| 1 | !> @file diffusion_u.f90 |
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| 2 | !------------------------------------------------------------------------------! |
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| 3 | ! This file is part of PALM. |
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| 4 | ! |
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| 5 | ! PALM is free software: you can redistribute it and/or modify it under the |
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| 6 | ! terms of the GNU General Public License as published by the Free Software |
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| 7 | ! Foundation, either version 3 of the License, or (at your option) any later |
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| 8 | ! 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 1997-2017 Leibniz Universitaet 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_u.f90 2101 2017-01-05 16:42:31Z knoop $ |
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| 27 | ! |
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| 28 | ! 2037 2016-10-26 11:15:40Z knoop |
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| 29 | ! Anelastic approximation implemented |
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| 30 | ! |
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| 31 | ! 2000 2016-08-20 18:09:15Z knoop |
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| 32 | ! Forced header and separation lines into 80 columns |
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| 33 | ! |
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| 34 | ! 1873 2016-04-18 14:50:06Z maronga |
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| 35 | ! Module renamed (removed _mod) |
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| 36 | ! |
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| 37 | ! |
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| 38 | ! 1850 2016-04-08 13:29:27Z maronga |
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| 39 | ! Module renamed |
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| 40 | ! |
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| 41 | ! |
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| 42 | ! 1740 2016-01-13 08:19:40Z raasch |
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| 43 | ! unnecessary calculations of kmzm and kmzp in wall bounded parts removed |
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| 44 | ! |
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| 45 | ! 1691 2015-10-26 16:17:44Z maronga |
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| 46 | ! Formatting corrections. |
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| 47 | ! |
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| 48 | ! 1682 2015-10-07 23:56:08Z knoop |
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| 49 | ! Code annotations made doxygen readable |
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| 50 | ! |
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| 51 | ! 1340 2014-03-25 19:45:13Z kanani |
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| 52 | ! REAL constants defined as wp-kind |
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| 53 | ! |
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| 54 | ! 1320 2014-03-20 08:40:49Z raasch |
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| 55 | ! ONLY-attribute added to USE-statements, |
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| 56 | ! kind-parameters added to all INTEGER and REAL declaration statements, |
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| 57 | ! kinds are defined in new module kinds, |
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| 58 | ! revision history before 2012 removed, |
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| 59 | ! comment fields (!:) to be used for variable explanations added to |
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| 60 | ! all variable declaration statements |
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| 61 | ! |
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| 62 | ! 1257 2013-11-08 15:18:40Z raasch |
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| 63 | ! openacc loop and loop vector clauses removed, declare create moved after |
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| 64 | ! the FORTRAN declaration statement |
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| 65 | ! |
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| 66 | ! 1128 2013-04-12 06:19:32Z raasch |
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| 67 | ! loop index bounds in accelerator version replaced by i_left, i_right, j_south, |
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| 68 | ! j_north |
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| 69 | ! |
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| 70 | ! 1036 2012-10-22 13:43:42Z raasch |
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| 71 | ! code put under GPL (PALM 3.9) |
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| 72 | ! |
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| 73 | ! 1015 2012-09-27 09:23:24Z raasch |
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| 74 | ! accelerator version (*_acc) added |
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| 75 | ! |
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| 76 | ! 1001 2012-09-13 14:08:46Z raasch |
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| 77 | ! arrays comunicated by module instead of parameter list |
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| 78 | ! |
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| 79 | ! 978 2012-08-09 08:28:32Z fricke |
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| 80 | ! outflow damping layer removed |
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| 81 | ! kmym_x/_y and kmyp_x/_y change to kmym and kmyp |
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| 82 | ! |
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| 83 | ! Revision 1.1 1997/09/12 06:23:51 raasch |
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| 84 | ! Initial revision |
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| 85 | ! |
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| 86 | ! |
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| 87 | ! Description: |
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| 88 | ! ------------ |
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| 89 | !> Diffusion term of the u-component |
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| 90 | !> @todo additional damping (needed for non-cyclic bc) causes bad vectorization |
