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source: palm/trunk/SOURCE/diffusion_u.f90 @ 4590

Last change on this file since 4590 was 4583, checked in by raasch, 4 years ago
files re-formatted to follow the PALM coding standard
Property svn:keywords set to `Id`
File size: 23.7 KB

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1	!> @file diffusion_u.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 terms of the GNU General
6	! Public License as published by the Free Software Foundation, either version 3 of the License, or
7	! (at your option) any later version.
8	!
9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the
10	! implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
11	! Public License for more details.
12	!
13	! You should have received a copy of the GNU General Public License along with PALM. If not, see
14	! <http://www.gnu.org/licenses/>.
15	!
16	! Copyright 1997-2020 Leibniz Universitaet Hannover
17	!--------------------------------------------------------------------------------------------------!
18	!
19	! Current revisions:
20	! -----------------
21	!
22	!
23	! Former revisions:
24	! -----------------
25	! $Id: diffusion_u.f90 4583 2020-06-29 12:36:47Z suehring $
26	! file re-formatted to follow the PALM coding standard
27	!
28	! 4360 2020-01-07 11:25:50Z suehring
29	! Introduction of wall_flags_total_0, which currently sets bits based on static topography
30	! information used in wall_flags_static_0
31	!
32	! 4329 2019-12-10 15:46:36Z motisi
33	! Renamed wall_flags_0 to wall_flags_static_0
34	!
35	! 4182 2019-08-22 15:20:23Z scharf
36	! Corrected "Former revisions" section
37	!
38	! 3655 2019-01-07 16:51:22Z knoop
39	! OpenACC port for SPEC
40	!
41	! Revision 1.1 1997/09/12 06:23:51 raasch
42	! Initial revision
43	!
44	!
45	! Description:
46	! ------------
47	!> Diffusion term of the u-component
48	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization and slows down the
49	! speed on NEC about 5-10%
50	!--------------------------------------------------------------------------------------------------!
51	MODULE diffusion_u_mod
52
53
54	PRIVATE
55	PUBLIC diffusion_u
56
57	INTERFACE diffusion_u
58	MODULE PROCEDURE diffusion_u
59	MODULE PROCEDURE diffusion_u_ij
60	END INTERFACE diffusion_u
61
62	CONTAINS
63
64
65	!--------------------------------------------------------------------------------------------------!
66	! Description:
67	! ------------
68	!> Call for all grid points
69	!--------------------------------------------------------------------------------------------------!
70	SUBROUTINE diffusion_u
71
72	USE arrays_3d, &
73	ONLY: ddzu, ddzw, drho_air, km, rho_air_zw, tend, u, v, w
74
75	USE control_parameters, &
76	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
77
78	USE grid_variables, &
79	ONLY: ddx, ddx2, ddy
80
81	USE indices, &
82	ONLY: nxlu, nxr, nyn, nys, nzb, nzt, wall_flags_total_0
83
84	USE kinds
85
86	USE surface_mod, &
87	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, surf_usm_v
88
89	IMPLICIT NONE
90
91	INTEGER(iwp) :: i !< running index x direction
92	INTEGER(iwp) :: j !< running index y direction
93	INTEGER(iwp) :: k !< running index z direction
94	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
95	INTEGER(iwp) :: m !< running index surface elements
96	INTEGER(iwp) :: surf_e !< end index of surface elements at (j,i)-gridpoint
97	INTEGER(iwp) :: surf_s !< start index of surface elements at (j,i)-gridpoint
98
99	REAL(wp) :: flag !< flag to mask topography grid points
100	REAL(wp) :: kmym !< diffusion coefficient on southward side of the u-gridbox - interpolated onto xu-yv grid
101	REAL(wp) :: kmyp !< diffusion coefficient on northward side of the u-gridbox - interpolated onto xu-yv grid
102	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
103	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
104	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
105	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
106	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
107	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
108
109
110
111	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k, l, m) &
112	!$ACC PRIVATE(surf_e, surf_s, flag, kmym, kmyp, kmzm, kmzp) &
113	!$ACC PRIVATE(mask_bottom, mask_north, mask_south, mask_top) &
114	!$ACC PRESENT(wall_flags_total_0, km) &
115	!$ACC PRESENT(u, v, w) &
116	!$ACC PRESENT(ddzu, ddzw, drho_air, rho_air_zw) &
117	!$ACC PRESENT(surf_def_h(0:2), surf_def_v(0:1)) &
118	!$ACC PRESENT(surf_lsm_h, surf_lsm_v(0:1)) &
119	!$ACC PRESENT(surf_usm_h, surf_usm_v(0:1)) &
120	!$ACC PRESENT(tend)
121	DO i = nxlu, nxr
122	DO j = nys, nyn
123	!
