[1] | 1 | MODULE diffusion_s_mod |
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| 2 | |
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[1036] | 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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[484] | 20 | ! Current revisions: |
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[1001] | 21 | ! ------------------ |
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[1128] | 22 | ! loop index bounds in accelerator version replaced by i_left, i_right, j_south, |
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| 23 | ! j_north |
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[1] | 24 | ! |
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| 25 | ! Former revisions: |
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| 26 | ! ----------------- |
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[3] | 27 | ! $Id: diffusion_s.f90 1128 2013-04-12 06:19:32Z raasch $ |
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[39] | 28 | ! |
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[1093] | 29 | ! 1092 2013-02-02 11:24:22Z raasch |
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| 30 | ! unused variables removed |
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| 31 | ! |
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[1037] | 32 | ! 1036 2012-10-22 13:43:42Z raasch |
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| 33 | ! code put under GPL (PALM 3.9) |
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| 34 | ! |
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[1017] | 35 | ! 1015 2012-09-27 09:23:24Z raasch |
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| 36 | ! accelerator version (*_acc) added |
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| 37 | ! |
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[1011] | 38 | ! 1010 2012-09-20 07:59:54Z raasch |
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| 39 | ! cpp switch __nopointer added for pointer free version |
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| 40 | ! |
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[1002] | 41 | ! 1001 2012-09-13 14:08:46Z raasch |
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| 42 | ! some arrays comunicated by module instead of parameter list |
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| 43 | ! |
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[668] | 44 | ! 667 2010-12-23 12:06:00Z suehring/gryschka |
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| 45 | ! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng |
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| 46 | ! |
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[198] | 47 | ! 183 2008-08-04 15:39:12Z letzel |
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| 48 | ! bugfix: calculation of fluxes at vertical surfaces |
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| 49 | ! |
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[139] | 50 | ! 129 2007-10-30 12:12:24Z letzel |
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| 51 | ! replace wall_heatflux by wall_s_flux that is now included in the parameter |
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| 52 | ! list, bugfix for assignment of fluxes at walls |
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| 53 | ! |
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[39] | 54 | ! 20 2007-02-26 00:12:32Z raasch |
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| 55 | ! Bugfix: ddzw dimensioned 1:nzt"+1" |
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| 56 | ! Calculation extended for gridpoint nzt, fluxes can be given at top, |
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| 57 | ! +s_flux_t in parameter list, s_flux renamed s_flux_b |
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| 58 | ! |
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[3] | 59 | ! RCS Log replace by Id keyword, revision history cleaned up |
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| 60 | ! |
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[1] | 61 | ! Revision 1.8 2006/02/23 10:34:17 raasch |
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| 62 | ! nzb_2d replaced by nzb_s_outer in horizontal diffusion and by nzb_s_inner |
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| 63 | ! or nzb_diff_s_inner, respectively, in vertical diffusion, prescribed surface |
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| 64 | ! fluxes at vertically oriented topography |
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| 65 | ! |
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| 66 | ! Revision 1.1 2000/04/13 14:54:02 schroeter |
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| 67 | ! Initial revision |
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| 68 | ! |
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| 69 | ! |
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| 70 | ! Description: |
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| 71 | ! ------------ |
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| 72 | ! Diffusion term of scalar quantities (temperature and water content) |
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| 73 | !------------------------------------------------------------------------------! |
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| 74 | |
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| 75 | PRIVATE |
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[1015] | 76 | PUBLIC diffusion_s, diffusion_s_acc |
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[1] | 77 | |
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| 78 | INTERFACE diffusion_s |
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| 79 | MODULE PROCEDURE diffusion_s |
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| 80 | MODULE PROCEDURE diffusion_s_ij |
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| 81 | END INTERFACE diffusion_s |
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| 82 | |
