| 1 | MODULE diffusion_e_mod |
|---|
| 2 | |
|---|
| 3 | !------------------------------------------------------------------------------! |
|---|
| 4 | ! Current revisions: |
|---|
| 5 | ! ----------------- |
|---|
| 6 | ! |
|---|
| 7 | ! |
|---|
| 8 | ! Former revisions: |
|---|
| 9 | ! ----------------- |
|---|
| 10 | ! $Id: diffusion_e.f90 826 2012-02-19 03:41:34Z heinze $ |
|---|
| 11 | ! |
|---|
| 12 | ! 825 2012-02-19 03:03:44Z raasch |
|---|
| 13 | ! wang_collision_kernel renamed wang_kernel |
|---|
| 14 | ! |
|---|
| 15 | ! 790 2011-11-29 03:11:20Z raasch |
|---|
| 16 | ! diss is also calculated in case that the Wang kernel is used |
|---|
| 17 | ! |
|---|
| 18 | ! 667 2010-12-23 12:06:00Z suehring/gryschka |
|---|
| 19 | ! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng |
|---|
| 20 | ! |
|---|
| 21 | ! 97 2007-06-21 08:23:15Z raasch |
|---|
| 22 | ! Adjustment of mixing length calculation for the ocean version. zw added to |
|---|
| 23 | ! argument list. |
|---|
| 24 | ! This is also a bugfix, because the height above the topography is now |
|---|
| 25 | ! used instead of the height above level k=0. |
|---|
| 26 | ! theta renamed var, dpt_dz renamed dvar_dz, +new argument var_reference |
|---|
| 27 | ! use_pt_reference renamed use_reference |
|---|
| 28 | ! |
|---|
| 29 | ! 65 2007-03-13 12:11:43Z raasch |
|---|
| 30 | ! Reference temperature pt_reference can be used in buoyancy term |
|---|
| 31 | ! |
|---|
| 32 | ! 20 2007-02-26 00:12:32Z raasch |
|---|
| 33 | ! Bugfix: ddzw dimensioned 1:nzt"+1" |
|---|
| 34 | ! Calculation extended for gridpoint nzt |
|---|
| 35 | ! |
|---|
| 36 | ! RCS Log replace by Id keyword, revision history cleaned up |
|---|
| 37 | ! |
|---|
| 38 | ! Revision 1.18 2006/08/04 14:29:43 raasch |
|---|
| 39 | ! dissipation is stored in extra array diss if needed later on for calculating |
|---|
| 40 | ! the sgs particle velocities |
|---|
| 41 | ! |
|---|
| 42 | ! Revision 1.1 1997/09/19 07:40:24 raasch |
|---|
| 43 | ! Initial revision |
|---|
| 44 | ! |
|---|
| 45 | ! |
|---|
| 46 | ! Description: |
|---|
| 47 | ! ------------ |
|---|
| 48 | ! Diffusion- and dissipation terms for the TKE |
|---|
| 49 | !------------------------------------------------------------------------------! |
|---|
| 50 | |
|---|
| 51 | PRIVATE |
|---|
| 52 | PUBLIC diffusion_e |
|---|
| 53 | |
|---|
| 54 | |
|---|
| 55 | INTERFACE diffusion_e |
|---|
| 56 | MODULE PROCEDURE diffusion_e |
|---|
| 57 | MODULE PROCEDURE diffusion_e_ij |
|---|
| 58 | END INTERFACE diffusion_e |
|---|
| 59 | |
|---|
| 60 | CONTAINS |
|---|
| 61 | |
|---|
| 62 | |
|---|
| 63 | !------------------------------------------------------------------------------! |