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| 91 | !> and slows down the speed on NEC about 5-10% |
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| 92 | !------------------------------------------------------------------------------! |
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| 93 | MODULE diffusion_u_mod |
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| 94 | |
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| 95 | |
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| 96 | USE wall_fluxes_mod |
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| 97 | |
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| 98 | PRIVATE |
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| 99 | PUBLIC diffusion_u, diffusion_u_acc |
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| 100 | |
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| 101 | INTERFACE diffusion_u |
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| 102 | MODULE PROCEDURE diffusion_u |
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| 103 | MODULE PROCEDURE diffusion_u_ij |
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| 104 | END INTERFACE diffusion_u |
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| 105 | |
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| 106 | INTERFACE diffusion_u_acc |
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| 107 | MODULE PROCEDURE diffusion_u_acc |
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| 108 | END INTERFACE diffusion_u_acc |
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| 109 | |
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| 110 | CONTAINS |
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| 111 | |
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| 112 | |
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| 113 | !------------------------------------------------------------------------------! |
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| 114 | ! Description: |
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| 115 | ! ------------ |
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| 116 | !> Call for all grid points |
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| 117 | !------------------------------------------------------------------------------! |
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| 118 | SUBROUTINE diffusion_u |
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| 119 | |
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| 120 | USE arrays_3d, & |
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| 121 | ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w, & |
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| 122 | drho_air, rho_air_zw |
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| 123 | |
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| 124 | USE control_parameters, & |
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| 125 | ONLY: constant_top_momentumflux, topography, use_surface_fluxes, & |
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| 126 | use_top_fluxes |
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| 127 | |
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| 128 | USE grid_variables, & |
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| 129 | ONLY: ddx, ddx2, ddy, fym, fyp, wall_u |
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| 130 | |
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| 131 | USE indices, & |
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| 132 | ONLY: nxl, nxlu, nxr, nyn, nys, nzb, nzb_diff_u, nzb_u_inner, & |
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| 133 | nzb_u_outer, nzt, nzt_diff |
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| 134 | |
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| 135 | USE kinds |
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| 136 | |
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| 137 | IMPLICIT NONE |
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| 138 | |
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| 139 | INTEGER(iwp) :: i !< |
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| 140 | INTEGER(iwp) :: j !< |
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| 141 | INTEGER(iwp) :: k !< |
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| 142 | REAL(wp) :: kmym !< |
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| 143 | REAL(wp) :: kmyp !< |
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| 144 | REAL(wp) :: kmzm !< |
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| 145 | REAL(wp) :: kmzp !< |
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| 146 | |
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| 147 | REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs !< |
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| 148 | |
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| 149 | ! |
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| 150 | !-- First calculate horizontal momentum flux u'v' at vertical walls, |
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| 151 | !-- if neccessary |
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| 152 | IF ( topography /= 'flat' ) THEN |
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| 153 | CALL wall_fluxes( usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, nzb_u_inner, & |
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| 154 | nzb_u_outer, wall_u ) |
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| 155 | ENDIF |
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| 156 | |
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| 157 | DO i = nxlu, nxr |
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| 158 | DO j = nys, nyn |
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| 159 | ! |
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| 160 | !-- Compute horizontal diffusion |
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| 161 | DO k = nzb_u_outer(j,i)+1, nzt |
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| 162 | ! |
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| 163 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 164 | kmyp = 0.25_wp * & |
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| 165 | ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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| 166 | kmym = 0.25_wp * & |
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| 167 | ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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| 168 | |