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[1015] | 83 | INTERFACE diffusion_s_acc |
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| 84 | MODULE PROCEDURE diffusion_s_acc |
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| 85 | END INTERFACE diffusion_s_acc |
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| 86 | |
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[1] | 87 | CONTAINS |
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| 88 | |
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| 89 | |
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| 90 | !------------------------------------------------------------------------------! |
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| 91 | ! Call for all grid points |
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| 92 | !------------------------------------------------------------------------------! |
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[1001] | 93 | SUBROUTINE diffusion_s( s, s_flux_b, s_flux_t, wall_s_flux ) |
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[1] | 94 | |
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[1001] | 95 | USE arrays_3d |
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[1] | 96 | USE control_parameters |
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| 97 | USE grid_variables |
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| 98 | USE indices |
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| 99 | |
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| 100 | IMPLICIT NONE |
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| 101 | |
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| 102 | INTEGER :: i, j, k |
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[129] | 103 | REAL :: wall_s_flux(0:4) |
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[1001] | 104 | REAL, DIMENSION(nysg:nyng,nxlg:nxrg) :: s_flux_b, s_flux_t |
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[1010] | 105 | #if defined( __nopointer ) |
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| 106 | REAL, DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: s |
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| 107 | #else |
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[1001] | 108 | REAL, DIMENSION(:,:,:), POINTER :: s |
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[1010] | 109 | #endif |
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[1] | 110 | |
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| 111 | DO i = nxl, nxr |
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| 112 | DO j = nys,nyn |
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| 113 | ! |
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| 114 | !-- Compute horizontal diffusion |
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[19] | 115 | DO k = nzb_s_outer(j,i)+1, nzt |
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[1] | 116 | |
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| 117 | tend(k,j,i) = tend(k,j,i) & |
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| 118 | + 0.5 * ( & |
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| 119 | ( kh(k,j,i) + kh(k,j,i+1) ) * ( s(k,j,i+1)-s(k,j,i) ) & |
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| 120 | - ( kh(k,j,i) + kh(k,j,i-1) ) * ( s(k,j,i)-s(k,j,i-1) ) & |
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| 121 | ) * ddx2 & |
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| 122 | + 0.5 * ( & |
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| 123 | ( kh(k,j,i) + kh(k,j+1,i) ) * ( s(k,j+1,i)-s(k,j,i) ) & |
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| 124 | - ( kh(k,j,i) + kh(k,j-1,i) ) * ( s(k,j,i)-s(k,j-1,i) ) & |
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| 125 | ) * ddy2 |
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| 126 | ENDDO |
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| 127 | |
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| 128 | ! |
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| 129 | !-- Apply prescribed horizontal wall heatflux where necessary |
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| 130 | IF ( ( wall_w_x(j,i) .NE. 0.0 ) .OR. ( wall_w_y(j,i) .NE. 0.0 ) ) & |
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| 131 | THEN |
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| 132 | DO k = nzb_s_inner(j,i)+1, nzb_s_outer(j,i) |
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| 133 | |
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| 134 | tend(k,j,i) = tend(k,j,i) & |
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[183] | 135 | + ( fwxp(j,i) * 0.5 * & |
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[1] | 136 | ( kh(k,j,i) + kh(k,j,i+1) ) * ( s(k,j,i+1)-s(k,j,i) ) & |
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[129] | 137 | + ( 1.0 - fwxp(j,i) ) * wall_s_flux(1) & |
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[183] | 138 | -fwxm(j,i) * 0.5 * & |
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[1] | 139 | ( kh(k,j,i) + kh(k,j,i-1) ) * ( s(k,j,i)-s(k,j,i-1) ) & |
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[129] | 140 | + ( 1.0 - fwxm(j,i) ) * wall_s_flux(2) & |
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[1] | 141 | ) * ddx2 & |
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[183] | 142 | + ( fwyp(j,i) * 0.5 * & |
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[1] | 143 | ( kh(k,j,i) + kh(k,j+1,i) ) * ( s(k,j+1,i)-s(k,j,i) ) & |
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[129] | 144 | + ( 1.0 - fwyp(j,i) ) * wall_s_flux(3) & |
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[183] | 145 | -fwym(j,i) * 0.5 * & |
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[1] | 146 | ( kh(k,j,i) + kh(k,j-1,i) ) * ( s(k,j,i)-s(k,j-1,i) ) & |
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[129] | 147 | + ( 1.0 - fwym(j,i) ) * wall_s_flux(4) & |
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[1] | 148 | ) * ddy2 |
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| 149 | ENDDO |
