1 | !> @file diffusion_w.f90 |
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2 | !------------------------------------------------------------------------------! |
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3 | ! This file is part of the PALM model system. |
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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 1997-2019 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_w.f90 3655 2019-01-07 16:51:22Z hellstea $ |
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27 | ! OpenACC port for SPEC |
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28 | ! |
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29 | ! 3547 2018-11-21 13:21:24Z suehring |
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30 | ! variables documented |
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31 | ! |
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32 | ! 3241 2018-09-12 15:02:00Z raasch |
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33 | ! unused variables removed |
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34 | ! |
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35 | ! 2718 2018-01-02 08:49:38Z maronga |
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36 | ! Corrected "Former revisions" section |
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37 | ! |
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38 | ! 2696 2017-12-14 17:12:51Z kanani |
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39 | ! Change in file header (GPL part) |
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40 | ! |
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41 | ! 2233 2017-05-30 18:08:54Z suehring |
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42 | ! |
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43 | ! 2232 2017-05-30 17:47:52Z suehring |
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44 | ! Adjustments to new topography and surface concept |
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45 | ! |
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46 | ! 2118 2017-01-17 16:38:49Z raasch |
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47 | ! OpenACC version of subroutine removed |
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48 | ! |
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49 | ! 2037 2016-10-26 11:15:40Z knoop |
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50 | ! Anelastic approximation implemented |
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51 | ! |
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52 | ! 2000 2016-08-20 18:09:15Z knoop |
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53 | ! Forced header and separation lines into 80 columns |
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54 | ! |
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55 | ! 1873 2016-04-18 14:50:06Z maronga |
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56 | ! Module renamed (removed _mod) |
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57 | ! |
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58 | ! 1850 2016-04-08 13:29:27Z maronga |
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59 | ! Module renamed |
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60 | ! |
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61 | ! 1682 2015-10-07 23:56:08Z knoop |
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62 | ! Code annotations made doxygen readable |
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63 | ! |
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64 | ! 1374 2014-04-25 12:55:07Z raasch |
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65 | ! vsws + vswst removed from acc-present-list |
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66 | ! |
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67 | ! 1353 2014-04-08 15:21:23Z heinze |
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68 | ! REAL constants provided with KIND-attribute |
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69 | ! |
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70 | ! 1340 2014-03-25 19:45:13Z kanani |
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71 | ! REAL constants defined as wp-kind |
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72 | ! |
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73 | ! 1322 2014-03-20 16:38:49Z raasch |
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74 | ! REAL constants defined as wp-kind |
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75 | ! |
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76 | ! 1320 2014-03-20 08:40:49Z raasch |
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77 | ! ONLY-attribute added to USE-statements, |
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78 | ! kind-parameters added to all INTEGER and REAL declaration statements, |
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79 | ! kinds are defined in new module kinds, |
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80 | ! revision history before 2012 removed, |
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81 | ! comment fields (!:) to be used for variable explanations added to |
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82 | ! all variable declaration statements |
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83 | ! |
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84 | ! 1257 2013-11-08 15:18:40Z raasch |
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85 | ! openacc loop and loop vector clauses removed, declare create moved after |
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86 | ! the FORTRAN declaration statement |
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87 | ! |
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88 | ! 1128 2013-04-12 06:19:32Z raasch |
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89 | ! loop index bounds in accelerator version replaced by i_left, i_right, j_south, |
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90 | ! j_north |
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91 | ! |
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92 | ! 1036 2012-10-22 13:43:42Z raasch |
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93 | ! code put under GPL (PALM 3.9) |
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94 | ! |
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95 | ! 1015 2012-09-27 09:23:24Z raasch |
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96 | ! accelerator version (*_acc) added |
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97 | ! |
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98 | ! 1001 2012-09-13 14:08:46Z raasch |
