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source: palm/trunk/SOURCE/boundary_conds.f90 @ 2322

Last change on this file since 2322 was 2320, checked in by suehring, 7 years ago
large-scale forcing and nudging modularized
Property svn:keywords set to `Id`
File size: 39.3 KB

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1	!> @file boundary_conds.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of PALM.
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 1997-2017 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: boundary_conds.f90 2320 2017-07-21 12:47:43Z Giersch $
27	! Remove unused control parameter large_scale_forcing from only-list
28	!
29	! 2292 2017-06-20 09:51:42Z schwenkel
30	! Implementation of new microphysic scheme: cloud_scheme = 'morrison'
31	! includes two more prognostic equations for cloud drop concentration (nc)
32	! and cloud water content (qc).
33	!
34	! 2233 2017-05-30 18:08:54Z suehring
35	!
36	! 2232 2017-05-30 17:47:52Z suehring
37	! Set boundary conditions on topography top using flag method.
38	!
39	! 2118 2017-01-17 16:38:49Z raasch
40	! OpenACC directives removed
41	!
42	! 2000 2016-08-20 18:09:15Z knoop
43	! Forced header and separation lines into 80 columns
44	!
45	! 1992 2016-08-12 15:14:59Z suehring
46	! Adjustments for top boundary condition for passive scalar
47	!
48	! 1960 2016-07-12 16:34:24Z suehring
49	! Treat humidity and passive scalar separately
50	!
51	! 1823 2016-04-07 08:57:52Z hoffmann
52	! Initial version of purely vertical nesting introduced.
53	!
54	! 1822 2016-04-07 07:49:42Z hoffmann
55	! icloud_scheme removed. microphyisics_seifert added.
56	!
57	! 1764 2016-02-28 12:45:19Z raasch
58	! index bug for u_p at left outflow removed
59	!
60	! 1762 2016-02-25 12:31:13Z hellstea
61	! Introduction of nested domain feature
62	!
63	! 1742 2016-01-13 09:50:06Z raasch
64	! bugfix for outflow Neumann boundary conditions at bottom and top
65	!
66	! 1717 2015-11-11 15:09:47Z raasch
67	! Bugfix: index error in outflow conditions for left boundary
68	!
69	! 1682 2015-10-07 23:56:08Z knoop
70	! Code annotations made doxygen readable
71	!
72	! 1410 2014-05-23 12:16:18Z suehring
73	! Bugfix: set dirichlet boundary condition for passive_scalar at model domain
74	! top
75	!
76	! 1399 2014-05-07 11:16:25Z heinze
77	! Bugfix: set inflow boundary conditions also if no humidity or passive_scalar
78	! is used.
79	!
80	! 1398 2014-05-07 11:15:00Z heinze
81	! Dirichlet-condition at the top for u and v changed to u_init and v_init also
82	! for large_scale_forcing
83	!
84	! 1380 2014-04-28 12:40:45Z heinze
85	! Adjust Dirichlet-condition at the top for pt in case of nudging
86	!
87	! 1361 2014-04-16 15:17:48Z hoffmann
88	! Bottom and top boundary conditions of rain water content (qr) and
89	! rain drop concentration (nr) changed to Dirichlet
90	!
91	! 1353 2014-04-08 15:21:23Z heinze
92	! REAL constants provided with KIND-attribute
93	!
94	! 1320 2014-03-20 08:40:49Z raasch
95	! ONLY-attribute added to USE-statements,
96	! kind-parameters added to all INTEGER and REAL declaration statements,
97	! kinds are defined in new module kinds,
98	! revision history before 2012 removed,
99	! comment fields (!:) to be used for variable explanations added to
100	! all variable declaration statements
101	!
102	! 1257 2013-11-08 15:18:40Z raasch
103	! loop independent clauses added
104	!
105	! 1241 2013-10-30 11:36:58Z heinze
106	! Adjust ug and vg at each timestep in case of large_scale_forcing
107	!
108	! 1159 2013-05-21 11:58:22Z fricke
109	! Bugfix: Neumann boundary conditions for the velocity components at the
110	! outflow are in fact radiation boundary conditions using the maximum phase
111	! velocity that ensures numerical stability (CFL-condition).