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| 169 | tend(k,j,i) = tend(k,j,i) & |
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| 170 | & + 2.0_wp * ( & |
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| 171 | & km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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| 172 | & - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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| 173 | & ) * ddx2 & |
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| 174 | & + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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| 175 | & + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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| 176 | & - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 177 | & - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 178 | & ) * ddy |
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| 179 | ENDDO |
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| 180 | |
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| 181 | ! |
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| 182 | !-- Wall functions at the north and south walls, respectively |
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| 183 | IF ( wall_u(j,i) /= 0.0_wp ) THEN |
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| 184 | |
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| 185 | DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i) |
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| 186 | kmyp = 0.25_wp * & |
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| 187 | ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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| 188 | kmym = 0.25_wp * & |
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| 189 | ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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| 190 | |
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| 191 | tend(k,j,i) = tend(k,j,i) & |
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| 192 | + 2.0_wp * ( & |
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| 193 | km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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| 194 | - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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| 195 | ) * ddx2 & |
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| 196 | + ( fyp(j,i) * ( & |
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| 197 | kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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| 198 | + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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| 199 | ) & |
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| 200 | - fym(j,i) * ( & |
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| 201 | kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 202 | + kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 203 | ) & |
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| 204 | + wall_u(j,i) * usvs(k,j,i) & |
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| 205 | ) * ddy |
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| 206 | ENDDO |
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| 207 | ENDIF |
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| 208 | |
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| 209 | ! |
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| 210 | !-- Compute vertical diffusion. In case of simulating a Prandtl layer, |
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| 211 | !-- index k starts at nzb_u_inner+2. |
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| 212 | DO k = nzb_diff_u(j,i), nzt_diff |
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| 213 | ! |
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| 214 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 215 | kmzp = 0.25_wp * & |
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| 216 | ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 217 | kmzm = 0.25_wp * & |
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| 218 | ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 219 | |
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| 220 | tend(k,j,i) = tend(k,j,i) & |
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| 221 | & + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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| 222 | & + ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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| 223 | & ) * rho_air_zw(k) & |
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| 224 | & - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & |
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| 225 | & + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
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| 226 | & ) * rho_air_zw(k-1) & |
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| 227 | & ) * ddzw(k) * drho_air(k) |
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| 228 | ENDDO |
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| 229 | |
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| 230 | ! |
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| 231 | !-- Vertical diffusion at the first grid point above the surface, |
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| 232 | !-- if the momentum flux at the bottom is given by the Prandtl law or |
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| 233 | !-- if it is prescribed by the user. |
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| 234 | !-- Difference quotient of the momentum flux is not formed over half |
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| 235 | !-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison |
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| 236 | !-- with other (LES) models showed that the values of the momentum |
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| 237 | !-- flux becomes too large in this case. |
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| 238 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 239 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 240 | IF ( use_surface_fluxes ) THEN |
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| 241 | k = nzb_u_inner(j,i)+1 |
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| 242 | ! |
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| 243 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 244 | kmzp = 0.25_wp * & |
