[1873] | 1 | !> @file diffusion_w.f90 |
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[2000] | 2 | !------------------------------------------------------------------------------! |
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[2696] | 3 | ! This file is part of the PALM model system. |
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[1036] | 4 | ! |
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[2000] | 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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[1036] | 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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[4360] | 17 | ! Copyright 1997-2020 Leibniz Universitaet Hannover |
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[2000] | 18 | !------------------------------------------------------------------------------! |
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[1036] | 19 | ! |
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[484] | 20 | ! Current revisions: |
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[1] | 21 | ! ----------------- |
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[1341] | 22 | ! |
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[2233] | 23 | ! |
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[1321] | 24 | ! Former revisions: |
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| 25 | ! ----------------- |
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| 26 | ! $Id: diffusion_w.f90 4360 2020-01-07 11:25:50Z raasch $ |
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[4346] | 27 | ! Introduction of wall_flags_total_0, which currently sets bits based on static |
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| 28 | ! topography information used in wall_flags_static_0 |
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| 29 | ! |
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| 30 | ! 4329 2019-12-10 15:46:36Z motisi |
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[4329] | 31 | ! Renamed wall_flags_0 to wall_flags_static_0 |
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| 32 | ! |
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| 33 | ! 4182 2019-08-22 15:20:23Z scharf |
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[4182] | 34 | ! Corrected "Former revisions" section |
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| 35 | ! |
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| 36 | ! 3655 2019-01-07 16:51:22Z knoop |
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[3634] | 37 | ! OpenACC port for SPEC |
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[1321] | 38 | ! |
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[4182] | 39 | ! Revision 1.1 1997/09/12 06:24:11 raasch |
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| 40 | ! Initial revision |
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| 41 | ! |
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| 42 | ! |
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[1] | 43 | ! Description: |
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| 44 | ! ------------ |
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[1682] | 45 | !> Diffusion term of the w-component |
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[1] | 46 | !------------------------------------------------------------------------------! |
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[1682] | 47 | MODULE diffusion_w_mod |
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| 48 | |
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[1] | 49 | |
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| 50 | PRIVATE |
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[2118] | 51 | PUBLIC diffusion_w |
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[1] | 52 | |
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| 53 | INTERFACE diffusion_w |
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| 54 | MODULE PROCEDURE diffusion_w |
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| 55 | MODULE PROCEDURE diffusion_w_ij |
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| 56 | END INTERFACE diffusion_w |
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| 57 | |
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| 58 | CONTAINS |
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| 59 | |
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| 60 | |
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| 61 | !------------------------------------------------------------------------------! |
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[1682] | 62 | ! Description: |
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| 63 | ! ------------ |
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| 64 | !> Call for all grid points |
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[1] | 65 | !------------------------------------------------------------------------------! |
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[1001] | 66 | SUBROUTINE diffusion_w |
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[1] | 67 | |
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[1320] | 68 | USE arrays_3d, & |
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[2037] | 69 | ONLY : ddzu, ddzw, km, tend, u, v, w, drho_air_zw, rho_air |
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[1320] | 70 | |
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| 71 | USE grid_variables, & |
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[2232] | 72 | ONLY : ddx, ddy |
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[1320] | 73 | |
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| 74 | USE indices, & |
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[4346] | 75 | ONLY : nxl, nxr, nyn, nys, nzb, nzt, wall_flags_total_0 |
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[1320] | 76 | |
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| 77 | USE kinds |
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[1] | 78 | |
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[2232] | 79 | USE surface_mod, & |
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| 80 | ONLY : surf_def_v, surf_lsm_v, surf_usm_v |
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| 81 | |
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[1] | 82 | IMPLICIT NONE |
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| 83 | |
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[2232] | 84 | INTEGER(iwp) :: i !< running index x direction |
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| 85 | INTEGER(iwp) :: j !< running index y direction |
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| 86 | INTEGER(iwp) :: k !< running index z direction |
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| 87 | INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall |
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| 88 | INTEGER(iwp) :: m !< running index surface elements |
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| 89 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
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| 90 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
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[1320] | 91 | |