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| 150 | ENDIF |
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| 151 | |
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| 152 | ! |
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| 153 | !-- Compute vertical diffusion. In case that surface fluxes have been |
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[19] | 154 | !-- prescribed or computed at bottom and/or top, index k starts/ends at |
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| 155 | !-- nzb+2 or nzt-1, respectively. |
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| 156 | DO k = nzb_diff_s_inner(j,i), nzt_diff |
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[1] | 157 | |
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| 158 | tend(k,j,i) = tend(k,j,i) & |
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| 159 | + 0.5 * ( & |
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| 160 | ( kh(k,j,i) + kh(k+1,j,i) ) * ( s(k+1,j,i)-s(k,j,i) ) * ddzu(k+1) & |
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| 161 | - ( kh(k,j,i) + kh(k-1,j,i) ) * ( s(k,j,i)-s(k-1,j,i) ) * ddzu(k) & |
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| 162 | ) * ddzw(k) |
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| 163 | ENDDO |
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| 164 | |
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| 165 | ! |
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[19] | 166 | !-- Vertical diffusion at the first computational gridpoint along |
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[1] | 167 | !-- z-direction |
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| 168 | IF ( use_surface_fluxes ) THEN |
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| 169 | |
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| 170 | k = nzb_s_inner(j,i)+1 |
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| 171 | |
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| 172 | tend(k,j,i) = tend(k,j,i) & |
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| 173 | + ( 0.5 * ( kh(k,j,i)+kh(k+1,j,i) ) & |
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| 174 | * ( s(k+1,j,i)-s(k,j,i) ) & |
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| 175 | * ddzu(k+1) & |
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[19] | 176 | + s_flux_b(j,i) & |
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[1] | 177 | ) * ddzw(k) |
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| 178 | |
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| 179 | ENDIF |
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| 180 | |
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[19] | 181 | ! |
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| 182 | !-- Vertical diffusion at the last computational gridpoint along |
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| 183 | !-- z-direction |
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| 184 | IF ( use_top_fluxes ) THEN |
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| 185 | |
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| 186 | k = nzt |
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| 187 | |
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| 188 | tend(k,j,i) = tend(k,j,i) & |
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| 189 | + ( - s_flux_t(j,i) & |
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[20] | 190 | - 0.5 * ( kh(k-1,j,i)+kh(k,j,i) ) & |
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| 191 | * ( s(k,j,i)-s(k-1,j,i) ) & |
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| 192 | * ddzu(k) & |
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[19] | 193 | ) * ddzw(k) |
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| 194 | |
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| 195 | ENDIF |
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| 196 | |
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[1] | 197 | ENDDO |
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| 198 | ENDDO |
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| 199 | |
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| 200 | END SUBROUTINE diffusion_s |
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| 201 | |
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| 202 | |
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| 203 | !------------------------------------------------------------------------------! |
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[1015] | 204 | ! Call for all grid points - accelerator version |
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| 205 | !------------------------------------------------------------------------------! |
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| 206 | SUBROUTINE diffusion_s_acc( s, s_flux_b, s_flux_t, wall_s_flux ) |
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| 207 | |
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| 208 | USE arrays_3d |
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| 209 | USE control_parameters |
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| 210 | USE grid_variables |
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| 211 | USE indices |
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| 212 | |
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| 213 | IMPLICIT NONE |
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| 214 | |
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| 215 | INTEGER :: i, j, k |
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| 216 | REAL :: wall_s_flux(0:4) |
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| 217 | REAL, DIMENSION(nysg:nyng,nxlg:nxrg) :: s_flux_b, s_flux_t |
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| 218 | #if defined( __nopointer ) |
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| 219 | REAL, DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: s |
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| 220 | #else |
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| 221 | REAL, DIMENSION(:,:,:), POINTER :: s |