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99 | ! arrays comunicated by module instead of parameter list |
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100 | ! |
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101 | ! 978 2012-08-09 08:28:32Z fricke |
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102 | ! outflow damping layer removed |
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103 | ! kmxm_x/_z and kmxp_x/_z change to kmxm and kmxp |
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104 | ! kmym_y/_z and kmyp_y/_z change to kmym and kmyp |
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105 | ! |
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106 | ! Revision 1.1 1997/09/12 06:24:11 raasch |
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107 | ! Initial revision |
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108 | ! |
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109 | ! |
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110 | ! Description: |
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111 | ! ------------ |
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112 | !> Diffusion term of the w-component |
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113 | !------------------------------------------------------------------------------! |
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114 | MODULE diffusion_w_mod |
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115 | |
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116 | |
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117 | PRIVATE |
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118 | PUBLIC diffusion_w |
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119 | |
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120 | INTERFACE diffusion_w |
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121 | MODULE PROCEDURE diffusion_w |
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122 | MODULE PROCEDURE diffusion_w_ij |
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123 | END INTERFACE diffusion_w |
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124 | |
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125 | CONTAINS |
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126 | |
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127 | |
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128 | !------------------------------------------------------------------------------! |
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129 | ! Description: |
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130 | ! ------------ |
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131 | !> Call for all grid points |
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132 | !------------------------------------------------------------------------------! |
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133 | SUBROUTINE diffusion_w |
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134 | |
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135 | USE arrays_3d, & |
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136 | ONLY : ddzu, ddzw, km, tend, u, v, w, drho_air_zw, rho_air |
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137 | |
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138 | USE grid_variables, & |
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139 | ONLY : ddx, ddy |
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140 | |
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141 | USE indices, & |
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142 | ONLY : nxl, nxr, nyn, nys, nzb, nzt, wall_flags_0 |
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143 | |
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144 | USE kinds |
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145 | |
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146 | USE surface_mod, & |
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147 | ONLY : surf_def_v, surf_lsm_v, surf_usm_v |
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148 | |
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149 | IMPLICIT NONE |
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150 | |
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151 | INTEGER(iwp) :: i !< running index x direction |
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152 | INTEGER(iwp) :: j !< running index y direction |
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153 | INTEGER(iwp) :: k !< running index z direction |
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154 | INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall |
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155 | INTEGER(iwp) :: m !< running index surface elements |
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156 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
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157 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
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158 | |
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159 | REAL(wp) :: flag !< flag to mask topography grid points |
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160 | REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the w-gridbox - interpolated onto xu-y grid |
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161 | REAL(wp) :: kmxp !<diffusion coefficient on rightward side of the w-gridbox - interpolated onto xu-y grid |
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162 | REAL(wp) :: kmym !< diffusion coefficient on southward side of the w-gridbox - interpolated onto x-yv grid |
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163 | REAL(wp) :: kmyp !< diffusion coefficient on northward side of the w-gridbox - interpolated onto x-yv grid |
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164 | REAL(wp) :: mask_west !< flag to mask vertical wall west of the grid point |
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165 | REAL(wp) :: mask_east !< flag to mask vertical wall east of the grid point |
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166 | REAL(wp) :: mask_south !< flag to mask vertical wall south of the grid point |
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167 | REAL(wp) :: mask_north !< flag to mask vertical wall north of the grid point |
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168 | |
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169 | |
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170 | |
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171 | !$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k, l, m) & |