124	!-- Compute horizontal diffusion
125	DO k = nzb+1, nzt
126	!
127	!-- Predetermine flag to mask topography and wall-bounded grid points.
128	!-- It is sufficient to masked only north- and south-facing surfaces, which need special
129	!-- treatment for the u-component.
130	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
131	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j-1,i), 1 ) )
132	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j+1,i), 1 ) )
133	!
134	!-- Interpolate eddy diffusivities on staggered gridpoints
135	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
136	kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
137
138	tend(k,j,i) = tend(k,j,i) &
139	+ 2.0_wp * ( &
140	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
141	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
142	) * ddx2 * flag &
143	+ ( mask_north * ( &
144	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
145	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
146	) &
147	- mask_south * ( &
148	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
149	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
150	) &
151	) * ddy * flag
152	ENDDO
153	!
154	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1) surfaces.
155	!-- Note, in the the flat case, loops won't be entered as start_index > end_index.
156	!-- Furtermore, note, no vertical natural surfaces so far.
157	!-- Default-type surfaces
158	DO l = 0, 1
159	surf_s = surf_def_v(l)%start_index(j,i)
160	surf_e = surf_def_v(l)%end_index(j,i)
161	DO m = surf_s, surf_e
162	k = surf_def_v(l)%k(m)
163	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy
164	ENDDO
165	ENDDO
166	!
167	!-- Natural-type surfaces
168	DO l = 0, 1
169	surf_s = surf_lsm_v(l)%start_index(j,i)
170	surf_e = surf_lsm_v(l)%end_index(j,i)
171	DO m = surf_s, surf_e
172	k = surf_lsm_v(l)%k(m)
173	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy
174	ENDDO
175	ENDDO
176	!
177	!-- Urban-type surfaces
178	DO l = 0, 1
179	surf_s = surf_usm_v(l)%start_index(j,i)
180	surf_e = surf_usm_v(l)%end_index(j,i)
181	DO m = surf_s, surf_e
182	k = surf_usm_v(l)%k(m)
183	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy
184	ENDDO
185	ENDDO
186
187	!
188	!-- Compute vertical diffusion. In case of simulating a surface layer, respective grid
189	!-- diffusive fluxes are masked (flag 8) within this loop, and added further below, else,
190	!-- simple gradient approach is applied. Model top is also mask if top-momentum flux is
191	!-- given.
192	DO k = nzb+1, nzt
193	!
194	!-- Determine flags to mask topography below and above. Flag 1 is used to mask
195	!-- topography in general, and flag 8 implies information about use_surface_fluxes.
196	!-- Flag 9 is used to control momentum flux at model top.
197	mask_bottom = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k-1,j,i), 8 ) )
198	mask_top = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k+1,j,i), 8 ) ) * &
199	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k+1,j,i), 9 ) )
200	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
201	!
202	!-- Interpolate eddy diffusivities on staggered gridpoints
203	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
204	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
205
206	tend(k,j,i) = tend(k,j,i) &
207	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
208	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
209	) * rho_air_zw(k) * mask_top &
210	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
211	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
212	) * rho_air_zw(k-1) * mask_bottom &
213	) * ddzw(k) * drho_air(k) * flag
214	ENDDO
215
216	!
217	!-- Vertical diffusion at the first grid point above the surface, if the momentum flux at
218	!-- the bottom is given by the Prandtl law or if it is prescribed by the user.
219	!-- Difference quotient of the momentum flux is not formed over half of the grid spacing
220	!-- (2.0*ddzw(k)) any more, since the comparison with other (LES) models showed that the
221	!-- values of the momentum flux becomes too large in this case.
222	!-- The term containing w(k-1,..) (see above equation) is removed here because the vertical
223	!-- velocity is assumed to be zero at the surface.
224	IF ( use_surface_fluxes ) THEN
225	!
226	!-- Default-type surfaces, upward-facing
227	surf_s = surf_def_h(0)%start_index(j,i)
228	surf_e = surf_def_h(0)%end_index(j,i)
229	DO m = surf_s, surf_e
230
231	k = surf_def_h(0)%k(m)
232
233	tend(k,j,i) = tend(k,j,i) &
234	+ ( - ( - surf_def_h(0)%usws(m) ) ) * ddzw(k) * drho_air(k)
235	ENDDO
236	!
237	!-- Default-type surfaces, dowward-facing
238	surf_s = surf_def_h(1)%start_index(j,i)
239	surf_e = surf_def_h(1)%end_index(j,i)
240	DO m = surf_s, surf_e
241
242	k = surf_def_h(1)%k(m)
243
244	tend(k,j,i) = tend(k,j,i) &
245	+ ( - surf_def_h(1)%usws(m) ) * ddzw(k) * drho_air(k)
246	ENDDO
247	!