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| 245 | ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 246 | |
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| 247 | tend(k,j,i) = tend(k,j,i) & |
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| 248 | & + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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| 249 | & + ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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| 250 | & ) * rho_air_zw(k) & |
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| 251 | & - ( -usws(j,i) ) & |
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| 252 | & ) * ddzw(k) * drho_air(k) |
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| 253 | ENDIF |
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| 254 | |
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| 255 | ! |
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| 256 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
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| 257 | !-- if the momentum flux at the top is prescribed by the user |
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| 258 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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| 259 | k = nzt |
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| 260 | ! |
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| 261 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 262 | kmzm = 0.25_wp * & |
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| 263 | ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 264 | |
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| 265 | tend(k,j,i) = tend(k,j,i) & |
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| 266 | & + ( ( -uswst(j,i) ) & |
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| 267 | & - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & |
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| 268 | & + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
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| 269 | & ) * rho_air_zw(k-1) & |
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| 270 | & ) * ddzw(k) * drho_air(k) |
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| 271 | ENDIF |
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| 272 | |
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| 273 | ENDDO |
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| 274 | ENDDO |
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| 275 | |
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| 276 | END SUBROUTINE diffusion_u |
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| 277 | |
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| 278 | |
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| 279 | !------------------------------------------------------------------------------! |
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| 280 | ! Description: |
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| 281 | ! ------------ |
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| 282 | !> Call for all grid points - accelerator version |
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| 283 | !------------------------------------------------------------------------------! |
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| 284 | SUBROUTINE diffusion_u_acc |
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| 285 | |
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| 286 | USE arrays_3d, & |
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| 287 | ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w, & |
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| 288 | drho_air, rho_air_zw |
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| 289 | |
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| 290 | USE control_parameters, & |
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| 291 | ONLY: constant_top_momentumflux, topography, use_surface_fluxes, & |
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| 292 | use_top_fluxes |
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| 293 | |
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| 294 | USE grid_variables, & |
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| 295 | ONLY: ddx, ddx2, ddy, fym, fyp, wall_u |
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| 296 | |
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| 297 | USE indices, & |
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| 298 | ONLY: i_left, i_right, j_north, j_south, nxl, nxr, nyn, nys, nzb, & |
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| 299 | nzb_diff_u, nzb_u_inner, nzb_u_outer, nzt, nzt_diff |
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| 300 | |
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| 301 | USE kinds |
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| 302 | |
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| 303 | IMPLICIT NONE |
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| 304 | |
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| 305 | INTEGER(iwp) :: i !< |
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| 306 | INTEGER(iwp) :: j !< |
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| 307 | INTEGER(iwp) :: k !< |
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| 308 | REAL(wp) :: kmym !< |
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| 309 | REAL(wp) :: kmyp !< |
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| 310 | REAL(wp) :: kmzm !< |
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| 311 | REAL(wp) :: kmzp !< |
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| 312 | |
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| 313 | REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs !< |
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| 314 | !$acc declare create ( usvs ) |
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| 315 | |
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| 316 | ! |
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| 317 | !-- First calculate horizontal momentum flux u'v' at vertical walls, |
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| 318 | !-- if neccessary |
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| 319 | IF ( topography /= 'flat' ) THEN |
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| 320 | CALL wall_fluxes_acc( usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, & |
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| 321 | nzb_u_inner, nzb_u_outer, wall_u ) |