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172 | !$ACC PRIVATE(surf_e, surf_s, flag, kmxm, kmxp, kmym, kmyp) & |
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173 | !$ACC PRIVATE(mask_west, mask_east, mask_south, mask_north) & |
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174 | !$ACC PRESENT(wall_flags_0, km) & |
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175 | !$ACC PRESENT(u, v, w) & |
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176 | !$ACC PRESENT(ddzu, ddzw, rho_air, drho_air_zw) & |
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177 | !$ACC PRESENT(surf_def_v(0:3)) & |
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178 | !$ACC PRESENT(surf_lsm_v(0:3)) & |
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179 | !$ACC PRESENT(surf_usm_v(0:3)) & |
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180 | !$ACC PRESENT(tend) |
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181 | DO i = nxl, nxr |
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182 | DO j = nys, nyn |
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183 | DO k = nzb+1, nzt-1 |
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184 | ! |
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185 | !-- Predetermine flag to mask topography and wall-bounded grid points. |
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186 | flag = MERGE( 1.0_wp, 0.0_wp, & |
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187 | BTEST( wall_flags_0(k,j,i), 3 ) ) |
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188 | mask_east = MERGE( 1.0_wp, 0.0_wp, & |
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189 | BTEST( wall_flags_0(k,j,i+1), 3 ) ) |
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190 | mask_west = MERGE( 1.0_wp, 0.0_wp, & |
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191 | BTEST( wall_flags_0(k,j,i-1), 3 ) ) |
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192 | mask_south = MERGE( 1.0_wp, 0.0_wp, & |
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193 | BTEST( wall_flags_0(k,j-1,i), 3 ) ) |
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194 | mask_north = MERGE( 1.0_wp, 0.0_wp, & |
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195 | BTEST( wall_flags_0(k,j+1,i), 3 ) ) |
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196 | ! |
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197 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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198 | kmxp = 0.25_wp * ( km(k,j,i) + km(k,j,i+1) + & |
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199 | km(k+1,j,i) + km(k+1,j,i+1) ) |
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200 | kmxm = 0.25_wp * ( km(k,j,i) + km(k,j,i-1) + & |
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201 | km(k+1,j,i) + km(k+1,j,i-1) ) |
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202 | kmyp = 0.25_wp * ( km(k,j,i) + km(k+1,j,i) + & |
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203 | km(k,j+1,i) + km(k+1,j+1,i) ) |
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204 | kmym = 0.25_wp * ( km(k,j,i) + km(k+1,j,i) + & |
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205 | km(k,j-1,i) + km(k+1,j-1,i) ) |
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206 | |
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207 | tend(k,j,i) = tend(k,j,i) & |
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208 | + ( mask_east * kmxp * ( & |
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209 | ( w(k,j,i+1) - w(k,j,i) ) * ddx & |
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210 | + ( u(k+1,j,i+1) - u(k,j,i+1) ) * ddzu(k+1) & |
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211 | ) & |
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212 | - mask_west * kmxm * ( & |
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213 | ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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214 | + ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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215 | ) & |
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216 | ) * ddx * flag & |
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217 | + ( mask_north * kmyp * ( & |
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218 | ( w(k,j+1,i) - w(k,j,i) ) * ddy & |
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219 | + ( v(k+1,j+1,i) - v(k,j+1,i) ) * ddzu(k+1) & |
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220 | ) & |
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221 | - mask_south * kmym * ( & |
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222 | ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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223 | + ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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224 | ) & |
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225 | ) * ddy * flag & |
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226 | + 2.0_wp * ( & |
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227 | km(k+1,j,i) * ( w(k+1,j,i) - w(k,j,i) ) * ddzw(k+1) & |
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228 | * rho_air(k+1) & |
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229 | - km(k,j,i) * ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) & |
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230 | * rho_air(k) & |
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231 | ) * ddzu(k+1) * drho_air_zw(k) * flag |
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232 | ENDDO |
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233 | |
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234 | ! |
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235 | !-- Add horizontal momentum flux v'w' at north- (l=0) and south-facing (l=1) |
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236 | !-- surfaces. Note, in the the flat case, loops won't be entered as |
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237 | !-- start_index > end_index. Furtermore, note, no vertical natural surfaces |
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238 | !-- so far. |
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239 | !-- Default-type surfaces |
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240 | DO l = 0, 1 |
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241 | surf_s = surf_def_v(l)%start_index(j,i) |
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242 | surf_e = surf_def_v(l)%end_index(j,i) |
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243 | DO m = surf_s, surf_e |
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244 | k = surf_def_v(l)%k(m) |