248	!-- Natural-type surfaces, upward-facing
249	surf_s = surf_lsm_h%start_index(j,i)
250	surf_e = surf_lsm_h%end_index(j,i)
251	DO m = surf_s, surf_e
252
253	k = surf_lsm_h%k(m)
254
255	tend(k,j,i) = tend(k,j,i) &
256	+ ( - ( - surf_lsm_h%usws(m) ) ) * ddzw(k) * drho_air(k)
257	ENDDO
258	!
259	!-- Urban-type surfaces, upward-facing
260	surf_s = surf_usm_h%start_index(j,i)
261	surf_e = surf_usm_h%end_index(j,i)
262	DO m = surf_s, surf_e
263
264	k = surf_usm_h%k(m)
265
266	tend(k,j,i) = tend(k,j,i) &
267	+ ( - ( - surf_usm_h%usws(m) ) ) * ddzw(k) * drho_air(k)
268	ENDDO
269
270	ENDIF
271	!
272	!-- Add momentum flux at model top
273	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
274	surf_s = surf_def_h(2)%start_index(j,i)
275	surf_e = surf_def_h(2)%end_index(j,i)
276	DO m = surf_s, surf_e
277
278	k = surf_def_h(2)%k(m)
279
280	tend(k,j,i) = tend(k,j,i) &
281	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
282	ENDDO
283	ENDIF
284
285	ENDDO
286	ENDDO
287
288	END SUBROUTINE diffusion_u
289
290
291	!--------------------------------------------------------------------------------------------------!
292	! Description:
293	! ------------
294	!> Call for grid point i,j
295	!--------------------------------------------------------------------------------------------------!
296	SUBROUTINE diffusion_u_ij( i, j )
297
298	USE arrays_3d, &
299	ONLY: ddzu, ddzw, drho_air, km, tend, u, v, w, rho_air_zw
300
301	USE control_parameters, &
302	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
303
304	USE grid_variables, &
305	ONLY: ddx, ddx2, ddy
306
307	USE indices, &
308	ONLY: nzb, nzt, wall_flags_total_0
309
310	USE kinds
311
312	USE surface_mod, &
313	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, surf_usm_v
314
315	IMPLICIT NONE
316
317	INTEGER(iwp) :: i !< running index x direction
318	INTEGER(iwp) :: j !< running index y direction
319	INTEGER(iwp) :: k !< running index z direction
320	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
321	INTEGER(iwp) :: m !< running index surface elements
322	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
323	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
324
325	REAL(wp) :: flag !< flag to mask topography grid points
326	REAL(wp) :: kmym !< diffusion coefficient on southward side of the u-gridbox - interpolated onto xu-yv grid
327	REAL(wp) :: kmyp !<diffusion coefficient on northward side of the u-gridbox - interpolated onto xu-yv grid
328	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
329	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
330	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
331	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
332	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
333	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
334	!
335	!-- Compute horizontal diffusion
336	DO k = nzb+1, nzt
337	!
338	!-- Predetermine flag to mask topography and wall-bounded grid points.
339	!-- It is sufficient to masked only north- and south-facing surfaces, which need special
340	!-- treatment for the u-component.
341	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
342	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j-1,i), 1 ) )
343	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j+1,i), 1 ) )
344	!
345	!-- Interpolate eddy diffusivities on staggered gridpoints
346	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
347	kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
348
349	tend(k,j,i) = tend(k,j,i) &
350	+ 2.0_wp * ( &
351	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
352	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
353	) * ddx2 * flag &
354	+ ( &
355	mask_north * kmyp * ( ( u(k,j+1,i) - u(k,j,i) ) * ddy &
356	+ ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
357	) &
358	- mask_south * kmym * ( ( u(k,j,i) - u(k,j-1,i) ) * ddy &
359	+ ( v(k,j,i) - v(k,j,i-1) ) * ddx &
360	) &
361	) * ddy * flag
362	ENDDO
363
364	!
365	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1) surfaces. Note, in
366	!-- the the flat case, loops won't be entered as start_index > end_index. Furtermore, note, no
367	!-- vertical natural surfaces so far.
368	!-- Default-type surfaces
369	DO l = 0, 1
370	surf_s = surf_def_v(l)%start_index(j,i)
371	surf_e = surf_def_v(l)%end_index(j,i)
372	DO m = surf_s, surf_e
373	k = surf_def_v(l)%k(m)
374	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy
375	ENDDO
376	ENDDO
377	!