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[2232] | 92 | REAL(wp) :: flag !< flag to mask topography grid points |
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[3547] | 93 | REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the w-gridbox - interpolated onto xu-y grid |
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| 94 | REAL(wp) :: kmxp !<diffusion coefficient on rightward side of the w-gridbox - interpolated onto xu-y grid |
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| 95 | REAL(wp) :: kmym !< diffusion coefficient on southward side of the w-gridbox - interpolated onto x-yv grid |
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| 96 | REAL(wp) :: kmyp !< diffusion coefficient on northward side of the w-gridbox - interpolated onto x-yv grid |
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[2232] | 97 | REAL(wp) :: mask_west !< flag to mask vertical wall west of the grid point |
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| 98 | REAL(wp) :: mask_east !< flag to mask vertical wall east of the grid point |
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| 99 | REAL(wp) :: mask_south !< flag to mask vertical wall south of the grid point |
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| 100 | REAL(wp) :: mask_north !< flag to mask vertical wall north of the grid point |
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[1001] | 101 | |
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[1] | 102 | |
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| 103 | |
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[3634] | 104 | !$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k, l, m) & |
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| 105 | !$ACC PRIVATE(surf_e, surf_s, flag, kmxm, kmxp, kmym, kmyp) & |
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| 106 | !$ACC PRIVATE(mask_west, mask_east, mask_south, mask_north) & |
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[4346] | 107 | !$ACC PRESENT(wall_flags_total_0, km) & |
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[3634] | 108 | !$ACC PRESENT(u, v, w) & |
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| 109 | !$ACC PRESENT(ddzu, ddzw, rho_air, drho_air_zw) & |
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| 110 | !$ACC PRESENT(surf_def_v(0:3)) & |
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| 111 | !$ACC PRESENT(surf_lsm_v(0:3)) & |
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| 112 | !$ACC PRESENT(surf_usm_v(0:3)) & |
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| 113 | !$ACC PRESENT(tend) |
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[1] | 114 | DO i = nxl, nxr |
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| 115 | DO j = nys, nyn |
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[2232] | 116 | DO k = nzb+1, nzt-1 |
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[1] | 117 | ! |
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[2232] | 118 | !-- Predetermine flag to mask topography and wall-bounded grid points. |
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| 119 | flag = MERGE( 1.0_wp, 0.0_wp, & |
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[4346] | 120 | BTEST( wall_flags_total_0(k,j,i), 3 ) ) |
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[2232] | 121 | mask_east = MERGE( 1.0_wp, 0.0_wp, & |
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[4346] | 122 | BTEST( wall_flags_total_0(k,j,i+1), 3 ) ) |
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[2232] | 123 | mask_west = MERGE( 1.0_wp, 0.0_wp, & |
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[4346] | 124 | BTEST( wall_flags_total_0(k,j,i-1), 3 ) ) |
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[2232] | 125 | mask_south = MERGE( 1.0_wp, 0.0_wp, & |
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[4346] | 126 | BTEST( wall_flags_total_0(k,j-1,i), 3 ) ) |
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[2232] | 127 | mask_north = MERGE( 1.0_wp, 0.0_wp, & |
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[4346] | 128 | BTEST( wall_flags_total_0(k,j+1,i), 3 ) ) |
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[2232] | 129 | ! |
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[1] | 130 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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[3547] | 131 | kmxp = 0.25_wp * ( km(k,j,i) + km(k,j,i+1) + & |
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[2232] | 132 | km(k+1,j,i) + km(k+1,j,i+1) ) |
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| 133 | kmxm = 0.25_wp * ( km(k,j,i) + km(k,j,i-1) + & |
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| 134 | km(k+1,j,i) + km(k+1,j,i-1) ) |
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| 135 | kmyp = 0.25_wp * ( km(k,j,i) + km(k+1,j,i) + & |
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| 136 | km(k,j+1,i) + km(k+1,j+1,i) ) |
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| 137 | kmym = 0.25_wp * ( km(k,j,i) + km(k+1,j,i) + & |
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| 138 | km(k,j-1,i) + km(k+1,j-1,i) ) |
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[1] | 139 | |
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| 140 | tend(k,j,i) = tend(k,j,i) & |
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[2232] | 141 | + ( mask_east * kmxp * ( & |
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| 142 | ( w(k,j,i+1) - w(k,j,i) ) * ddx & |
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| 143 | + ( u(k+1,j,i+1) - u(k,j,i+1) ) * ddzu(k+1) & |
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| 144 | ) & |
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| 145 | - mask_west * kmxm * ( & |
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| 146 | ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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| 147 | + ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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| 148 | ) & |
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| 149 | ) * ddx * flag & |
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| 150 | + ( mask_north * kmyp * ( & |
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| 151 | ( w(k,j+1,i) - w(k,j,i) ) * ddy & |
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| 152 | + ( v(k+1,j+1,i) - v(k,j+1,i) ) * ddzu(k+1) & |
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| 153 | ) & |
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| 154 | - mask_south * kmym * ( & |
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| 155 | ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 156 | + ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 157 | ) & |
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| 158 | ) * ddy * flag & |
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| 159 | + 2.0_wp * ( & |
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| 160 | km(k+1,j,i) * ( w(k+1,j,i) - w(k,j,i) ) * ddzw(k+1) & |
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| 161 | * rho_air(k+1) & |
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| 162 | - km(k,j,i) * ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) & |
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| 163 | * rho_air(k) & |
