Home

Context Navigation

source: palm/trunk/SOURCE/diffusion_v.f90 @ 4250

Last change on this file since 4250 was 4182, checked in by scharf, 5 years ago
corrected "Former revisions" section minor formatting in "Former revisions" section added "Author" section
Property svn:keywords set to `Id`
File size: 23.5 KB

Line
1	!> @file diffusion_v.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of the PALM model system.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the
6	! terms of the GNU General Public License as published by the Free Software
7	! Foundation, either version 3 of the License, or (at your option) any later
8	! version.
9	!
10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
13	!
14	! You should have received a copy of the GNU General Public License along with
15	! PALM. If not, see <http://www.gnu.org/licenses/>.
16	!
17	! Copyright 1997-2019 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: diffusion_v.f90 4182 2019-08-22 15:20:23Z maronga $
27	! Corrected "Former revisions" section
28	!
29	! 3655 2019-01-07 16:51:22Z knoop
30	! OpenACC port for SPEC
31	!
32	! Revision 1.1 1997/09/12 06:24:01 raasch
33	! Initial revision
34	!
35	!
36	! Description:
37	! ------------
38	!> Diffusion term of the v-component
39	!------------------------------------------------------------------------------!
40	MODULE diffusion_v_mod
41
42
43	PRIVATE
44	PUBLIC diffusion_v
45
46	INTERFACE diffusion_v
47	MODULE PROCEDURE diffusion_v
48	MODULE PROCEDURE diffusion_v_ij
49	END INTERFACE diffusion_v
50
51	CONTAINS
52
53
54	!------------------------------------------------------------------------------!
55	! Description:
56	! ------------
57	!> Call for all grid points
58	!------------------------------------------------------------------------------!
59	SUBROUTINE diffusion_v
60
61	USE arrays_3d, &
62	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
63
64	USE control_parameters, &
65	ONLY: constant_top_momentumflux, use_surface_fluxes, &
66	use_top_fluxes
67
68	USE grid_variables, &
69	ONLY: ddx, ddy, ddy2
70
71	USE indices, &
72	ONLY: nxl, nxr, nyn, nysv, nzb, nzt, wall_flags_0
73
74	USE kinds
75
76	USE surface_mod, &
77	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
78	surf_usm_v
79
80	IMPLICIT NONE
81
82	INTEGER(iwp) :: i !< running index x direction
83	INTEGER(iwp) :: j !< running index y direction
84	INTEGER(iwp) :: k !< running index z direction
85	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
86	INTEGER(iwp) :: m !< running index surface elements
87	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
88	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
89
90	REAL(wp) :: flag !< flag to mask topography grid points
91	REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid
92	REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid
93	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto yv-zw grid
94	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto yv-zw grid
95	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
96	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
97	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
98	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
99
100	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k, l, m) &
101	!$ACC PRIVATE(surf_e, surf_s, flag, kmxm, kmxp, kmzm, kmzp) &
102	!$ACC PRIVATE(mask_bottom, mask_east, mask_west, mask_top) &
103	!$ACC PRESENT(wall_flags_0, km) &
104	!$ACC PRESENT(u, v, w) &
105	!$ACC PRESENT(ddzu, ddzw, drho_air, rho_air_zw) &
106	!$ACC PRESENT(surf_def_h(0:2), surf_def_v(2:3)) &
107	!$ACC PRESENT(surf_lsm_h, surf_lsm_v(2:3)) &
108	!$ACC PRESENT(surf_usm_h, surf_usm_v(0:3)) &
109	!$ACC PRESENT(tend)
110	DO i = nxl, nxr
111	DO j = nysv, nyn
112	!
113	!-- Compute horizontal diffusion
114	DO k = nzb+1, nzt
115
116	!
117	!-- Predetermine flag to mask topography and wall-bounded grid points.
118	!-- It is sufficient to masked only east- and west-facing surfaces, which
119	!-- need special treatment for the v-component.
120	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
121	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
122	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
123	!
124	!-- Interpolate eddy diffusivities on staggered gridpoints
125	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