|---|
| 64 | ! Call for all grid points |
|---|
| 65 | !------------------------------------------------------------------------------! |
|---|
| 66 | SUBROUTINE diffusion_e( ddzu, dd2zu, ddzw, diss, e, km, l_grid, var, & |
|---|
| 67 | var_reference, rif, tend, zu, zw ) |
|---|
| 68 | |
|---|
| 69 | USE control_parameters |
|---|
| 70 | USE grid_variables |
|---|
| 71 | USE indices |
|---|
| 72 | USE particle_attributes |
|---|
| 73 | |
|---|
| 74 | IMPLICIT NONE |
|---|
| 75 | |
|---|
| 76 | INTEGER :: i, j, k |
|---|
| 77 | REAL :: dvar_dz, l_stable, phi_m, var_reference |
|---|
| 78 | REAL :: ddzu(1:nzt+1), dd2zu(1:nzt), ddzw(1:nzt+1), & |
|---|
| 79 | l_grid(1:nzt), zu(nzb:nzt+1), zw(nzb:nzt+1) |
|---|
| 80 | REAL, DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: diss, tend |
|---|
| 81 | REAL, DIMENSION(:,:), POINTER :: rif |
|---|
| 82 | REAL, DIMENSION(:,:,:), POINTER :: e, km, var |
|---|
| 83 | REAL, DIMENSION(nzb+1:nzt,nys:nyn) :: dissipation, l, ll |
|---|
| 84 | |
|---|
| 85 | |
|---|
| 86 | ! |
|---|
| 87 | !-- This if clause must be outside the k-loop because otherwise |
|---|
| 88 | !-- runtime errors occur with -C hopt on NEC |
|---|
| 89 | IF ( use_reference ) THEN |
|---|
| 90 | |
|---|
| 91 | DO i = nxl, nxr |
|---|
| 92 | DO j = nys, nyn |
|---|
| 93 | ! |
|---|
| 94 | !-- First, calculate phi-function for eventually adjusting the & |
|---|
| 95 | !-- mixing length to the prandtl mixing length |
|---|
| 96 | IF ( adjust_mixing_length .AND. prandtl_layer ) THEN |
|---|
| 97 | IF ( rif(j,i) >= 0.0 ) THEN |
|---|
| 98 | phi_m = 1.0 + 5.0 * rif(j,i) |
|---|
| 99 | ELSE |
|---|
| 100 | phi_m = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rif(j,i) ) ) |
|---|
| 101 | ENDIF |
|---|
| 102 | ENDIF |
|---|
| 103 | |
|---|
| 104 | DO k = nzb_s_inner(j,i)+1, nzt |
|---|
| 105 | ! |
|---|
| 106 | !-- Calculate the mixing length (for dissipation) |
|---|
| 107 | dvar_dz = atmos_ocean_sign * & |
|---|
| 108 | ( var(k+1,j,i) - var(k-1,j,i) ) * dd2zu(k) |
|---|
| 109 | IF ( dvar_dz > 0.0 ) THEN |
|---|
| 110 | l_stable = 0.76 * SQRT( e(k,j,i) ) / & |
|---|
| 111 | SQRT( g / var_reference * dvar_dz ) + 1E-5 |
|---|
| 112 | ELSE |
|---|
| 113 | l_stable = l_grid(k) |
|---|
| 114 | ENDIF |
|---|
| 115 | ! |
|---|
| 116 | !-- Adjustment of the mixing length |
|---|
| 117 | IF ( wall_adjustment ) THEN |
|---|
| 118 | l(k,j) = MIN( wall_adjustment_factor * & |
|---|
| 119 | ( zu(k) - zw(nzb_s_inner(j,i)) ), & |
|---|
| 120 | l_grid(k), l_stable ) |
|---|
| 121 | ll(k,j) = MIN( wall_adjustment_factor * & |
|---|
| 122 | ( zu(k) - zw(nzb_s_inner(j,i)) ), & |
|---|
| 123 | l_grid(k) ) |