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| 164 | ) * ddzu(k+1) * drho_air_zw(k) * flag |
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[1] | 165 | ENDDO |
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| 166 | |
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| 167 | ! |
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[2232] | 168 | !-- Add horizontal momentum flux v'w' at north- (l=0) and south-facing (l=1) |
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| 169 | !-- surfaces. Note, in the the flat case, loops won't be entered as |
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| 170 | !-- start_index > end_index. Furtermore, note, no vertical natural surfaces |
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| 171 | !-- so far. |
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| 172 | !-- Default-type surfaces |
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| 173 | DO l = 0, 1 |
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| 174 | surf_s = surf_def_v(l)%start_index(j,i) |
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| 175 | surf_e = surf_def_v(l)%end_index(j,i) |
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| 176 | DO m = surf_s, surf_e |
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| 177 | k = surf_def_v(l)%k(m) |
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| 178 | tend(k,j,i) = tend(k,j,i) + & |
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| 179 | surf_def_v(l)%mom_flux_w(m) * ddy |
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| 180 | ENDDO |
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| 181 | ENDDO |
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[1] | 182 | ! |
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[2232] | 183 | !-- Natural-type surfaces |
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| 184 | DO l = 0, 1 |
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| 185 | surf_s = surf_lsm_v(l)%start_index(j,i) |
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| 186 | surf_e = surf_lsm_v(l)%end_index(j,i) |
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| 187 | DO m = surf_s, surf_e |
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| 188 | k = surf_lsm_v(l)%k(m) |
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| 189 | tend(k,j,i) = tend(k,j,i) + & |
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| 190 | surf_lsm_v(l)%mom_flux_w(m) * ddy |
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| 191 | ENDDO |
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| 192 | ENDDO |
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| 193 | ! |
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| 194 | !-- Urban-type surfaces |
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| 195 | DO l = 0, 1 |
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| 196 | surf_s = surf_usm_v(l)%start_index(j,i) |
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| 197 | surf_e = surf_usm_v(l)%end_index(j,i) |
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| 198 | DO m = surf_s, surf_e |
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| 199 | k = surf_usm_v(l)%k(m) |
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| 200 | tend(k,j,i) = tend(k,j,i) + & |
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| 201 | surf_usm_v(l)%mom_flux_w(m) * ddy |
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| 202 | ENDDO |
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| 203 | ENDDO |
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| 204 | ! |
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| 205 | !-- Add horizontal momentum flux u'w' at east- (l=2) and west-facing (l=3) |
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| 206 | !-- surface. |
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| 207 | !-- Default-type surfaces |
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| 208 | DO l = 2, 3 |
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| 209 | surf_s = surf_def_v(l)%start_index(j,i) |
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| 210 | surf_e = surf_def_v(l)%end_index(j,i) |
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| 211 | DO m = surf_s, surf_e |
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| 212 | k = surf_def_v(l)%k(m) |
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| 213 | tend(k,j,i) = tend(k,j,i) + & |
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| 214 | surf_def_v(l)%mom_flux_w(m) * ddx |
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| 215 | ENDDO |
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| 216 | ENDDO |
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| 217 | ! |
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| 218 | !-- Natural-type surfaces |
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| 219 | DO l = 2, 3 |
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| 220 | surf_s = surf_lsm_v(l)%start_index(j,i) |
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| 221 | surf_e = surf_lsm_v(l)%end_index(j,i) |
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| 222 | DO m = surf_s, surf_e |
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| 223 | k = surf_lsm_v(l)%k(m) |
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| 224 | tend(k,j,i) = tend(k,j,i) + & |
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| 225 | surf_lsm_v(l)%mom_flux_w(m) * ddx |
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| 226 | ENDDO |
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| 227 | ENDDO |
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| 228 | ! |
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| 229 | !-- Urban-type surfaces |
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| 230 | DO l = 2, 3 |
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| 231 | surf_s = surf_usm_v(l)%start_index(j,i) |
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| 232 | surf_e = surf_usm_v(l)%end_index(j,i) |
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| 233 | DO m = surf_s, surf_e |
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| 234 | k = surf_usm_v(l)%k(m) |
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| 235 | tend(k,j,i) = tend(k,j,i) + & |
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| 236 | surf_usm_v(l)%mom_flux_w(m) * ddx |
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| 237 | ENDDO |
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| 238 | ENDDO |
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[1] | 239 | |
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| 240 | ENDDO |
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| 241 | ENDDO |
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| 242 | |
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| 243 | END SUBROUTINE diffusion_w |
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| 244 | |
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| 245 | |
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| 246 | !------------------------------------------------------------------------------! |
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[1682] | 247 | ! Description: |
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| 248 | ! ------------ |
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| 249 | !> Call for grid point i,j |