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| 322 | ENDIF |
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| 323 | |
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| 324 | !$acc kernels present ( u, v, w, km, tend, usws, uswst ) & |
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| 325 | !$acc present ( ddzu, ddzw, fym, fyp, wall_u ) & |
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| 326 | !$acc present ( nzb_u_inner, nzb_u_outer, nzb_diff_u ) |
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| 327 | DO i = i_left, i_right |
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| 328 | DO j = j_south, j_north |
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| 329 | ! |
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| 330 | !-- Compute horizontal diffusion |
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| 331 | DO k = 1, nzt |
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| 332 | IF ( k > nzb_u_outer(j,i) ) THEN |
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| 333 | ! |
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| 334 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 335 | kmyp = 0.25_wp * & |
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| 336 | ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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| 337 | kmym = 0.25_wp * & |
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| 338 | ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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| 339 | |
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| 340 | tend(k,j,i) = tend(k,j,i) & |
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| 341 | & + 2.0_wp * ( & |
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| 342 | & km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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| 343 | & - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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| 344 | & ) * ddx2 & |
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| 345 | & + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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| 346 | & + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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| 347 | & - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 348 | & - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 349 | & ) * ddy |
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| 350 | ENDIF |
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| 351 | ENDDO |
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| 352 | |
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| 353 | ! |
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| 354 | !-- Wall functions at the north and south walls, respectively |
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| 355 | DO k = 1, nzt |
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| 356 | IF( k > nzb_u_inner(j,i) .AND. k <= nzb_u_outer(j,i) .AND. & |
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| 357 | wall_u(j,i) /= 0.0_wp ) THEN |
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| 358 | |
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| 359 | kmyp = 0.25_wp * & |
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| 360 | ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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| 361 | kmym = 0.25_wp * & |
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| 362 | ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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| 363 | |
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| 364 | tend(k,j,i) = tend(k,j,i) & |
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| 365 | + 2.0_wp * ( & |
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| 366 | km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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| 367 | - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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| 368 | ) * ddx2 & |
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| 369 | + ( fyp(j,i) * ( & |
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| 370 | kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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| 371 | + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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| 372 | ) & |
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| 373 | - fym(j,i) * ( & |
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| 374 | kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 375 | + kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 376 | ) & |
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| 377 | + wall_u(j,i) * usvs(k,j,i) & |
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| 378 | ) * ddy |
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| 379 | ENDIF |
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| 380 | ENDDO |
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| 381 | |
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| 382 | ! |
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| 383 | !-- Compute vertical diffusion. In case of simulating a Prandtl layer, |
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| 384 | !-- index k starts at nzb_u_inner+2. |
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| 385 | DO k = 1, nzt_diff |
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| 386 | IF ( k >= nzb_diff_u(j,i) ) THEN |
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| 387 | ! |
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| 388 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 389 | kmzp = 0.25_wp * & |
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| 390 | ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 391 | kmzm = 0.25_wp * & |
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| 392 | ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 393 | |
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| 394 | tend(k,j,i) = tend(k,j,i) & |
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| 395 | & + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1)& |
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| 396 | & + ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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| 397 | & ) * rho_air_zw(k) & |
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| 398 | & - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k)& |