|---|
| 124 | ELSE |
|---|
| 125 | l(k,j) = MIN( l_grid(k), l_stable ) |
|---|
| 126 | ll(k,j) = l_grid(k) |
|---|
| 127 | ENDIF |
|---|
| 128 | IF ( adjust_mixing_length .AND. prandtl_layer ) THEN |
|---|
| 129 | l(k,j) = MIN( l(k,j), kappa * & |
|---|
| 130 | ( zu(k) - zw(nzb_s_inner(j,i)) ) & |
|---|
| 131 | / phi_m ) |
|---|
| 132 | ll(k,j) = MIN( ll(k,j), kappa * & |
|---|
| 133 | ( zu(k) - zw(nzb_s_inner(j,i)) ) & |
|---|
| 134 | / phi_m ) |
|---|
| 135 | ENDIF |
|---|
| 136 | |
|---|
| 137 | ENDDO |
|---|
| 138 | ENDDO |
|---|
| 139 | |
|---|
| 140 | ! |
|---|
| 141 | !-- Calculate the tendency terms |
|---|
| 142 | DO j = nys, nyn |
|---|
| 143 | DO k = nzb_s_inner(j,i)+1, nzt |
|---|
| 144 | |
|---|
| 145 | dissipation(k,j) = ( 0.19 + 0.74 * l(k,j) / ll(k,j) ) * & |
|---|
| 146 | e(k,j,i) * SQRT( e(k,j,i) ) / l(k,j) |
|---|
| 147 | |
|---|
| 148 | tend(k,j,i) = tend(k,j,i) & |
|---|
| 149 | + ( & |
|---|
| 150 | ( km(k,j,i)+km(k,j,i+1) ) * ( e(k,j,i+1)-e(k,j,i) ) & |
|---|
| 151 | - ( km(k,j,i)+km(k,j,i-1) ) * ( e(k,j,i)-e(k,j,i-1) ) & |
|---|
| 152 | ) * ddx2 & |
|---|
| 153 | + ( & |
|---|
| 154 | ( km(k,j,i)+km(k,j+1,i) ) * ( e(k,j+1,i)-e(k,j,i) ) & |
|---|
| 155 | - ( km(k,j,i)+km(k,j-1,i) ) * ( e(k,j,i)-e(k,j-1,i) ) & |
|---|
| 156 | ) * ddy2 & |
|---|
| 157 | + ( & |
|---|
| 158 | ( km(k,j,i)+km(k+1,j,i) ) * ( e(k+1,j,i)-e(k,j,i) ) * ddzu(k+1) & |
|---|
| 159 | - ( km(k,j,i)+km(k-1,j,i) ) * ( e(k,j,i)-e(k-1,j,i) ) * ddzu(k) & |
|---|
| 160 | ) * ddzw(k) & |
|---|
| 161 | - dissipation(k,j) |
|---|
| 162 | |
|---|
| 163 | ENDDO |
|---|
| 164 | ENDDO |
|---|
| 165 | |
|---|
| 166 | ! |
|---|
| 167 | !-- Store dissipation if needed for calculating the sgs particle |
|---|
| 168 | !-- velocities |
|---|
| 169 | IF ( use_sgs_for_particles .OR. wang_kernel ) THEN |
|---|
| 170 | DO j = nys, nyn |
|---|
| 171 | DO k = nzb_s_inner(j,i)+1, nzt |
|---|
| 172 | diss(k,j,i) = dissipation(k,j) |
|---|
| 173 | ENDDO |
|---|
| 174 | ENDDO |
|---|
| 175 | ENDIF |
|---|
| 176 | |
|---|
| 177 | ENDDO |
|---|
| 178 | |
|---|
| 179 | ELSE |
|---|
| 180 | |
|---|
| 181 | DO i = nxl, nxr |
|---|
| 182 | DO j = nys, nyn |
|---|
| 183 | ! |
|---|
| 184 | !-- First, calculate phi-function for eventually adjusting the & |
|---|
| 185 | !-- mixing length to the prandtl mixing length |
|---|
| 186 | IF ( adjust_mixing_length .AND. prandtl_layer ) THEN |
|---|
| 187 | IF ( rif(j,i) >= 0.0 ) THEN |
|---|
| 188 | phi_m = 1.0 + 5.0 * rif(j,i) |
|---|
| 189 | ELSE |
|---|
| 190 | phi_m = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rif(j,i) ) ) |
|---|
| 191 | ENDIF |
|---|
| 192 | ENDIF |
|---|
| 193 | |
|---|