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[1] | 250 | !------------------------------------------------------------------------------! |
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[1001] | 251 | SUBROUTINE diffusion_w_ij( i, j ) |
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[1] | 252 | |
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[1320] | 253 | USE arrays_3d, & |
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[2037] | 254 | ONLY : ddzu, ddzw, km, tend, u, v, w, drho_air_zw, rho_air |
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[1320] | 255 | |
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| 256 | USE grid_variables, & |
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[2232] | 257 | ONLY : ddx, ddy |
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[1320] | 258 | |
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| 259 | USE indices, & |
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[4346] | 260 | ONLY : nzb, nzt, wall_flags_total_0 |
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[1320] | 261 | |
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| 262 | USE kinds |
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[1] | 263 | |
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[2232] | 264 | USE surface_mod, & |
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| 265 | ONLY : surf_def_v, surf_lsm_v, surf_usm_v |
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| 266 | |
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[1] | 267 | IMPLICIT NONE |
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| 268 | |
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[2232] | 269 | |
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| 270 | INTEGER(iwp) :: i !< running index x direction |
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| 271 | INTEGER(iwp) :: j !< running index y direction |
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| 272 | INTEGER(iwp) :: k !< running index z direction |
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| 273 | INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall |
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| 274 | INTEGER(iwp) :: m !< running index surface elements |
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| 275 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
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| 276 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
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[1320] | 277 | |
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[2232] | 278 | REAL(wp) :: flag !< flag to mask topography grid points |
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[3547] | 279 | REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the w-gridbox - interpolated onto xu-y grid |
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| 280 | REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the w-gridbox - interpolated onto xu-y grid |
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| 281 | REAL(wp) :: kmym !< diffusion coefficient on southward side of the w-gridbox - interpolated onto x-yv grid |
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| 282 | REAL(wp) :: kmyp !< diffusion coefficient on northward side of the w-gridbox - interpolated onto x-yv grid |
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[2232] | 283 | REAL(wp) :: mask_west !< flag to mask vertical wall west of the grid point |
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| 284 | REAL(wp) :: mask_east !< flag to mask vertical wall east of the grid point |
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| 285 | REAL(wp) :: mask_south !< flag to mask vertical wall south of the grid point |
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| 286 | REAL(wp) :: mask_north !< flag to mask vertical wall north of the grid point |
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[1] | 287 | |
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| 288 | |
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[2232] | 289 | DO k = nzb+1, nzt-1 |
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[1] | 290 | ! |
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[2232] | 291 | !-- Predetermine flag to mask topography and wall-bounded grid points. |
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[4346] | 292 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) ) |
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| 293 | mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i+1), 3 ) ) |
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| 294 | mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i-1), 3 ) ) |
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| 295 | mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j-1,i), 3 ) ) |
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| 296 | mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j+1,i), 3 ) ) |
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[2232] | 297 | ! |
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[1] | 298 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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[1322] | 299 | 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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| 300 | 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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| 301 | 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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| 302 | 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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[1] | 303 | |
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| 304 | tend(k,j,i) = tend(k,j,i) & |
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[2232] | 305 | + ( mask_east * kmxp * ( & |
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| 306 | ( w(k,j,i+1) - w(k,j,i) ) * ddx & |
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| 307 | + ( u(k+1,j,i+1) - u(k,j,i+1) ) * ddzu(k+1) & |
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| 308 | ) & |
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| 309 | - mask_west * kmxm * ( & |
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| 310 | ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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| 311 | + ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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| 312 | ) & |
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| 313 | ) * ddx * flag & |
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| 314 | + ( mask_north * kmyp * ( & |
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| 315 | ( w(k,j+1,i) - w(k,j,i) ) * ddy & |
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| 316 | + ( v(k+1,j+1,i) - v(k,j+1,i) ) * ddzu(k+1) & |
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| 317 | ) & |
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| 318 | - mask_south * kmym * ( & |
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| 319 | ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 320 | + ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 321 | ) & |
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| 322 | ) * ddy * flag & |