112	! Hence, logical operator use_cmax is now used instead of bc_lr_dirneu/_neudir.
113	! Bugfix: In case of use_cmax at the outflow, u, v, w are replaced by
114	! u_p, v_p, w_p
115	!
116	! 1115 2013-03-26 18:16:16Z hoffmann
117	! boundary conditions of two-moment cloud scheme are restricted to Neumann-
118	! boundary-conditions
119	!
120	! 1113 2013-03-10 02:48:14Z raasch
121	! GPU-porting
122	! dummy argument "range" removed
123	! Bugfix: wrong index in loops of radiation boundary condition
124	!
125	! 1053 2012-11-13 17:11:03Z hoffmann
126	! boundary conditions for the two new prognostic equations (nr, qr) of the
127	! two-moment cloud scheme
128	!
129	! 1036 2012-10-22 13:43:42Z raasch
130	! code put under GPL (PALM 3.9)
131	!
132	! 996 2012-09-07 10:41:47Z raasch
133	! little reformatting
134	!
135	! 978 2012-08-09 08:28:32Z fricke
136	! Neumann boudnary conditions are added at the inflow boundary for the SGS-TKE.
137	! Outflow boundary conditions for the velocity components can be set to Neumann
138	! conditions or to radiation conditions with a horizontal averaged phase
139	! velocity.
140	!
141	! 875 2012-04-02 15:35:15Z gryschka
142	! Bugfix in case of dirichlet inflow bc at the right or north boundary
143	!
144	! Revision 1.1 1997/09/12 06:21:34 raasch
145	! Initial revision
146	!
147	!
148	! Description:
149	! ------------
150	!> Boundary conditions for the prognostic quantities.
151	!> One additional bottom boundary condition is applied for the TKE (=(u)*2)
152	!> in prandtl_fluxes. The cyclic lateral boundary conditions are implicitly
153	!> handled in routine exchange_horiz. Pressure boundary conditions are
154	!> explicitly set in routines pres, poisfft, poismg and sor.
155	!------------------------------------------------------------------------------!
156	SUBROUTINE boundary_conds
157
158
159	USE arrays_3d, &
160	ONLY: c_u, c_u_m, c_u_m_l, c_v, c_v_m, c_v_m_l, c_w, c_w_m, c_w_m_l, &
161	dzu, e_p, nc_p, nr_p, pt, pt_p, q, q_p, qc_p, qr_p, s, s_p, sa, &
162	sa_p, u, ug, u_init, u_m_l, u_m_n, u_m_r, u_m_s, u_p, &
163	v, vg, v_init, v_m_l, v_m_n, v_m_r, v_m_s, v_p, &
164	w, w_p, w_m_l, w_m_n, w_m_r, w_m_s, pt_init
165
166	USE control_parameters, &
167	ONLY: bc_pt_t_val, bc_q_t_val, bc_s_t_val, constant_diffusion, &
168	cloud_physics, dt_3d, humidity, &
169	ibc_pt_b, ibc_pt_t, ibc_q_b, ibc_q_t, ibc_s_b, ibc_s_t, &
170	ibc_sa_t, ibc_uv_b, ibc_uv_t, inflow_l, inflow_n, inflow_r, &
171	inflow_s, intermediate_timestep_count, &
172	microphysics_morrison, microphysics_seifert, nest_domain, &
173	nest_bound_l, nest_bound_s, nudging, ocean, outflow_l, &
174	outflow_n, outflow_r, outflow_s, passive_scalar, tsc, use_cmax
175
176	USE grid_variables, &
177	ONLY: ddx, ddy, dx, dy
178
179	USE indices, &
180	ONLY: nx, nxl, nxlg, nxr, nxrg, ny, nyn, nyng, nys, nysg, &
181	nzb, nzt, wall_flags_0
182
183	USE kinds
184
185	USE pegrid
186
187	USE pmc_interface, &
188	ONLY : nesting_mode
189
190	USE surface_mod, &
191	ONLY : bc_h
192
193	IMPLICIT NONE
194
195	INTEGER(iwp) :: i !< grid index x direction
196	INTEGER(iwp) :: j !< grid index y direction
197	INTEGER(iwp) :: k !< grid index z direction
198	INTEGER(iwp) :: kb !< variable to set respective boundary value, depends on facing.
199	INTEGER(iwp) :: l !< running index boundary type, for up- and downward-facing walls
200	INTEGER(iwp) :: m !< running index surface elements
201
202	REAL(wp) :: c_max !<
203	REAL(wp) :: denom !<
204
205
206	!