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| 222 | #endif |
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| 223 | |
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| 224 | !$acc kernels present( ddzu, ddzw, fwxm, fwxp, fwym, fwyp, kh ) & |
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| 225 | !$acc present( nzb_diff_s_inner, nzb_s_inner, nzb_s_outer, s ) & |
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| 226 | !$acc present( s_flux_b, s_flux_t, tend, wall_s_flux ) & |
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| 227 | !$acc present( wall_w_x, wall_w_y ) |
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| 228 | !$acc loop |
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[1128] | 229 | DO i = i_left, i_right |
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| 230 | DO j = j_south, j_north |
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[1015] | 231 | ! |
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| 232 | !-- Compute horizontal diffusion |
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| 233 | !$acc loop vector( 32 ) |
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| 234 | DO k = 1, nzt |
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| 235 | IF ( k > nzb_s_outer(j,i) ) THEN |
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| 236 | |
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| 237 | tend(k,j,i) = tend(k,j,i) & |
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| 238 | + 0.5 * ( & |
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| 239 | ( kh(k,j,i) + kh(k,j,i+1) ) * ( s(k,j,i+1)-s(k,j,i) ) & |
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| 240 | - ( kh(k,j,i) + kh(k,j,i-1) ) * ( s(k,j,i)-s(k,j,i-1) ) & |
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| 241 | ) * ddx2 & |
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| 242 | + 0.5 * ( & |
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| 243 | ( kh(k,j,i) + kh(k,j+1,i) ) * ( s(k,j+1,i)-s(k,j,i) ) & |
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| 244 | - ( kh(k,j,i) + kh(k,j-1,i) ) * ( s(k,j,i)-s(k,j-1,i) ) & |
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| 245 | ) * ddy2 |
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| 246 | ENDIF |
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| 247 | ENDDO |
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| 248 | |
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| 249 | ! |
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| 250 | !-- Apply prescribed horizontal wall heatflux where necessary |
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| 251 | !$acc loop vector(32) |
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| 252 | DO k = 1, nzt |
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| 253 | IF ( k > nzb_s_inner(j,i) .AND. k <= nzb_s_outer(j,i) .AND. & |
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| 254 | ( wall_w_x(j,i) /= 0.0 .OR. wall_w_y(j,i) /= 0.0 ) ) & |
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| 255 | THEN |
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| 256 | tend(k,j,i) = tend(k,j,i) & |
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| 257 | + ( fwxp(j,i) * 0.5 * & |
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| 258 | ( kh(k,j,i) + kh(k,j,i+1) ) * ( s(k,j,i+1)-s(k,j,i) ) & |
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| 259 | + ( 1.0 - fwxp(j,i) ) * wall_s_flux(1) & |
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| 260 | -fwxm(j,i) * 0.5 * & |
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| 261 | ( kh(k,j,i) + kh(k,j,i-1) ) * ( s(k,j,i)-s(k,j,i-1) ) & |
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| 262 | + ( 1.0 - fwxm(j,i) ) * wall_s_flux(2) & |
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| 263 | ) * ddx2 & |
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| 264 | + ( fwyp(j,i) * 0.5 * & |
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| 265 | ( kh(k,j,i) + kh(k,j+1,i) ) * ( s(k,j+1,i)-s(k,j,i) ) & |
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| 266 | + ( 1.0 - fwyp(j,i) ) * wall_s_flux(3) & |
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| 267 | -fwym(j,i) * 0.5 * & |
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| 268 | ( kh(k,j,i) + kh(k,j-1,i) ) * ( s(k,j,i)-s(k,j-1,i) ) & |
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| 269 | + ( 1.0 - fwym(j,i) ) * wall_s_flux(4) & |
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| 270 | ) * ddy2 |
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| 271 | ENDIF |
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| 272 | ENDDO |
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| 273 | |
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| 274 | ! |
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| 275 | !-- Compute vertical diffusion. In case that surface fluxes have been |
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| 276 | !-- prescribed or computed at bottom and/or top, index k starts/ends at |
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| 277 | !-- nzb+2 or nzt-1, respectively. |
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| 278 | !$acc loop vector( 32 ) |
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| 279 | DO k = 1, nzt_diff |
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| 280 | IF ( k >= nzb_diff_s_inner(j,i) ) THEN |
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| 281 | tend(k,j,i) = tend(k,j,i) & |
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| 282 | + 0.5 * ( & |
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| 283 | ( kh(k,j,i) + kh(k+1,j,i) ) * ( s(k+1,j,i)-s(k,j,i) ) * ddzu(k+1) & |
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| 284 | - ( kh(k,j,i) + kh(k-1,j,i) ) * ( s(k,j,i)-s(k-1,j,i) ) * ddzu(k) & |
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| 285 | ) * ddzw(k) |
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| 286 | ENDIF |
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| 287 | ENDDO |
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| 288 | |