126	kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
127
128	tend(k,j,i) = tend(k,j,i) + ( &
129	mask_east * kmxp * ( &
130	( v(k,j,i+1) - v(k,j,i) ) * ddx &
131	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
132	) &
133	- mask_west * kmxm * ( &
134	( v(k,j,i) - v(k,j,i-1) ) * ddx &
135	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
136	) &
137	) * ddx * flag &
138	+ 2.0_wp * ( &
139	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
140	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
141	) * ddy2 * flag
142
143	ENDDO
144
145	!
146	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
147	!-- surfaces. Note, in the the flat case, loops won't be entered as
148	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
149	!-- so far.
150	!-- Default-type surfaces
151	DO l = 2, 3
152	surf_s = surf_def_v(l)%start_index(j,i)
153	surf_e = surf_def_v(l)%end_index(j,i)
154	DO m = surf_s, surf_e
155	k = surf_def_v(l)%k(m)
156	tend(k,j,i) = tend(k,j,i) + &
157	surf_def_v(l)%mom_flux_uv(m) * ddx
158	ENDDO
159	ENDDO
160	!
161	!-- Natural-type surfaces
162	DO l = 2, 3
163	surf_s = surf_lsm_v(l)%start_index(j,i)
164	surf_e = surf_lsm_v(l)%end_index(j,i)
165	DO m = surf_s, surf_e
166	k = surf_lsm_v(l)%k(m)
167	tend(k,j,i) = tend(k,j,i) + &
168	surf_lsm_v(l)%mom_flux_uv(m) * ddx
169	ENDDO
170	ENDDO
171	!
172	!-- Urban-type surfaces
173	DO l = 2, 3
174	surf_s = surf_usm_v(l)%start_index(j,i)
175	surf_e = surf_usm_v(l)%end_index(j,i)
176	DO m = surf_s, surf_e
177	k = surf_usm_v(l)%k(m)
178	tend(k,j,i) = tend(k,j,i) + &
179	surf_usm_v(l)%mom_flux_uv(m) * ddx
180	ENDDO
181	ENDDO
182	!
183	!-- Compute vertical diffusion. In case of simulating a surface layer,
184	!-- respective grid diffusive fluxes are masked (flag 10) within this
185	!-- loop, and added further below, else, simple gradient approach is
186	!-- applied. Model top is also mask if top-momentum flux is given.
187	DO k = nzb+1, nzt
188	!
189	!-- Determine flags to mask topography below and above. Flag 2 is
190	!-- used to mask topography in general, while flag 8 implies also
191	!-- information about use_surface_fluxes. Flag 9 is used to control
192	!-- momentum flux at model top.
193	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
194	BTEST( wall_flags_0(k-1,j,i), 8 ) )
195	mask_top = MERGE( 1.0_wp, 0.0_wp, &
196	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
197	MERGE( 1.0_wp, 0.0_wp, &
198	BTEST( wall_flags_0(k+1,j,i), 9 ) )
199	flag = MERGE( 1.0_wp, 0.0_wp, &
200	BTEST( wall_flags_0(k,j,i), 2 ) )
201	!
202	!-- Interpolate eddy diffusivities on staggered gridpoints
203	kmzp = 0.25_wp * &
204	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
205	kmzm = 0.25_wp * &
206	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
207
208	tend(k,j,i) = tend(k,j,i) &
209	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
210	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
211	& ) * rho_air_zw(k) * mask_top &
212	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
213	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
214	& ) * rho_air_zw(k-1) * mask_bottom &
215	& ) * ddzw(k) * drho_air(k) * flag
216	ENDDO
217
218	!
219	!-- Vertical diffusion at the first grid point above the surface,
220	!-- if the momentum flux at the bottom is given by the Prandtl law
221	!-- or if it is prescribed by the user.
222	!-- Difference quotient of the momentum flux is not formed over
223	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
224	!-- comparison with other (LES) models showed that the values of
225	!-- the momentum flux becomes too large in this case.
226	IF ( use_surface_fluxes ) THEN
227	!
228	!-- Default-type surfaces, upward-facing
229	surf_s = surf_def_h(0)%start_index(j,i)
230	surf_e = surf_def_h(0)%end_index(j,i)
231	DO m = surf_s, surf_e
232	k = surf_def_h(0)%k(m)
233
234	tend(k,j,i) = tend(k,j,i) &
235	+ ( - ( - surf_def_h(0)%vsws(m) ) &
236	) * ddzw(k) * drho_air(k)
237	ENDDO
238	!
239	!-- Default-type surfaces, dowward-facing
240	surf_s = surf_def_h(1)%start_index(j,i)
241	surf_e = surf_def_h(1)%end_index(j,i)
242	DO m = surf_s, surf_e
243	k = surf_def_h(1)%k(m)
244
245	tend(k,j,i) = tend(k,j,i) &
246	+ ( - surf_def_h(1)%vsws(m) &
247	) * ddzw(k) * drho_air(k)
248	ENDDO
249	!