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| 399 | & + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
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| 400 | & ) * rho_air_zw(k-1) & |
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| 401 | & ) * ddzw(k) * drho_air(k) |
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| 402 | ENDIF |
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| 403 | ENDDO |
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| 404 | |
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| 405 | ENDDO |
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| 406 | ENDDO |
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| 407 | |
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| 408 | ! |
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| 409 | !-- Vertical diffusion at the first grid point above the surface, |
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| 410 | !-- if the momentum flux at the bottom is given by the Prandtl law or |
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| 411 | !-- if it is prescribed by the user. |
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| 412 | !-- Difference quotient of the momentum flux is not formed over half |
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| 413 | !-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison |
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| 414 | !-- with other (LES) models showed that the values of the momentum |
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| 415 | !-- flux becomes too large in this case. |
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| 416 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 417 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 418 | IF ( use_surface_fluxes ) THEN |
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| 419 | |
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| 420 | DO i = i_left, i_right |
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| 421 | DO j = j_south, j_north |
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| 422 | |
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| 423 | k = nzb_u_inner(j,i)+1 |
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| 424 | ! |
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| 425 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 426 | kmzp = 0.25_wp * & |
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| 427 | ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 428 | |
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| 429 | tend(k,j,i) = tend(k,j,i) & |
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| 430 | & + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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| 431 | & + ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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| 432 | & ) * rho_air_zw(k) & |
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| 433 | & - ( -usws(j,i) ) & |
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| 434 | & ) * ddzw(k) * drho_air(k) |
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| 435 | ENDDO |
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| 436 | ENDDO |
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| 437 | |
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| 438 | ENDIF |
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| 439 | |
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| 440 | ! |
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| 441 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
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| 442 | !-- if the momentum flux at the top is prescribed by the user |
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| 443 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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| 444 | |
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| 445 | k = nzt |
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| 446 | |
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| 447 | DO i = i_left, i_right |
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| 448 | DO j = j_south, j_north |
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| 449 | |
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| 450 | ! |
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| 451 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 452 | kmzm = 0.25_wp * & |
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| 453 | ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 454 | |
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| 455 | tend(k,j,i) = tend(k,j,i) & |
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| 456 | & + ( ( -uswst(j,i) ) & |
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| 457 | & - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & |
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| 458 | & + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
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| 459 | & ) * rho_air_zw(k-1) & |
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| 460 | & ) * ddzw(k) * drho_air(k) |
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| 461 | ENDDO |
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| 462 | ENDDO |
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| 463 | |
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| 464 | ENDIF |
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| 465 | !$acc end kernels |
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| 466 | |
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| 467 | END SUBROUTINE diffusion_u_acc |
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| 468 | |
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| 469 | |
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| 470 | !------------------------------------------------------------------------------! |
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| 471 | ! Description: |
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| 472 | ! ------------ |
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| 473 | !> Call for grid point i,j |
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| 474 | !------------------------------------------------------------------------------! |
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| 475 | SUBROUTINE diffusion_u_ij( i, j ) |
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| 476 | |
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| 477 | USE arrays_3d, & |
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| 478 | ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w, & |