| 194 | DO k = nzb_s_inner(j,i)+1, nzt |
|---|
| 195 | ! |
|---|
| 196 | !-- Calculate the mixing length (for dissipation) |
|---|
| 197 | dvar_dz = atmos_ocean_sign * & |
|---|
| 198 | ( var(k+1,j,i) - var(k-1,j,i) ) * dd2zu(k) |
|---|
| 199 | IF ( dvar_dz > 0.0 ) THEN |
|---|
| 200 | l_stable = 0.76 * SQRT( e(k,j,i) ) / & |
|---|
| 201 | SQRT( g / var(k,j,i) * dvar_dz ) + 1E-5 |
|---|
| 202 | ELSE |
|---|
| 203 | l_stable = l_grid(k) |
|---|
| 204 | ENDIF |
|---|
| 205 | ! |
|---|
| 206 | !-- Adjustment of the mixing length |
|---|
| 207 | IF ( wall_adjustment ) THEN |
|---|
| 208 | l(k,j) = MIN( wall_adjustment_factor * & |
|---|
| 209 | ( zu(k) - zw(nzb_s_inner(j,i)) ), & |
|---|
| 210 | l_grid(k), l_stable ) |
|---|
| 211 | ll(k,j) = MIN( wall_adjustment_factor * & |
|---|
| 212 | ( zu(k) - zw(nzb_s_inner(j,i)) ), & |
|---|
| 213 | l_grid(k) ) |
|---|
| 214 | ELSE |
|---|
| 215 | l(k,j) = MIN( l_grid(k), l_stable ) |
|---|
| 216 | ll(k,j) = l_grid(k) |
|---|
| 217 | ENDIF |
|---|
| 218 | IF ( adjust_mixing_length .AND. prandtl_layer ) THEN |
|---|
| 219 | l(k,j) = MIN( l(k,j), kappa * & |
|---|
| 220 | ( zu(k) - zw(nzb_s_inner(j,i)) ) & |
|---|
| 221 | / phi_m ) |
|---|
| 222 | ll(k,j) = MIN( ll(k,j), kappa * & |
|---|
| 223 | ( zu(k) - zw(nzb_s_inner(j,i)) ) & |
|---|
| 224 | / phi_m ) |
|---|
| 225 | ENDIF |
|---|
| 226 | |
|---|
| 227 | ENDDO |
|---|
| 228 | ENDDO |
|---|
| 229 | |
|---|
| 230 | ! |
|---|
| 231 | !-- Calculate the tendency terms |
|---|
| 232 | DO j = nys, nyn |
|---|
| 233 | DO k = nzb_s_inner(j,i)+1, nzt |
|---|
| 234 | |
|---|
| 235 | dissipation(k,j) = ( 0.19 + 0.74 * l(k,j) / ll(k,j) ) * & |
|---|
| 236 | e(k,j,i) * SQRT( e(k,j,i) ) / l(k,j) |
|---|
| 237 | |
|---|
| 238 | tend(k,j,i) = tend(k,j,i) & |
|---|
| 239 | + ( & |
|---|
| 240 | ( km(k,j,i)+km(k,j,i+1) ) * ( e(k,j,i+1)-e(k,j,i) ) & |
|---|
| 241 | - ( km(k,j,i)+km(k,j,i-1) ) * ( e(k,j,i)-e(k,j,i-1) ) & |
|---|
| 242 | ) * ddx2 & |
|---|
| 243 | + ( & |
|---|
| 244 | ( km(k,j,i)+km(k,j+1,i) ) * ( e(k,j+1,i)-e(k,j,i) ) & |
|---|
| 245 | - ( km(k,j,i)+km(k,j-1,i) ) * ( e(k,j,i)-e(k,j-1,i) ) & |
|---|
| 246 | ) * ddy2 & |
|---|
| 247 | + ( & |
|---|
| 248 | ( km(k,j,i)+km(k+1,j,i) ) * ( e(k+1,j,i)-e(k,j,i) ) * ddzu(k+1) & |
|---|
| 249 | - ( km(k,j,i)+km(k-1,j,i) ) * ( e(k,j,i)-e(k-1,j,i) ) * ddzu(k) & |
|---|
| 250 | ) * ddzw(k) & |
|---|
| 251 | - dissipation(k,j) |
|---|
| 252 | |
|---|
| 253 | ENDDO |
|---|
| 254 | ENDDO |
|---|
| 255 | |
|---|
| 256 | ! |
|---|
| 257 | !-- Store dissipation if needed for calculating the sgs particle |
|---|
| 258 | !-- velocities |
|---|
| 259 | IF ( use_sgs_for_particles .OR. wang_kernel ) THEN |
|---|