250	!-- Natural-type surfaces, upward-facing
251	surf_s = surf_lsm_h%start_index(j,i)
252	surf_e = surf_lsm_h%end_index(j,i)
253	DO m = surf_s, surf_e
254	k = surf_lsm_h%k(m)
255
256	tend(k,j,i) = tend(k,j,i) &
257	+ ( - ( - surf_lsm_h%vsws(m) ) &
258	) * ddzw(k) * drho_air(k)
259
260	ENDDO
261	!
262	!-- Urban-type surfaces, upward-facing
263	surf_s = surf_usm_h%start_index(j,i)
264	surf_e = surf_usm_h%end_index(j,i)
265	DO m = surf_s, surf_e
266	k = surf_usm_h%k(m)
267
268	tend(k,j,i) = tend(k,j,i) &
269	+ ( - ( - surf_usm_h%vsws(m) ) &
270	) * ddzw(k) * drho_air(k)
271
272	ENDDO
273	ENDIF
274	!
275	!-- Add momentum flux at model top
276	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
277	surf_s = surf_def_h(2)%start_index(j,i)
278	surf_e = surf_def_h(2)%end_index(j,i)
279	DO m = surf_s, surf_e
280
281	k = surf_def_h(2)%k(m)
282
283	tend(k,j,i) = tend(k,j,i) &
284	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
285	ENDDO
286	ENDIF
287
288	ENDDO
289	ENDDO
290
291	END SUBROUTINE diffusion_v
292
293
294	!------------------------------------------------------------------------------!
295	! Description:
296	! ------------
297	!> Call for grid point i,j
298	!------------------------------------------------------------------------------!
299	SUBROUTINE diffusion_v_ij( i, j )
300
301	USE arrays_3d, &
302	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
303
304	USE control_parameters, &
305	ONLY: constant_top_momentumflux, use_surface_fluxes, &
306	use_top_fluxes
307
308	USE grid_variables, &
309	ONLY: ddx, ddy, ddy2
310
311	USE indices, &
312	ONLY: nzb, nzt, wall_flags_0
313
314	USE kinds
315
316	USE surface_mod, &
317	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
318	surf_usm_v
319
320	IMPLICIT NONE
321
322
323	INTEGER(iwp) :: i !< running index x direction
324	INTEGER(iwp) :: j !< running index y direction
325	INTEGER(iwp) :: k !< running index z direction
326	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
327	INTEGER(iwp) :: m !< running index surface elements
328	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
329	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
330
331	REAL(wp) :: flag !< flag to mask topography grid points
332	REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid
333	REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid
334	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
335	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
336	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
337	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
338	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
339	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
340
341	!
342	!-- Compute horizontal diffusion
343	DO k = nzb+1, nzt
344	!
345	!-- Predetermine flag to mask topography and wall-bounded grid points.
346	!-- It is sufficient to masked only east- and west-facing surfaces, which
347	!-- need special treatment for the v-component.
348	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
349	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
350	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
351	!
352	!-- Interpolate eddy diffusivities on staggered gridpoints
353	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
354	kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
355
356	tend(k,j,i) = tend(k,j,i) + ( &
357	mask_east * kmxp * ( &
358	( v(k,j,i+1) - v(k,j,i) ) * ddx &
359	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
360	) &
361	- mask_west * kmxm * ( &
362	( v(k,j,i) - v(k,j,i-1) ) * ddx &
363	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
364	) &
365	) * ddx * flag &
366	+ 2.0_wp * ( &
367	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
368	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
369	) * ddy2 * flag
370	ENDDO
371
372	!
373	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
374	!-- surfaces. Note, in the the flat case, loops won't be entered as
375	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
376	!-- so far.
377	!-- Default-type surfaces
378	DO l = 2, 3
379	surf_s = surf_def_v(l)%start_index(j,i)
380	surf_e = surf_def_v(l)%end_index(j,i)
381	DO m = surf_s, surf_e
382	k = surf_def_v(l)%k(m)
383	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx
384	ENDDO
385	ENDDO
386	!