207	!-- Bottom boundary
208	IF ( ibc_uv_b == 1 ) THEN
209	u_p(nzb,:,:) = u_p(nzb+1,:,:)
210	v_p(nzb,:,:) = v_p(nzb+1,:,:)
211	ENDIF
212	!
213	!-- Set zero vertical velocity at topography top (l=0), or bottom (l=1) in case
214	!-- of downward-facing surfaces.
215	DO l = 0, 1
216	!
217	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
218	!-- for downward-facing surfaces at topography bottom (k+1).
219	kb = MERGE( -1, 1, l == 0 )
220	!$OMP PARALLEL DO PRIVATE( i, j, k )
221	DO m = 1, bc_h(l)%ns
222	i = bc_h(l)%i(m)
223	j = bc_h(l)%j(m)
224	k = bc_h(l)%k(m)
225	w_p(k+kb,j,i) = 0.0_wp
226	ENDDO
227	ENDDO
228
229	!
230	!-- Top boundary. A nested domain ( ibc_uv_t = 3 ) does not require settings.
231	IF ( ibc_uv_t == 0 ) THEN
232	u_p(nzt+1,:,:) = u_init(nzt+1)
233	v_p(nzt+1,:,:) = v_init(nzt+1)
234	ELSEIF ( ibc_uv_t == 1 ) THEN
235	u_p(nzt+1,:,:) = u_p(nzt,:,:)
236	v_p(nzt+1,:,:) = v_p(nzt,:,:)
237	ENDIF
238
239	IF ( .NOT. nest_domain ) THEN
240	w_p(nzt:nzt+1,:,:) = 0.0_wp ! nzt is not a prognostic level (but cf. pres)
241	ENDIF
242
243	!
244	!-- Temperature at bottom and top boundary.
245	!-- In case of coupled runs (ibc_pt_b = 2) the temperature is given by
246	!-- the sea surface temperature of the coupled ocean model.
247	!-- Dirichlet
248	IF ( ibc_pt_b == 0 ) THEN
249	DO l = 0, 1
250	!
251	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
252	!-- for downward-facing surfaces at topography bottom (k+1).
253	kb = MERGE( -1, 1, l == 0 )
254	!$OMP PARALLEL DO PRIVATE( i, j, k )
255	DO m = 1, bc_h(l)%ns
256	i = bc_h(l)%i(m)
257	j = bc_h(l)%j(m)
258	k = bc_h(l)%k(m)
259	pt_p(k+kb,j,i) = pt(k+kb,j,i)
260	ENDDO
261	ENDDO
262	!
263	!-- Neumann, zero-gradient
264	ELSEIF ( ibc_pt_b == 1 ) THEN
265	DO l = 0, 1
266	!
267	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
268	!-- for downward-facing surfaces at topography bottom (k+1).
269	kb = MERGE( -1, 1, l == 0 )
270	!$OMP PARALLEL DO PRIVATE( i, j, k )
271	DO m = 1, bc_h(l)%ns
272	i = bc_h(l)%i(m)
273	j = bc_h(l)%j(m)
274	k = bc_h(l)%k(m)
275	pt_p(k+kb,j,i) = pt_p(k,j,i)
276	ENDDO
277	ENDDO
278	ENDIF
279
280	!
281	!-- Temperature at top boundary
282	IF ( ibc_pt_t == 0 ) THEN
283	pt_p(nzt+1,:,:) = pt(nzt+1,:,:)
284	!