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| 289 | ! |
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| 290 | !-- Vertical diffusion at the first computational gridpoint along |
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| 291 | !-- z-direction |
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| 292 | !$acc loop vector( 32 ) |
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| 293 | DO k = 1, nzt |
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| 294 | IF ( use_surface_fluxes .AND. k == nzb_s_inner(j,i)+1 ) THEN |
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| 295 | tend(k,j,i) = tend(k,j,i) & |
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| 296 | + ( 0.5 * ( kh(k,j,i)+kh(k+1,j,i) ) & |
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| 297 | * ( s(k+1,j,i)-s(k,j,i) ) & |
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| 298 | * ddzu(k+1) & |
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| 299 | + s_flux_b(j,i) & |
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| 300 | ) * ddzw(k) |
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| 301 | ENDIF |
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| 302 | |
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| 303 | ! |
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| 304 | !-- Vertical diffusion at the last computational gridpoint along |
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| 305 | !-- z-direction |
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| 306 | IF ( use_top_fluxes .AND. k == nzt ) THEN |
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| 307 | tend(k,j,i) = tend(k,j,i) & |
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| 308 | + ( - s_flux_t(j,i) & |
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| 309 | - 0.5 * ( kh(k-1,j,i)+kh(k,j,i) )& |
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| 310 | * ( s(k,j,i)-s(k-1,j,i) ) & |
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| 311 | * ddzu(k) & |
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| 312 | ) * ddzw(k) |
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| 313 | ENDIF |
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| 314 | ENDDO |
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| 315 | |
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| 316 | ENDDO |
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| 317 | ENDDO |
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| 318 | !$acc end kernels |
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| 319 | |
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| 320 | END SUBROUTINE diffusion_s_acc |
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| 321 | |
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| 322 | |
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| 323 | !------------------------------------------------------------------------------! |
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[1] | 324 | ! Call for grid point i,j |
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| 325 | !------------------------------------------------------------------------------! |
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[1001] | 326 | SUBROUTINE diffusion_s_ij( i, j, s, s_flux_b, s_flux_t, wall_s_flux ) |
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[1] | 327 | |
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[1001] | 328 | USE arrays_3d |
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[1] | 329 | USE control_parameters |
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| 330 | USE grid_variables |
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| 331 | USE indices |
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| 332 | |
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| 333 | IMPLICIT NONE |
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| 334 | |
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| 335 | INTEGER :: i, j, k |
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[129] | 336 | REAL :: wall_s_flux(0:4) |
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[1001] | 337 | REAL, DIMENSION(nysg:nyng,nxlg:nxrg) :: s_flux_b, s_flux_t |
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[1010] | 338 | #if defined( __nopointer ) |
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| 339 | REAL, DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: s |
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| 340 | #else |
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[1001] | 341 | REAL, DIMENSION(:,:,:), POINTER :: s |
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[1010] | 342 | #endif |
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[1] | 343 | |
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| 344 | ! |
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| 345 | !-- Compute horizontal diffusion |
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[19] | 346 | DO k = nzb_s_outer(j,i)+1, nzt |
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[1] | 347 | |
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| 348 | tend(k,j,i) = tend(k,j,i) & |
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| 349 | + 0.5 * ( & |
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| 350 | ( kh(k,j,i) + kh(k,j,i+1) ) * ( s(k,j,i+1)-s(k,j,i) ) & |
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| 351 | - ( kh(k,j,i) + kh(k,j,i-1) ) * ( s(k,j,i)-s(k,j,i-1) ) & |
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| 352 | ) * ddx2 & |
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| 353 | + 0.5 * ( & |
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| 354 | ( kh(k,j,i) + kh(k,j+1,i) ) * ( s(k,j+1,i)-s(k,j,i) ) & |
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| 355 | - ( kh(k,j,i) + kh(k,j-1,i) ) * ( s(k,j,i)-s(k,j-1,i) ) & |
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| 356 | ) * ddy2 |
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| 357 | ENDDO |
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| 358 | |
