k,j,i) & |
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| 328 | ) * ddx |
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| 329 | ENDIF |
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| 330 | ENDDO |
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| 331 | |
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| 332 | ! |
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| 333 | !-- Compute vertical diffusion. In case of simulating a Prandtl |
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| 334 | !-- layer, index k starts at nzb_v_inner+2. |
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| 335 | !$acc loop vector(32) |
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| 336 | DO k = 1, nzt_diff |
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| 337 | IF ( k >= nzb_diff_v(j,i) ) THEN |
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| 338 | ! |
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| 339 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 340 | kmzp = 0.25 * & |
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| 341 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 342 | kmzm = 0.25 * & |
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| 343 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 344 | |
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| 345 | tend(k,j,i) = tend(k,j,i) & |
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| 346 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1)& |
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| 347 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 348 | & ) & |
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| 349 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k)& |
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| 350 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 351 | & ) & |
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| 352 | & ) * ddzw(k) |
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| 353 | ENDIF |
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| 354 | ENDDO |
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| 355 | |
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| 356 | ENDDO |
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| 357 | ENDDO |
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| 358 | |
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| 359 | ! |
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| 360 | !-- Vertical diffusion at the first grid point above the surface, |
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| 361 | !-- if the momentum flux at the bottom is given by the Prandtl law |
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| 362 | !-- or if it is prescribed by the user. |
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| 363 | !-- Difference quotient of the momentum flux is not formed over |
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| 364 | !-- half of the grid spacing (2.0*ddzw(k)) any more, since the |
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| 365 | !-- comparison with other (LES) modell showed that the values of |
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| 366 | !-- the momentum flux becomes too large in this case. |
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| 367 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 368 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 369 | IF ( use_surface_fluxes ) THEN |
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| 370 | |
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| 371 | !$acc loop |
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| 372 | DO i = nxl, nxr |
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| 373 | !$acc loop vector(32) |
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| 374 | DO j = nysv, nyn |
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| 375 | |
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| 376 | k = nzb_v_inner(j,i)+1 |
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| 377 | ! |
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| 378 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 379 | kmzp = 0.25 * & |
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| 380 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 381 | kmzm = 0.25 * & |
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| 382 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 383 | |
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| 384 | tend(k,j,i) = tend(k,j,i) & |
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| 385 | & + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 386 | & ) * ddzw(k) & |
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| 387 | & + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 388 | & + vsws(j,i) & |
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| 389 | & ) * ddzw(k) |
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| 390 | ENDDO |
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| 391 | ENDDO |
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| 392 | |
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| 393 | ENDIF |
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| 394 | |
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| 395 | ! |
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| 396 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
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| 397 | !-- if the momentum flux at the top is prescribed by the user |
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| 398 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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| 399 | |
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| 400 | k = nzt |
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| 401 | |
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| 402 | !$acc loop |
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| 403 | DO i = nxl, nxr |
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| 404 | !$acc loop vector(32) |
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| 405 | DO j = nysv, nyn |
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| 406 | |
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| 407 | ! |
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| 408 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 409 | kmzp = 0.25 * & |
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| 410 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 411 | kmzm = 0.25 * & |
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| 412 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 413 | |
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| 414 | tend(k,j,i) = tend(k,j,i) & |
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| 415 | & - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 416 | & ) * ddzw(k) & |
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| 417 | & + ( -vswst(j,i) & |
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| 418 | & - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 419 | & ) * ddzw(k) |
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| 420 | ENDDO |
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| 421 | ENDDO |
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| 422 | |
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| 423 | ENDIF |
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| 424 | !$acc end kernels |
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| 425 | |
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| 426 | END SUBROUTINE diffusion_v_acc |
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| 427 | |
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| 428 | |
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| 429 | !------------------------------------------------------------------------------! |
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| 430 | ! Call for grid point i,j |
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| 431 | !------------------------------------------------------------------------------! |
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| 432 | SUBROUTINE diffusion_v_ij( i, j ) |
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| 433 | |
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| 434 | USE arrays_3d |
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| 435 | USE control_parameters |
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| 436 | USE grid_variables |
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| 437 | USE indices |
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| 438 | |
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| 439 | IMPLICIT NONE |
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| 440 | |
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| 441 | INTEGER :: i, j, k |
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| 442 | REAL :: kmxm, kmxp, kmzm, kmzp |
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| 443 | |
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| 444 | REAL, DIMENSION(nzb:nzt+1) :: vsus |
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| 445 | |