285	!-- In case of nudging adjust top boundary to pt which is
286	!-- read in from NUDGING-DATA
287	IF ( nudging ) THEN
288	pt_p(nzt+1,:,:) = pt_init(nzt+1)
289	ENDIF
290	ELSEIF ( ibc_pt_t == 1 ) THEN
291	pt_p(nzt+1,:,:) = pt_p(nzt,:,:)
292	ELSEIF ( ibc_pt_t == 2 ) THEN
293	pt_p(nzt+1,:,:) = pt_p(nzt,:,:) + bc_pt_t_val * dzu(nzt+1)
294	ENDIF
295
296	!
297	!-- Boundary conditions for TKE
298	!-- Generally Neumann conditions with de/dz=0 are assumed
299	IF ( .NOT. constant_diffusion ) THEN
300
301	DO l = 0, 1
302	!
303	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
304	!-- for downward-facing surfaces at topography bottom (k+1).
305	kb = MERGE( -1, 1, l == 0 )
306	!$OMP PARALLEL DO PRIVATE( i, j, k )
307	DO m = 1, bc_h(l)%ns
308	i = bc_h(l)%i(m)
309	j = bc_h(l)%j(m)
310	k = bc_h(l)%k(m)
311	e_p(k+kb,j,i) = e_p(k,j,i)
312	ENDDO
313	ENDDO
314
315	IF ( .NOT. nest_domain ) THEN
316	e_p(nzt+1,:,:) = e_p(nzt,:,:)
317	ENDIF
318	ENDIF
319
320	!
321	!-- Boundary conditions for salinity
322	IF ( ocean ) THEN
323	!
324	!-- Bottom boundary: Neumann condition because salinity flux is always
325	!-- given.
326	DO l = 0, 1
327	!
328	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
329	!-- for downward-facing surfaces at topography bottom (k+1).
330	kb = MERGE( -1, 1, l == 0 )
331	!$OMP PARALLEL DO PRIVATE( i, j, k )
332	DO m = 1, bc_h(l)%ns
333	i = bc_h(l)%i(m)
334	j = bc_h(l)%j(m)
335	k = bc_h(l)%k(m)
336	sa_p(k+kb,j,i) = sa_p(k,j,i)
337	ENDDO
338	ENDDO
339	!
340	!-- Top boundary: Dirichlet or Neumann
341	IF ( ibc_sa_t == 0 ) THEN
342	sa_p(nzt+1,:,:) = sa(nzt+1,:,:)
343	ELSEIF ( ibc_sa_t == 1 ) THEN
344	sa_p(nzt+1,:,:) = sa_p(nzt,:,:)
345	ENDIF
346
347	ENDIF
348
349	!
350	!-- Boundary conditions for total water content,
351	!-- bottom and top boundary (see also temperature)
352	IF ( humidity ) THEN
353	!
354	!-- Surface conditions for constant_humidity_flux
355	!-- Run loop over all non-natural and natural walls. Note, in wall-datatype
356	!-- the k coordinate belongs to the atmospheric grid point, therefore, set
357	!-- q_p at k-1
358	IF ( ibc_q_b == 0 ) THEN
359
360	DO l = 0, 1
361	!
362	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
363	!-- for downward-facing surfaces at topography bottom (k+1).
364	kb = MERGE( -1, 1, l == 0 )
365	!$OMP PARALLEL DO PRIVATE( i, j, k )
366	DO m = 1, bc_h(l)%ns
367	i = bc_h(l)%i(m)
368	j = bc_h(l)%j(m)
369	k = bc_h(l)%k(m)
370	q_p(k+kb,j,i) = q(k+kb,j,i)
371	ENDDO
372	ENDDO
373
374	ELSE
375	!$OMP PARALLEL DO PRIVATE( i, j, k )
376	DO m = 1, bc_h(0)%ns
377	i = bc_h(0)%i(m)
378	j = bc_h(0)%j(m)
379	k = bc_h(0)%k(m)
380	q_p(k-1,j,i) = q_p(k,j,i)
381	ENDDO
382
383	DO l = 0, 1
384	!
385	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
386	!-- for downward-facing surfaces at topography bottom (k+1).