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245 | tend(k,j,i) = tend(k,j,i) + & |
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246 | surf_def_v(l)%mom_flux_w(m) * ddy |
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247 | ENDDO |
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248 | ENDDO |
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249 | ! |
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250 | !-- Natural-type surfaces |
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251 | DO l = 0, 1 |
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252 | surf_s = surf_lsm_v(l)%start_index(j,i) |
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253 | surf_e = surf_lsm_v(l)%end_index(j,i) |
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254 | DO m = surf_s, surf_e |
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255 | k = surf_lsm_v(l)%k(m) |
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256 | tend(k,j,i) = tend(k,j,i) + & |
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257 | surf_lsm_v(l)%mom_flux_w(m) * ddy |
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258 | ENDDO |
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259 | ENDDO |
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260 | ! |
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261 | !-- Urban-type surfaces |
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262 | DO l = 0, 1 |
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263 | surf_s = surf_usm_v(l)%start_index(j,i) |
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264 | surf_e = surf_usm_v(l)%end_index(j,i) |
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265 | DO m = surf_s, surf_e |
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266 | k = surf_usm_v(l)%k(m) |
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267 | tend(k,j,i) = tend(k,j,i) + & |
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268 | surf_usm_v(l)%mom_flux_w(m) * ddy |
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269 | ENDDO |
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270 | ENDDO |
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271 | ! |
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272 | !-- Add horizontal momentum flux u'w' at east- (l=2) and west-facing (l=3) |
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273 | !-- surface. |
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274 | !-- Default-type surfaces |
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275 | DO l = 2, 3 |
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276 | surf_s = surf_def_v(l)%start_index(j,i) |
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277 | surf_e = surf_def_v(l)%end_index(j,i) |
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278 | DO m = surf_s, surf_e |
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279 | k = surf_def_v(l)%k(m) |
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280 | tend(k,j,i) = tend(k,j,i) + & |
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281 | surf_def_v(l)%mom_flux_w(m) * ddx |
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282 | ENDDO |
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283 | ENDDO |
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284 | ! |
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285 | !-- Natural-type surfaces |
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286 | DO l = 2, 3 |
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287 | surf_s = surf_lsm_v(l)%start_index(j,i) |
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288 | surf_e = surf_lsm_v(l)%end_index(j,i) |
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289 | DO m = surf_s, surf_e |
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290 | k = surf_lsm_v(l)%k(m) |
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291 | tend(k,j,i) = tend(k,j,i) + & |
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292 | surf_lsm_v(l)%mom_flux_w(m) * ddx |
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293 | ENDDO |
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294 | ENDDO |
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295 | ! |
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296 | !-- Urban-type surfaces |
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297 | DO l = 2, 3 |
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298 | surf_s = surf_usm_v(l)%start_index(j,i) |
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299 | surf_e = surf_usm_v(l)%end_index(j,i) |
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300 | DO m = surf_s, surf_e |
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301 | k = surf_usm_v(l)%k(m) |
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302 | tend(k,j,i) = tend(k,j,i) + & |
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303 | surf_usm_v(l)%mom_flux_w(m) * ddx |
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304 | ENDDO |
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305 | ENDDO |
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306 | |
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307 | ENDDO |
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308 | ENDDO |
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309 | |
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310 | END SUBROUTINE diffusion_w |
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311 | |
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312 | |
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313 | !------------------------------------------------------------------------------! |
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314 | ! Description: |
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315 | ! ------------ |
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316 | !> Call for grid point i,j |
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317 | !------------------------------------------------------------------------------! |
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318 | SUBROUTINE diffusion_w_ij( i, j ) |
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319 | |
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320 | USE arrays_3d, & |
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321 | ONLY : ddzu, ddzw, km, tend, u, v, w, drho_air_zw, rho_air |
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322 | |
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323 | USE grid_variables, & |
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324 | ONLY : ddx, ddy |
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325 | |
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326 | USE indices, & |