387	!-- Natural-type surfaces
388	DO l = 2, 3
389	surf_s = surf_lsm_v(l)%start_index(j,i)
390	surf_e = surf_lsm_v(l)%end_index(j,i)
391	DO m = surf_s, surf_e
392	k = surf_lsm_v(l)%k(m)
393	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx
394	ENDDO
395	ENDDO
396	!
397	!-- Urban-type surfaces
398	DO l = 2, 3
399	surf_s = surf_usm_v(l)%start_index(j,i)
400	surf_e = surf_usm_v(l)%end_index(j,i)
401	DO m = surf_s, surf_e
402	k = surf_usm_v(l)%k(m)
403	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx
404	ENDDO
405	ENDDO
406	!
407	!-- Compute vertical diffusion. In case of simulating a surface layer,
408	!-- respective grid diffusive fluxes are masked (flag 8) within this
409	!-- loop, and added further below, else, simple gradient approach is
410	!-- applied. Model top is also mask if top-momentum flux is given.
411	DO k = nzb+1, nzt
412	!
413	!-- Determine flags to mask topography below and above. Flag 2 is
414	!-- used to mask topography in general, while flag 10 implies also
415	!-- information about use_surface_fluxes. Flag 9 is used to control
416	!-- momentum flux at model top.
417	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
418	BTEST( wall_flags_0(k-1,j,i), 8 ) )
419	mask_top = MERGE( 1.0_wp, 0.0_wp, &
420	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
421	MERGE( 1.0_wp, 0.0_wp, &
422	BTEST( wall_flags_0(k+1,j,i), 9 ) )
423	flag = MERGE( 1.0_wp, 0.0_wp, &
424	BTEST( wall_flags_0(k,j,i), 2 ) )
425	!
426	!-- Interpolate eddy diffusivities on staggered gridpoints
427	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
428	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
429
430	tend(k,j,i) = tend(k,j,i) &
431	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
432	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
433	& ) * rho_air_zw(k) * mask_top &
434	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
435	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
436	& ) * rho_air_zw(k-1) * mask_bottom &
437	& ) * ddzw(k) * drho_air(k) * flag
438	ENDDO
439
440	!
441	!-- Vertical diffusion at the first grid point above the surface, if the
442	!-- momentum flux at the bottom is given by the Prandtl law or if it is
443	!-- prescribed by the user.
444	!-- Difference quotient of the momentum flux is not formed over half of
445	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
446	!-- other (LES) models showed that the values of the momentum flux becomes
447	!-- too large in this case.
448	IF ( use_surface_fluxes ) THEN
449	!
450	!-- Default-type surfaces, upward-facing
451	surf_s = surf_def_h(0)%start_index(j,i)
452	surf_e = surf_def_h(0)%end_index(j,i)
453	DO m = surf_s, surf_e
454	k = surf_def_h(0)%k(m)
455
456	tend(k,j,i) = tend(k,j,i) &
457	+ ( - ( - surf_def_h(0)%vsws(m) ) &
458	) * ddzw(k) * drho_air(k)
459	ENDDO
460	!
461	!-- Default-type surfaces, dowward-facing
462	surf_s = surf_def_h(1)%start_index(j,i)
463	surf_e = surf_def_h(1)%end_index(j,i)
464	DO m = surf_s, surf_e
465	k = surf_def_h(1)%k(m)
466
467	tend(k,j,i) = tend(k,j,i) &
468	+ ( - surf_def_h(1)%vsws(m) &
469	) * ddzw(k) * drho_air(k)
470	ENDDO
471	!
472	!-- Natural-type surfaces, upward-facing
473	surf_s = surf_lsm_h%start_index(j,i)
474	surf_e = surf_lsm_h%end_index(j,i)
475	DO m = surf_s, surf_e
476	k = surf_lsm_h%k(m)
477
478	tend(k,j,i) = tend(k,j,i) &
479	+ ( - ( - surf_lsm_h%vsws(m) ) &
480	) * ddzw(k) * drho_air(k)
481
482	ENDDO
483	!
484	!-- Urban-type surfaces, upward-facing
485	surf_s = surf_usm_h%start_index(j,i)
486	surf_e = surf_usm_h%end_index(j,i)
487	DO m = surf_s, surf_e
488	k = surf_usm_h%k(m)
489
490	tend(k,j,i) = tend(k,j,i) &
491	+ ( - ( - surf_usm_h%vsws(m) ) &
492	) * ddzw(k) * drho_air(k)
493
494	ENDDO
495	ENDIF
496	!
497	!-- Add momentum flux at model top
498	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
499	surf_s = surf_def_h(2)%start_index(j,i)
500	surf_e = surf_def_h(2)%end_index(j,i)
501	DO m = surf_s, surf_e
502
503	k = surf_def_h(2)%k(m)
504
505	tend(k,j,i) = tend(k,j,i) &
506	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
507	ENDDO
508	ENDIF
509
510	END SUBROUTINE diffusion_v_ij
511
512	END MODULE diffusion_v_mod

Note: See TracBrowser for help on using the repository browser.

Download in other formats:

| Impressum | ©Leibniz Universität Hannover |