387	kb = MERGE( -1, 1, l == 0 )
388	!$OMP PARALLEL DO PRIVATE( i, j, k )
389	DO m = 1, bc_h(l)%ns
390	i = bc_h(l)%i(m)
391	j = bc_h(l)%j(m)
392	k = bc_h(l)%k(m)
393	q_p(k+kb,j,i) = q_p(k,j,i)
394	ENDDO
395	ENDDO
396	ENDIF
397	!
398	!-- Top boundary
399	IF ( ibc_q_t == 0 ) THEN
400	q_p(nzt+1,:,:) = q(nzt+1,:,:)
401	ELSEIF ( ibc_q_t == 1 ) THEN
402	q_p(nzt+1,:,:) = q_p(nzt,:,:) + bc_q_t_val * dzu(nzt+1)
403	ENDIF
404
405	IF ( cloud_physics .AND. microphysics_morrison ) THEN
406	!
407	!-- Surface conditions cloud water (Dirichlet)
408	!-- Run loop over all non-natural and natural walls. Note, in wall-datatype
409	!-- the k coordinate belongs to the atmospheric grid point, therefore, set
410	!-- qr_p and nr_p at k-1
411	!$OMP PARALLEL DO PRIVATE( i, j, k )
412	DO m = 1, bc_h(0)%ns
413	i = bc_h(0)%i(m)
414	j = bc_h(0)%j(m)
415	k = bc_h(0)%k(m)
416	qc_p(k-1,j,i) = 0.0_wp
417	nc_p(k-1,j,i) = 0.0_wp
418	ENDDO
419	!
420	!-- Top boundary condition for cloud water (Dirichlet)
421	qc_p(nzt+1,:,:) = 0.0_wp
422	nc_p(nzt+1,:,:) = 0.0_wp
423
424	ENDIF
425
426	IF ( cloud_physics .AND. microphysics_seifert ) THEN
427	!
428	!-- Surface conditions rain water (Dirichlet)
429	!-- Run loop over all non-natural and natural walls. Note, in wall-datatype
430	!-- the k coordinate belongs to the atmospheric grid point, therefore, set
431	!-- qr_p and nr_p at k-1
432	!$OMP PARALLEL DO PRIVATE( i, j, k )
433	DO m = 1, bc_h(0)%ns
434	i = bc_h(0)%i(m)
435	j = bc_h(0)%j(m)
436	k = bc_h(0)%k(m)
437	qr_p(k-1,j,i) = 0.0_wp
438	nr_p(k-1,j,i) = 0.0_wp
439	ENDDO
440	!
441	!-- Top boundary condition for rain water (Dirichlet)
442	qr_p(nzt+1,:,:) = 0.0_wp
443	nr_p(nzt+1,:,:) = 0.0_wp
444
445	ENDIF
446	ENDIF
447	!
448	!-- Boundary conditions for scalar,
449	!-- bottom and top boundary (see also temperature)
450	IF ( passive_scalar ) THEN
451	!
452	!-- Surface conditions for constant_humidity_flux
453	!-- Run loop over all non-natural and natural walls. Note, in wall-datatype
454	!-- the k coordinate belongs to the atmospheric grid point, therefore, set
455	!-- s_p at k-1
456	IF ( ibc_s_b == 0 ) THEN
457
458	DO l = 0, 1
459	!
460	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
461	!-- for downward-facing surfaces at topography bottom (k+1).
462	kb = MERGE( -1, 1, l == 0 )
463	!$OMP PARALLEL DO PRIVATE( i, j, k )
464	DO m = 1, bc_h(l)%ns
465	i = bc_h(l)%i(m)
466	j = bc_h(l)%j(m)
467	k = bc_h(l)%k(m)
468	s_p(k+kb,j,i) = s(k+kb,j,i)
469	ENDDO
470	ENDDO
471
472	ELSE
473	!$OMP PARALLEL DO PRIVATE( i, j, k )
474	DO m = 1, bc_h(0)%ns
475	i = bc_h(0)%i(m)
476	j = bc_h(0)%j(m)
477	k = bc_h(0)%k(m)
478	s_p(k-1,j,i) = s_p(k,j,i)
479	ENDDO
480
481	DO l = 0, 1
482	!