378	!-- Natural-type surfaces
379	DO l = 0, 1
380	surf_s = surf_lsm_v(l)%start_index(j,i)
381	surf_e = surf_lsm_v(l)%end_index(j,i)
382	DO m = surf_s, surf_e
383	k = surf_lsm_v(l)%k(m)
384	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy
385	ENDDO
386	ENDDO
387	!
388	!-- Urban-type surfaces
389	DO l = 0, 1
390	surf_s = surf_usm_v(l)%start_index(j,i)
391	surf_e = surf_usm_v(l)%end_index(j,i)
392	DO m = surf_s, surf_e
393	k = surf_usm_v(l)%k(m)
394	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy
395	ENDDO
396	ENDDO
397	!
398	!-- Compute vertical diffusion. In case of simulating a surface layer, respective grid diffusive
399	!-- fluxes are masked (flag 8) within this loop, and added further below, else, simple gradient
400	!-- approach is applied. Model top is also mask if top-momentum flux is given.
401	DO k = nzb+1, nzt
402	!
403	!-- Determine flags to mask topography below and above. Flag 1 is used to mask topography in
404	!-- general, and flag 8 implies information about use_surface_fluxes. Flag 9 is used to
405	!-- control momentum flux at model top.
406	mask_bottom = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k-1,j,i), 8 ) )
407	mask_top = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k+1,j,i), 8 ) ) * &
408	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k+1,j,i), 9 ) )
409	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
410	!
411	!-- Interpolate eddy diffusivities on staggered gridpoints
412	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
413	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
414
415	tend(k,j,i) = tend(k,j,i) &
416	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
417	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
418	) * rho_air_zw(k) * mask_top &
419	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
420	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
421	) * rho_air_zw(k-1) * mask_bottom &
422	) * ddzw(k) * drho_air(k) * flag
423	ENDDO
424
425	!
426	!-- Vertical diffusion at the first surface grid points, if the momentum flux at the bottom is
427	!-- given by the Prandtl law or if it is prescribed by the user.
428	!-- Difference quotient of the momentum flux is not formed over half of the grid spacing
429	!-- (2.0*ddzw(k)) any more, since the comparison with other (LES) models showed that the values
430	!-- of the momentum flux becomes too large in this case.
431	IF ( use_surface_fluxes ) THEN
432	!
433	!-- Default-type surfaces, upward-facing
434	surf_s = surf_def_h(0)%start_index(j,i)
435	surf_e = surf_def_h(0)%end_index(j,i)
436	DO m = surf_s, surf_e
437
438	k = surf_def_h(0)%k(m)
439
440	tend(k,j,i) = tend(k,j,i) + ( - ( - surf_def_h(0)%usws(m) ) ) * ddzw(k) * drho_air(k)
441	ENDDO
442	!
443	!-- Default-type surfaces, dowward-facing (except for model-top fluxes)
444	surf_s = surf_def_h(1)%start_index(j,i)
445	surf_e = surf_def_h(1)%end_index(j,i)
446	DO m = surf_s, surf_e
447
448	k = surf_def_h(1)%k(m)
449
450	tend(k,j,i) = tend(k,j,i) + ( - surf_def_h(1)%usws(m) ) * ddzw(k) * drho_air(k)
451	ENDDO
452	!
453	!-- Natural-type surfaces, upward-facing
454	surf_s = surf_lsm_h%start_index(j,i)
455	surf_e = surf_lsm_h%end_index(j,i)
456	DO m = surf_s, surf_e
457
458	k = surf_lsm_h%k(m)
459
460	tend(k,j,i) = tend(k,j,i) + ( - ( - surf_lsm_h%usws(m) ) ) * ddzw(k) * drho_air(k)
461	ENDDO
462	!
463	!-- Urban-type surfaces, upward-facing
464	surf_s = surf_usm_h%start_index(j,i)
465	surf_e = surf_usm_h%end_index(j,i)
466	DO m = surf_s, surf_e
467
468	k = surf_usm_h%k(m)
469
470	tend(k,j,i) = tend(k,j,i) + ( - ( - surf_usm_h%usws(m) ) ) * ddzw(k) * drho_air(k)
471	ENDDO
472
473	ENDIF
474	!
475	!-- Add momentum flux at model top
476	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
477	surf_s = surf_def_h(2)%start_index(j,i)
478	surf_e = surf_def_h(2)%end_index(j,i)
479	DO m = surf_s, surf_e
480
481	k = surf_def_h(2)%k(m)
482
483	tend(k,j,i) = tend(k,j,i) + ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
484	ENDDO
485	ENDIF
486
487
488	END SUBROUTINE diffusion_u_ij
489
490	END MODULE diffusion_u_mod

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