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| 479 | drho_air, rho_air_zw |
|---|
| 480 | |
|---|
| 481 | USE control_parameters, & |
|---|
| 482 | ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes |
|---|
| 483 | |
|---|
| 484 | USE grid_variables, & |
|---|
| 485 | ONLY: ddx, ddx2, ddy, fym, fyp, wall_u |
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| 486 | |
|---|
| 487 | USE indices, & |
|---|
| 488 | ONLY: nzb, nzb_diff_u, nzb_u_inner, nzb_u_outer, nzt, nzt_diff |
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| 489 | |
|---|
| 490 | USE kinds |
|---|
| 491 | |
|---|
| 492 | IMPLICIT NONE |
|---|
| 493 | |
|---|
| 494 | INTEGER(iwp) :: i !< |
|---|
| 495 | INTEGER(iwp) :: j !< |
|---|
| 496 | INTEGER(iwp) :: k !< |
|---|
| 497 | REAL(wp) :: kmym !< |
|---|
| 498 | REAL(wp) :: kmyp !< |
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| 499 | REAL(wp) :: kmzm !< |
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| 500 | REAL(wp) :: kmzp !< |
|---|
| 501 | |
|---|
| 502 | REAL(wp), DIMENSION(nzb:nzt+1) :: usvs !< |
|---|
| 503 | |
|---|
| 504 | ! |
|---|
| 505 | !-- Compute horizontal diffusion |
|---|
| 506 | DO k = nzb_u_outer(j,i)+1, nzt |
|---|
| 507 | ! |
|---|
| 508 | !-- Interpolate eddy diffusivities on staggered gridpoints |
|---|
| 509 | kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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| 510 | kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
|---|
| 511 | |
|---|
| 512 | tend(k,j,i) = tend(k,j,i) & |
|---|
| 513 | & + 2.0_wp * ( & |
|---|
| 514 | & km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
|---|
| 515 | & - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
|---|
| 516 | & ) * ddx2 & |
|---|
| 517 | & + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
|---|
| 518 | & + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
|---|
| 519 | & - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
|---|
| 520 | & - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
|---|
| 521 | & ) * ddy |
|---|
| 522 | ENDDO |
|---|
| 523 | |
|---|
| 524 | ! |
|---|
| 525 | !-- Wall functions at the north and south walls, respectively |
|---|
| 526 | IF ( wall_u(j,i) /= 0.0_wp ) THEN |
|---|
| 527 | |
|---|
| 528 | ! |
|---|
| 529 | !-- Calculate the horizontal momentum flux u'v' |
|---|
| 530 | CALL wall_fluxes( i, j, nzb_u_inner(j,i)+1, nzb_u_outer(j,i), & |
|---|
| 531 | usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp ) |
|---|
| 532 | |
|---|
| 533 | DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i) |
|---|
| 534 | kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
|---|
| 535 | kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
|---|
| 536 | |
|---|
| 537 | tend(k,j,i) = tend(k,j,i) & |
|---|
| 538 | + 2.0_wp * ( & |
|---|
| 539 | km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
|---|
| 540 | - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
|---|
| 541 | ) * ddx2 & |
|---|
| 542 | + ( fyp(j,i) * ( & |
|---|
| 543 | kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
|---|
| 544 | + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
|---|
| 545 | ) & |
|---|
| 546 | - fym(j,i) * ( & |
|---|
| 547 | kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
|---|
| 548 | + kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
|---|
| 549 | ) & |
|---|
| 550 | + wall_u(j,i) * usvs(k) & |
|---|
| 551 | ) * ddy |
|---|
| 552 | ENDDO |
|---|
| 553 | ENDIF |
|---|
| 554 | |
|---|
| 555 | ! |
|---|
| 556 | !-- Compute vertical diffusion. In case of simulating a Prandtl layer, |
|---|
| 557 | !-- index k starts at nzb_u_inner+2. |
|---|
| 558 | DO k = nzb_diff_u(j,i), nzt_diff |
|---|
| 559 | ! |
|---|
| 560 | !-- Interpolate eddy diffusivities on staggered gridpoints |
|---|
| 561 | kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
|---|
| 562 | kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
|---|
| 563 | |
|---|
| 564 | tend(k,j,i) = tend(k,j,i) & |
|---|
| 565 | & + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
|---|
| 566 | & + ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
|---|
| 567 | & ) * rho_air_zw(k) & |
|---|
| 568 | & - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & |
|---|
| 569 | & + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
|---|
| 570 | & ) * rho_air_zw(k-1) & |
|---|
| 571 | & ) * ddzw(k) * drho_air(k) |
|---|
| 572 | ENDDO |
|---|
| 573 | |
|---|
| 574 | ! |
|---|
| 575 | !-- Vertical diffusion at the first grid point above the surface, if the |
|---|
| 576 | !-- momentum flux at the bottom is given by the Prandtl law or if it is |
|---|
| 577 | !-- prescribed by the user. |
|---|
| 578 | !-- Difference quotient of the momentum flux is not formed over half of |
|---|
| 579 | !-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with |
|---|
| 580 | !-- other (LES) models showed that the values of the momentum flux becomes |
|---|
| 581 | !-- too large in this case. |
|---|
| 582 | !-- The term containing w(k-1,..) (see above equation) is removed here |
|---|
| 583 | !-- because the vertical velocity is assumed to be zero at the surface. |
|---|
| 584 | IF ( use_surface_fluxes ) THEN |
|---|
| 585 | k = nzb_u_inner(j,i)+1 |
|---|
| 586 | ! |
|---|
| 587 | !-- Interpolate eddy diffusivities on staggered gridpoints |
|---|
| 588 | kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
|---|
| 589 | |
|---|
| 590 | tend(k,j,i) = tend(k,j,i) & |
|---|
| 591 | & + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
|---|
| 592 | & + ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
|---|
| 593 | & ) * rho_air_zw(k) & |
|---|
| 594 | & - ( -usws(j,i) ) & |
|---|
| 595 | & ) * ddzw(k) * drho_air(k) |
|---|
| 596 | ENDIF |
|---|
| 597 | |
|---|
| 598 | ! |
|---|
| 599 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
|---|
| 600 | !-- if the momentum flux at the top is prescribed by the user |
|---|
| 601 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
|---|
| 602 | k = nzt |
|---|
| 603 | ! |
|---|
| 604 | !-- Interpolate eddy diffusivities on staggered gridpoints |
|---|
| 605 | kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
|---|
| 606 | |
|---|
| 607 | tend(k,j,i) = tend(k,j,i) & |
|---|
| 608 | & + ( ( -uswst(j,i) ) & |
|---|
| 609 | & - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & |
|---|
| 610 | & + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
|---|
| 611 | & ) * rho_air_zw(k-1) & |
|---|
| 612 | & ) * ddzw(k) * drho_air(k) |
|---|
| 613 | ENDIF |
|---|
| 614 | |
|---|
| 615 | END SUBROUTINE diffusion_u_ij |
|---|
| 616 | |
|---|
| 617 | END MODULE diffusion_u_mod |
|---|