483	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
484	!-- for downward-facing surfaces at topography bottom (k+1).
485	kb = MERGE( -1, 1, l == 0 )
486	!$OMP PARALLEL DO PRIVATE( i, j, k )
487	DO m = 1, bc_h(l)%ns
488	i = bc_h(l)%i(m)
489	j = bc_h(l)%j(m)
490	k = bc_h(l)%k(m)
491	s_p(k+kb,j,i) = s_p(k,j,i)
492	ENDDO
493	ENDDO
494	ENDIF
495	!
496	!-- Top boundary condition
497	IF ( ibc_s_t == 0 ) THEN
498	s_p(nzt+1,:,:) = s(nzt+1,:,:)
499	ELSEIF ( ibc_s_t == 1 ) THEN
500	s_p(nzt+1,:,:) = s_p(nzt,:,:)
501	ELSEIF ( ibc_s_t == 2 ) THEN
502	s_p(nzt+1,:,:) = s_p(nzt,:,:) + bc_s_t_val * dzu(nzt+1)
503	ENDIF
504
505	ENDIF
506	!
507	!-- In case of inflow or nest boundary at the south boundary the boundary for v
508	!-- is at nys and in case of inflow or nest boundary at the left boundary the
509	!-- boundary for u is at nxl. Since in prognostic_equations (cache optimized
510	!-- version) these levels are handled as a prognostic level, boundary values
511	!-- have to be restored here.
512	!-- For the SGS-TKE, Neumann boundary conditions are used at the inflow.
513	IF ( inflow_s ) THEN
514	v_p(:,nys,:) = v_p(:,nys-1,:)
515	IF ( .NOT. constant_diffusion ) e_p(:,nys-1,:) = e_p(:,nys,:)
516	ELSEIF ( inflow_n ) THEN
517	IF ( .NOT. constant_diffusion ) e_p(:,nyn+1,:) = e_p(:,nyn,:)
518	ELSEIF ( inflow_l ) THEN
519	u_p(:,:,nxl) = u_p(:,:,nxl-1)
520	IF ( .NOT. constant_diffusion ) e_p(:,:,nxl-1) = e_p(:,:,nxl)
521	ELSEIF ( inflow_r ) THEN
522	IF ( .NOT. constant_diffusion ) e_p(:,:,nxr+1) = e_p(:,:,nxr)
523	ENDIF
524
525	!
526	!-- The same restoration for u at i=nxl and v at j=nys as above must be made
527	!-- in case of nest boundaries. This must not be done in case of vertical nesting
528	!-- mode as in that case the lateral boundaries are actually cyclic.
529	IF ( nesting_mode /= 'vertical' ) THEN
530	IF ( nest_bound_s ) THEN
531	v_p(:,nys,:) = v_p(:,nys-1,:)
532	ENDIF
533	IF ( nest_bound_l ) THEN
534	u_p(:,:,nxl) = u_p(:,:,nxl-1)
535	ENDIF
536	ENDIF
537
538	!