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| 359 | ! |
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| 360 | !-- Apply prescribed horizontal wall heatflux where necessary |
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| 361 | IF ( ( wall_w_x(j,i) .NE. 0.0 ) .OR. ( wall_w_y(j,i) .NE. 0.0 ) ) & |
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| 362 | THEN |
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| 363 | DO k = nzb_s_inner(j,i)+1, nzb_s_outer(j,i) |
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| 364 | |
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| 365 | tend(k,j,i) = tend(k,j,i) & |
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[183] | 366 | + ( fwxp(j,i) * 0.5 * & |
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[1] | 367 | ( kh(k,j,i) + kh(k,j,i+1) ) * ( s(k,j,i+1)-s(k,j,i) ) & |
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[129] | 368 | + ( 1.0 - fwxp(j,i) ) * wall_s_flux(1) & |
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[183] | 369 | -fwxm(j,i) * 0.5 * & |
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[1] | 370 | ( kh(k,j,i) + kh(k,j,i-1) ) * ( s(k,j,i)-s(k,j,i-1) ) & |
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[129] | 371 | + ( 1.0 - fwxm(j,i) ) * wall_s_flux(2) & |
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[1] | 372 | ) * ddx2 & |
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[183] | 373 | + ( fwyp(j,i) * 0.5 * & |
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[1] | 374 | ( kh(k,j,i) + kh(k,j+1,i) ) * ( s(k,j+1,i)-s(k,j,i) ) & |
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[129] | 375 | + ( 1.0 - fwyp(j,i) ) * wall_s_flux(3) & |
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[183] | 376 | -fwym(j,i) * 0.5 * & |
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[1] | 377 | ( kh(k,j,i) + kh(k,j-1,i) ) * ( s(k,j,i)-s(k,j-1,i) ) & |
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[129] | 378 | + ( 1.0 - fwym(j,i) ) * wall_s_flux(4) & |
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[1] | 379 | ) * ddy2 |
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| 380 | ENDDO |
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| 381 | ENDIF |
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| 382 | |
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| 383 | ! |
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| 384 | !-- Compute vertical diffusion. In case that surface fluxes have been |
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[19] | 385 | !-- prescribed or computed at bottom and/or top, index k starts/ends at |
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| 386 | !-- nzb+2 or nzt-1, respectively. |
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| 387 | DO k = nzb_diff_s_inner(j,i), nzt_diff |
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[1] | 388 | |
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| 389 | tend(k,j,i) = tend(k,j,i) & |
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| 390 | + 0.5 * ( & |
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| 391 | ( kh(k,j,i) + kh(k+1,j,i) ) * ( s(k+1,j,i)-s(k,j,i) ) * ddzu(k+1) & |
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| 392 | - ( kh(k,j,i) + kh(k-1,j,i) ) * ( s(k,j,i)-s(k-1,j,i) ) * ddzu(k) & |
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| 393 | ) * ddzw(k) |
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| 394 | ENDDO |
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| 395 | |
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| 396 | ! |
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[19] | 397 | !-- Vertical diffusion at the first computational gridpoint along z-direction |
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[1] | 398 | IF ( use_surface_fluxes ) THEN |
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| 399 | |
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| 400 | k = nzb_s_inner(j,i)+1 |
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| 401 | |
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[19] | 402 | tend(k,j,i) = tend(k,j,i) + ( 0.5 * ( kh(k,j,i)+kh(k+1,j,i) ) & |
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| 403 | * ( s(k+1,j,i)-s(k,j,i) ) & |
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| 404 | * ddzu(k+1) & |
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| 405 | + s_flux_b(j,i) & |
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| 406 | ) * ddzw(k) |
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[1] | 407 | |
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| 408 | ENDIF |
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| 409 | |
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[19] | 410 | ! |
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| 411 | !-- Vertical diffusion at the last computational gridpoint along z-direction |
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| 412 | IF ( use_top_fluxes ) THEN |
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| 413 | |
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| 414 | k = nzt |
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| 415 | |
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| 416 | tend(k,j,i) = tend(k,j,i) + ( - s_flux_t(j,i) & |
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| 417 | - 0.5 * ( kh(k-1,j,i)+kh(k,j,i) ) & |
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| 418 | * ( s(k,j,i)-s(k-1,j,i) ) & |
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| 419 | * ddzu(k) & |
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| 420 | ) * ddzw(k) |
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| 421 | |
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| 422 | ENDIF |
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| 423 | |
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[1] | 424 | END SUBROUTINE diffusion_s_ij |
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| 425 | |
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| 426 | END MODULE diffusion_s_mod |
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