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| 323 | + 2.0_wp * ( & |
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| 324 | km(k+1,j,i) * ( w(k+1,j,i) - w(k,j,i) ) * ddzw(k+1) & |
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| 325 | * rho_air(k+1) & |
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| 326 | - km(k,j,i) * ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) & |
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| 327 | * rho_air(k) & |
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| 328 | ) * ddzu(k+1) * drho_air_zw(k) * flag |
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[1] | 329 | ENDDO |
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| 330 | ! |
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[2232] | 331 | !-- Add horizontal momentum flux v'w' at north- (l=0) and south-facing (l=1) |
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| 332 | !-- surfaces. Note, in the the flat case, loops won't be entered as |
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| 333 | !-- start_index > end_index. Furtermore, note, no vertical natural surfaces |
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| 334 | !-- so far. |
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| 335 | !-- Default-type surfaces |
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| 336 | DO l = 0, 1 |
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| 337 | surf_s = surf_def_v(l)%start_index(j,i) |
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| 338 | surf_e = surf_def_v(l)%end_index(j,i) |
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| 339 | DO m = surf_s, surf_e |
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| 340 | k = surf_def_v(l)%k(m) |
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| 341 | tend(k,j,i) = tend(k,j,i) + & |
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| 342 | surf_def_v(l)%mom_flux_w(m) * ddy |
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| 343 | ENDDO |
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| 344 | ENDDO |
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[51] | 345 | ! |
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[2232] | 346 | !-- Natural-type surfaces |
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| 347 | DO l = 0, 1 |
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| 348 | surf_s = surf_lsm_v(l)%start_index(j,i) |
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| 349 | surf_e = surf_lsm_v(l)%end_index(j,i) |
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| 350 | DO m = surf_s, surf_e |
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| 351 | k = surf_lsm_v(l)%k(m) |
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| 352 | tend(k,j,i) = tend(k,j,i) + & |
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| 353 | surf_lsm_v(l)%mom_flux_w(m) * ddy |
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| 354 | ENDDO |
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| 355 | ENDDO |
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[1] | 356 | ! |
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[2232] | 357 | !-- Urban-type surfaces |
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| 358 | DO l = 0, 1 |
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| 359 | surf_s = surf_usm_v(l)%start_index(j,i) |
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| 360 | surf_e = surf_usm_v(l)%end_index(j,i) |
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| 361 | DO m = surf_s, surf_e |
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| 362 | k = surf_usm_v(l)%k(m) |
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| 363 | tend(k,j,i) = tend(k,j,i) + & |
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| 364 | surf_usm_v(l)%mom_flux_w(m) * ddy |
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| 365 | ENDDO |
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| 366 | ENDDO |
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| 367 | ! |
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| 368 | !-- Add horizontal momentum flux u'w' at east- (l=2) and west-facing (l=3) |
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| 369 | !-- surfaces. |
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| 370 | !-- Default-type surfaces |
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| 371 | DO l = 2, 3 |
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| 372 | surf_s = surf_def_v(l)%start_index(j,i) |
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| 373 | surf_e = surf_def_v(l)%end_index(j,i) |
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| 374 | DO m = surf_s, surf_e |
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| 375 | k = surf_def_v(l)%k(m) |
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| 376 | tend(k,j,i) = tend(k,j,i) + & |
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| 377 | surf_def_v(l)%mom_flux_w(m) * ddx |
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| 378 | ENDDO |
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| 379 | ENDDO |
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| 380 | ! |
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| 381 | !-- Natural-type surfaces |
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| 382 | DO l = 2, 3 |
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| 383 | surf_s = surf_lsm_v(l)%start_index(j,i) |
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| 384 | surf_e = surf_lsm_v(l)%end_index(j,i) |
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| 385 | DO m = surf_s, surf_e |
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| 386 | k = surf_lsm_v(l)%k(m) |
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| 387 | tend(k,j,i) = tend(k,j,i) + & |
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| 388 | surf_lsm_v(l)%mom_flux_w(m) * ddx |
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| 389 | ENDDO |
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| 390 | ENDDO |
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| 391 | ! |
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| 392 | !-- Urban-type surfaces |
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| 393 | DO l = 2, 3 |
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| 394 | surf_s = surf_usm_v(l)%start_index(j,i) |
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| 395 | surf_e = surf_usm_v(l)%end_index(j,i) |
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| 396 | DO m = surf_s, surf_e |
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| 397 | k = surf_usm_v(l)%k(m) |
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| 398 | tend(k,j,i) = tend(k,j,i) + & |
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| 399 | surf_usm_v(l)%mom_flux_w(m) * ddx |
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| 400 | ENDDO |
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| 401 | ENDDO |
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[1] | 402 | |
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| 403 | |
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| 404 | END SUBROUTINE diffusion_w_ij |
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| 405 | |
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[1323] | 406 | END MODULE diffusion_w_mod |
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