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327 | ONLY : nzb, nzt, wall_flags_0 |
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328 | |
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329 | USE kinds |
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330 | |
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331 | USE surface_mod, & |
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332 | ONLY : surf_def_v, surf_lsm_v, surf_usm_v |
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333 | |
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334 | IMPLICIT NONE |
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335 | |
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336 | |
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337 | INTEGER(iwp) :: i !< running index x direction |
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338 | INTEGER(iwp) :: j !< running index y direction |
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339 | INTEGER(iwp) :: k !< running index z direction |
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340 | INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall |
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341 | INTEGER(iwp) :: m !< running index surface elements |
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342 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
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343 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
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344 | |
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345 | REAL(wp) :: flag !< flag to mask topography grid points |
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346 | REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the w-gridbox - interpolated onto xu-y grid |
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347 | REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the w-gridbox - interpolated onto xu-y grid |
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348 | REAL(wp) :: kmym !< diffusion coefficient on southward side of the w-gridbox - interpolated onto x-yv grid |
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349 | REAL(wp) :: kmyp !< diffusion coefficient on northward side of the w-gridbox - interpolated onto x-yv grid |
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350 | REAL(wp) :: mask_west !< flag to mask vertical wall west of the grid point |
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351 | REAL(wp) :: mask_east !< flag to mask vertical wall east of the grid point |
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352 | REAL(wp) :: mask_south !< flag to mask vertical wall south of the grid point |
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353 | REAL(wp) :: mask_north !< flag to mask vertical wall north of the grid point |
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354 | |
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355 | |
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356 | DO k = nzb+1, nzt-1 |
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357 | ! |
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358 | !-- Predetermine flag to mask topography and wall-bounded grid points. |
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359 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 3 ) ) |
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360 | mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 3 ) ) |
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361 | mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 3 ) ) |
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362 | mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 3 ) ) |
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363 | mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 3 ) ) |
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364 | ! |
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365 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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366 | kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k+1,j,i)+km(k+1,j,i+1) ) |
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367 | kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k+1,j,i)+km(k+1,j,i-1) ) |
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368 | kmyp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j+1,i)+km(k+1,j+1,i) ) |
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369 | kmym = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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370 | |
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371 | tend(k,j,i) = tend(k,j,i) & |
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372 | + ( mask_east * kmxp * ( & |
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373 | ( w(k,j,i+1) - w(k,j,i) ) * ddx & |
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374 | + ( u(k+1,j,i+1) - u(k,j,i+1) ) * ddzu(k+1) & |
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375 | ) & |
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376 | - mask_west * kmxm * ( & |
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377 | ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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378 | + ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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379 | ) & |
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380 | ) * ddx * flag & |
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381 | + ( mask_north * kmyp * ( & |
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382 | ( w(k,j+1,i) - w(k,j,i) ) * ddy & |
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383 | + ( v(k+1,j+1,i) - v(k,j+1,i) ) * ddzu(k+1) & |
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384 | ) & |
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385 | - mask_south * kmym * ( & |
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386 | ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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387 | + ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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388 | ) & |
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389 | ) * ddy * flag & |
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390 | + 2.0_wp * ( & |
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391 | km(k+1,j,i) * ( w(k+1,j,i) - w(k,j,i) ) * ddzw(k+1) & |
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392 | * rho_air(k+1) & |
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393 | - km(k,j,i) * ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) & |