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| 446 | ! |
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| 447 | !-- Compute horizontal diffusion |
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| 448 | DO k = nzb_v_outer(j,i)+1, nzt |
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| 449 | ! |
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| 450 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 451 | kmxp = 0.25 * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 452 | kmxm = 0.25 * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 453 | |
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| 454 | tend(k,j,i) = tend(k,j,i) & |
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| 455 | & + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 456 | & + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 457 | & - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 458 | & - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 459 | & ) * ddx & |
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| 460 | & + 2.0 * ( & |
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| 461 | & km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 462 | & - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 463 | & ) * ddy2 |
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| 464 | ENDDO |
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| 465 | |
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| 466 | ! |
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| 467 | !-- Wall functions at the left and right walls, respectively |
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| 468 | IF ( wall_v(j,i) /= 0.0 ) THEN |
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| 469 | |
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| 470 | ! |
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| 471 | !-- Calculate the horizontal momentum flux v'u' |
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| 472 | CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), & |
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| 473 | vsus, 0.0, 1.0, 0.0, 0.0 ) |
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| 474 | |
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| 475 | DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i) |
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| 476 | kmxp = 0.25 * & |
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| 477 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 478 | kmxm = 0.25 * & |
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| 479 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 480 | |
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| 481 | tend(k,j,i) = tend(k,j,i) & |
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| 482 | + 2.0 * ( & |
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| 483 | km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 484 | - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 485 | ) * ddy2 & |
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| 486 | + ( fxp(j,i) * ( & |
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| 487 | kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 488 | + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 489 | ) & |
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| 490 | - fxm(j,i) * ( & |
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| 491 | kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 492 | + kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 493 | ) & |
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| 494 | + wall_v(j,i) * vsus(k) & |
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| 495 | ) * ddx |
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| 496 | ENDDO |
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| 497 | ENDIF |
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| 498 | |
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| 499 | ! |
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| 500 | !-- Compute vertical diffusion. In case of simulating a Prandtl layer, |
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| 501 | !-- index k starts at nzb_v_inner+2. |
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| 502 | DO k = nzb_diff_v(j,i), nzt_diff |
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| 503 | ! |
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| 504 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 505 | kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 506 | kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 507 | |
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| 508 | tend(k,j,i) = tend(k,j,i) & |
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| 509 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 510 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 511 | & ) & |
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| 512 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 513 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 514 | & ) & |
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| 515 | & ) * ddzw(k) |
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| 516 | ENDDO |
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| 517 | |
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| 518 | ! |
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| 519 | !-- Vertical diffusion at the first grid point above the surface, if the |
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| 520 | !-- momentum flux at the bottom is given by the Prandtl law or if it is |
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| 521 | !-- prescribed by the user. |
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| 522 | !-- Difference quotient of the momentum flux is not formed over half of |
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| 523 | !-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with |
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| 524 | !-- other (LES) modell showed that the values of the momentum flux becomes |
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| 525 | !-- too large in this case. |
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| 526 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 527 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 528 | IF ( use_surface_fluxes ) THEN |
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| 529 | k = nzb_v_inner(j,i)+1 |
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| 530 | ! |
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| 531 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 532 | kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 533 | kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 534 | |
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| 535 | tend(k,j,i) = tend(k,j,i) & |
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| 536 | & + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 537 | & ) * ddzw(k) & |
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| 538 | & + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 539 | & + vsws(j,i) & |
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| 540 | & ) * ddzw(k) |
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| 541 | ENDIF |
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| 542 | |
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| 543 | ! |
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| 544 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
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| 545 | !-- if the momentum flux at the top is prescribed by the user |
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| 546 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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| 547 | k = nzt |
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| 548 | ! |
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| 549 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 550 | kmzp = 0.25 * & |
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| 551 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 552 | kmzm = 0.25 * & |
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| 553 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 554 | |
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| 555 | tend(k,j,i) = tend(k,j,i) & |
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| 556 | & - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 557 | & ) * ddzw(k) & |
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| 558 | & + ( -vswst(j,i) & |
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| 559 | & - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 560 | & ) * ddzw(k) |
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| 561 | ENDIF |
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| 562 | |
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| 563 | END SUBROUTINE diffusion_v_ij |
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| 564 | |
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| 565 | END MODULE diffusion_v_mod |
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