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 raasch $ |
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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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