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394 | * rho_air(k) & |
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395 | ) * ddzu(k+1) * drho_air_zw(k) * flag |
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396 | ENDDO |
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397 | ! |
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398 | !-- Add horizontal momentum flux v'w' at north- (l=0) and south-facing (l=1) |
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399 | !-- surfaces. Note, in the the flat case, loops won't be entered as |
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400 | !-- start_index > end_index. Furtermore, note, no vertical natural surfaces |
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401 | !-- so far. |
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402 | !-- Default-type surfaces |
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403 | DO l = 0, 1 |
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404 | surf_s = surf_def_v(l)%start_index(j,i) |
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405 | surf_e = surf_def_v(l)%end_index(j,i) |
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406 | DO m = surf_s, surf_e |
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407 | k = surf_def_v(l)%k(m) |
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408 | tend(k,j,i) = tend(k,j,i) + & |
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409 | surf_def_v(l)%mom_flux_w(m) * ddy |
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410 | ENDDO |
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411 | ENDDO |
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412 | ! |
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413 | !-- Natural-type surfaces |
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414 | DO l = 0, 1 |
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415 | surf_s = surf_lsm_v(l)%start_index(j,i) |
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416 | surf_e = surf_lsm_v(l)%end_index(j,i) |
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417 | DO m = surf_s, surf_e |
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418 | k = surf_lsm_v(l)%k(m) |
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419 | tend(k,j,i) = tend(k,j,i) + & |
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420 | surf_lsm_v(l)%mom_flux_w(m) * ddy |
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421 | ENDDO |
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422 | ENDDO |
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423 | ! |
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424 | !-- Urban-type surfaces |
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425 | DO l = 0, 1 |
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426 | surf_s = surf_usm_v(l)%start_index(j,i) |
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427 | surf_e = surf_usm_v(l)%end_index(j,i) |
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428 | DO m = surf_s, surf_e |
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429 | k = surf_usm_v(l)%k(m) |
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430 | tend(k,j,i) = tend(k,j,i) + & |
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431 | surf_usm_v(l)%mom_flux_w(m) * ddy |
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432 | ENDDO |
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433 | ENDDO |
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434 | ! |
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435 | !-- Add horizontal momentum flux u'w' at east- (l=2) and west-facing (l=3) |
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436 | !-- surfaces. |
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437 | !-- Default-type surfaces |
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438 | DO l = 2, 3 |
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439 | surf_s = surf_def_v(l)%start_index(j,i) |
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440 | surf_e = surf_def_v(l)%end_index(j,i) |
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441 | DO m = surf_s, surf_e |
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442 | k = surf_def_v(l)%k(m) |
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443 | tend(k,j,i) = tend(k,j,i) + & |
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444 | surf_def_v(l)%mom_flux_w(m) * ddx |
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445 | ENDDO |
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446 | ENDDO |
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447 | ! |
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448 | !-- Natural-type surfaces |
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449 | DO l = 2, 3 |
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450 | surf_s = surf_lsm_v(l)%start_index(j,i) |
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451 | surf_e = surf_lsm_v(l)%end_index(j,i) |
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452 | DO m = surf_s, surf_e |
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453 | k = surf_lsm_v(l)%k(m) |
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454 | tend(k,j,i) = tend(k,j,i) + & |
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455 | surf_lsm_v(l)%mom_flux_w(m) * ddx |
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456 | ENDDO |
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457 | ENDDO |
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458 | ! |
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459 | !-- Urban-type surfaces |
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460 | DO l = 2, 3 |
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461 | surf_s = surf_usm_v(l)%start_index(j,i) |
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462 | surf_e = surf_usm_v(l)%end_index(j,i) |
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463 | DO m = surf_s, surf_e |
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464 | k = surf_usm_v(l)%k(m) |
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465 | tend(k,j,i) = tend(k,j,i) + & |
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466 | surf_usm_v(l)%mom_flux_w(m) * ddx |
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467 | ENDDO |
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468 | ENDDO |
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469 | |
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470 | |
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471 | END SUBROUTINE diffusion_w_ij |
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472 | |
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473 | END MODULE diffusion_w_mod |
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