| 260 | DO j = nys, nyn |
|---|
| 261 | DO k = nzb_s_inner(j,i)+1, nzt |
|---|
| 262 | diss(k,j,i) = dissipation(k,j) |
|---|
| 263 | ENDDO |
|---|
| 264 | ENDDO |
|---|
| 265 | ENDIF |
|---|
| 266 | |
|---|
| 267 | ENDDO |
|---|
| 268 | |
|---|
| 269 | ENDIF |
|---|
| 270 | |
|---|
| 271 | ! |
|---|
| 272 | !-- Boundary condition for dissipation |
|---|
| 273 | IF ( use_sgs_for_particles .OR. wang_kernel ) THEN |
|---|
| 274 | DO i = nxl, nxr |
|---|
| 275 | DO j = nys, nyn |
|---|
| 276 | diss(nzb_s_inner(j,i),j,i) = diss(nzb_s_inner(j,i)+1,j,i) |
|---|
| 277 | ENDDO |
|---|
| 278 | ENDDO |
|---|
| 279 | ENDIF |
|---|
| 280 | |
|---|
| 281 | END SUBROUTINE diffusion_e |
|---|
| 282 | |
|---|
| 283 | |
|---|
| 284 | !------------------------------------------------------------------------------! |
|---|
| 285 | ! Call for grid point i,j |
|---|
| 286 | !------------------------------------------------------------------------------! |
|---|
| 287 | SUBROUTINE diffusion_e_ij( i, j, ddzu, dd2zu, ddzw, diss, e, km, l_grid, & |
|---|
| 288 | var, var_reference, rif, tend, zu, zw ) |
|---|
| 289 | |
|---|
| 290 | USE control_parameters |
|---|
| 291 | USE grid_variables |
|---|
| 292 | USE indices |
|---|
| 293 | USE particle_attributes |
|---|
| 294 | |
|---|
| 295 | IMPLICIT NONE |
|---|
| 296 | |
|---|
| 297 | INTEGER :: i, j, k |
|---|
| 298 | REAL :: dvar_dz, l_stable, phi_m, var_reference |
|---|
| 299 | REAL :: ddzu(1:nzt+1), dd2zu(1:nzt), ddzw(1:nzt+1), & |
|---|
| 300 | l_grid(1:nzt), zu(nzb:nzt+1), zw(nzb:nzt+1) |
|---|
| 301 | REAL, DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: diss, tend |
|---|
| 302 | REAL, DIMENSION(:,:), POINTER :: rif |
|---|
| 303 | REAL, DIMENSION(:,:,:), POINTER :: e, km, var |
|---|
| 304 | REAL, DIMENSION(nzb+1:nzt) :: dissipation, l, ll |
|---|
| 305 | |
|---|
| 306 | |
|---|
| 307 | ! |
|---|
| 308 | !-- First, calculate phi-function for eventually adjusting the mixing length |
|---|
| 309 | !-- to the prandtl mixing length |
|---|
| 310 | IF ( adjust_mixing_length .AND. prandtl_layer ) THEN |
|---|
| 311 | IF ( rif(j,i) >= 0.0 ) THEN |
|---|
| 312 | phi_m = 1.0 + 5.0 * rif(j,i) |
|---|
| 313 | ELSE |
|---|
| 314 | phi_m = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rif(j,i) ) ) |
|---|
| 315 | ENDIF |
|---|
| 316 | ENDIF |
|---|
| 317 | |
|---|
| 318 | ! |
|---|
| 319 | !-- Calculate the mixing length (for dissipation) |
|---|
| 320 | DO k = nzb_s_inner(j,i)+1, nzt |
|---|
| 321 | dvar_dz = atmos_ocean_sign * & |
|---|
| 322 | ( var(k+1,j,i) - var(k-1,j,i) ) * dd2zu(k) |
|---|
| 323 | IF ( dvar_dz > 0.0 ) THEN |
|---|
| 324 | IF ( use_reference ) THEN |
|---|
| 325 | l_stable = 0.76 * SQRT( e(k,j,i) ) / & |
|---|
| 326 | SQRT( g / var_reference * dvar_dz ) + 1E-5 |
|---|
| 327 | ELSE |
|---|
| 328 | l_stable = 0.76 * SQRT( e(k,j,i) ) / & |
|---|
| 329 | SQRT( g / var(k,j,i) * dvar_dz ) + 1E-5 |
|---|
| 330 | ENDIF |
|---|
| 331 | ELSE |
|---|
| 332 | l_stable = l_grid(k) |
|---|
| 333 | ENDIF |
|---|
| 334 | ! |
|---|
| 335 | !-- Adjustment of the mixing length |
|---|
| 336 | IF ( wall_adjustment ) THEN |
|---|
| 337 | l(k) = MIN( wall_adjustment_factor * & |
|---|
| 338 | ( zu(k) - zw(nzb_s_inner(j,i)) ), l_grid(k), & |
|---|
| 339 | l_stable ) |
|---|
| 340 | ll(k) = MIN( wall_adjustment_factor * & |
|---|
| 341 | ( zu(k) - zw(nzb_s_inner(j,i)) ), l_grid(k) ) |
|---|
| 342 | ELSE |
|---|
| 343 | l(k) = MIN( l_grid(k), l_stable ) |
|---|
| 344 | ll(k) = l_grid(k) |
|---|
| 345 | ENDIF |
|---|
| 346 | IF ( adjust_mixing_length .AND. prandtl_layer ) THEN |
|---|
| 347 | l(k) = MIN( l(k), kappa * & |
|---|
| 348 | ( zu(k) - zw(nzb_s_inner(j,i)) ) / phi_m ) |
|---|
| 349 | ll(k) = MIN( ll(k), kappa * & |
|---|
| 350 | ( zu(k) - zw(nzb_s_inner(j,i)) ) / phi_m ) |
|---|
| 351 | ENDIF |
|---|
| 352 | |
|---|
| 353 | ! |
|---|
| 354 | !-- Calculate the tendency term |
|---|
| 355 | dissipation(k) = ( 0.19 + 0.74 * l(k) / ll(k) ) * e(k,j,i) * & |
|---|
| 356 | SQRT( e(k,j,i) ) / l(k) |
|---|
| 357 | |
|---|
| 358 | tend(k,j,i) = tend(k,j,i) & |
|---|
| 359 | + ( & |
|---|
| 360 | ( km(k,j,i)+km(k,j,i+1) ) * ( e(k,j,i+1)-e(k,j,i) ) & |
|---|
| 361 | - ( km(k,j,i)+km(k,j,i-1) ) * ( e(k,j,i)-e(k,j,i-1) ) & |
|---|
| 362 | ) * ddx2 & |
|---|
| 363 | + ( & |
|---|
| 364 | ( km(k,j,i)+km(k,j+1,i) ) * ( e(k,j+1,i)-e(k,j,i) ) & |
|---|
| 365 | - ( km(k,j,i)+km(k,j-1,i) ) * ( e(k,j,i)-e(k,j-1,i) ) & |
|---|
| 366 | ) * ddy2 & |
|---|
| 367 | + ( & |
|---|
| 368 | ( km(k,j,i)+km(k+1,j,i) ) * ( e(k+1,j,i)-e(k,j,i) ) * ddzu(k+1) & |
|---|
| 369 | - ( km(k,j,i)+km(k-1,j,i) ) * ( e(k,j,i)-e(k-1,j,i) ) * ddzu(k) & |
|---|
| 370 | ) * ddzw(k) & |
|---|
| 371 | - dissipation(k) |
|---|
| 372 | |
|---|
| 373 | ENDDO |
|---|
| 374 | |
|---|
| 375 | ! |
|---|
| 376 | !-- Store dissipation if needed for calculating the sgs particle velocities |
|---|
| 377 | IF ( use_sgs_for_particles .OR. wang_kernel ) THEN |
|---|
| 378 | DO k = nzb_s_inner(j,i)+1, nzt |
|---|
| 379 | diss(k,j,i) = dissipation(k) |
|---|
| 380 | ENDDO |
|---|
| 381 | ! |
|---|
| 382 | !-- Boundary condition for dissipation |
|---|
| 383 | diss(nzb_s_inner(j,i),j,i) = diss(nzb_s_inner(j,i)+1,j,i) |
|---|
| 384 | ENDIF |
|---|
| 385 | |
|---|
| 386 | END SUBROUTINE diffusion_e_ij |
|---|
| 387 | |
|---|
| 388 | END MODULE diffusion_e_mod |
|---|