539	!-- Lateral boundary conditions for scalar quantities at the outflow
540	IF ( outflow_s ) THEN
541	pt_p(:,nys-1,:) = pt_p(:,nys,:)
542	IF ( .NOT. constant_diffusion ) e_p(:,nys-1,:) = e_p(:,nys,:)
543	IF ( humidity ) THEN
544	q_p(:,nys-1,:) = q_p(:,nys,:)
545	IF ( cloud_physics .AND. microphysics_morrison ) THEN
546	qc_p(:,nys-1,:) = qc_p(:,nys,:)
547	nc_p(:,nys-1,:) = nc_p(:,nys,:)
548	ENDIF
549	IF ( cloud_physics .AND. microphysics_seifert ) THEN
550	qr_p(:,nys-1,:) = qr_p(:,nys,:)
551	nr_p(:,nys-1,:) = nr_p(:,nys,:)
552	ENDIF
553	ENDIF
554	IF ( passive_scalar ) s_p(:,nys-1,:) = s_p(:,nys,:)
555	ELSEIF ( outflow_n ) THEN
556	pt_p(:,nyn+1,:) = pt_p(:,nyn,:)
557	IF ( .NOT. constant_diffusion ) e_p(:,nyn+1,:) = e_p(:,nyn,:)
558	IF ( humidity ) THEN
559	q_p(:,nyn+1,:) = q_p(:,nyn,:)
560	IF ( cloud_physics .AND. microphysics_morrison ) THEN
561	qc_p(:,nyn+1,:) = qc_p(:,nyn,:)
562	nc_p(:,nyn+1,:) = nc_p(:,nyn,:)
563	ENDIF
564	IF ( cloud_physics .AND. microphysics_seifert ) THEN
565	qr_p(:,nyn+1,:) = qr_p(:,nyn,:)
566	nr_p(:,nyn+1,:) = nr_p(:,nyn,:)
567	ENDIF
568	ENDIF
569	IF ( passive_scalar ) s_p(:,nyn+1,:) = s_p(:,nyn,:)
570	ELSEIF ( outflow_l ) THEN
571	pt_p(:,:,nxl-1) = pt_p(:,:,nxl)
572	IF ( .NOT. constant_diffusion ) e_p(:,:,nxl-1) = e_p(:,:,nxl)
573	IF ( humidity ) THEN
574	q_p(:,:,nxl-1) = q_p(:,:,nxl)
575	IF ( cloud_physics .AND. microphysics_morrison ) THEN
576	qc_p(:,:,nxl-1) = qc_p(:,:,nxl)
577	nc_p(:,:,nxl-1) = nc_p(:,:,nxl)
578	ENDIF
579	IF ( cloud_physics .AND. microphysics_seifert ) THEN
580	qr_p(:,:,nxl-1) = qr_p(:,:,nxl)
581	nr_p(:,:,nxl-1) = nr_p(:,:,nxl)
582	ENDIF
583	ENDIF
584	IF ( passive_scalar ) s_p(:,:,nxl-1) = s_p(:,:,nxl)
585	ELSEIF ( outflow_r ) THEN
586	pt_p(:,:,nxr+1) = pt_p(:,:,nxr)
587	IF ( .NOT. constant_diffusion ) e_p(:,:,nxr+1) = e_p(:,:,nxr)
588	IF ( humidity ) THEN
589	q_p(:,:,nxr+1) = q_p(:,:,nxr)
590	IF ( cloud_physics .AND. microphysics_morrison ) THEN
591	qc_p(:,:,nxr+1) = qc_p(:,:,nxr)
592	nc_p(:,:,nxr+1) = nc_p(:,:,nxr)
593	ENDIF
594	IF ( cloud_physics .AND. microphysics_seifert ) THEN
595	qr_p(:,:,nxr+1) = qr_p(:,:,nxr)
596	nr_p(:,:,nxr+1) = nr_p(:,:,nxr)
597	ENDIF
598	ENDIF
599	IF ( passive_scalar ) s_p(:,:,nxr+1) = s_p(:,:,nxr)
600	ENDIF
601
602	!
603	!-- Radiation boundary conditions for the velocities at the respective outflow.
604	!-- The phase velocity is either assumed to the maximum phase velocity that
605	!-- ensures numerical stability (CFL-condition) or calculated after
606	!-- Orlanski(1976) and averaged along the outflow boundary.
607	IF ( outflow_s ) THEN
608
609	IF ( use_cmax ) THEN
610	u_p(:,-1,:) = u(:,0,:)
611	v_p(:,0,:) = v(:,1,:)
612	w_p(:,-1,:) = w(:,0,:)
613	ELSEIF ( .NOT. use_cmax ) THEN
614
615	c_max = dy / dt_3d
616
617	c_u_m_l = 0.0_wp
618	c_v_m_l = 0.0_wp
619	c_w_m_l = 0.0_wp
620
621	c_u_m = 0.0_wp
622	c_v_m = 0.0_wp
623	c_w_m = 0.0_wp
624
625	!
626	!-- Calculate the phase speeds for u, v, and w, first local and then
627	!-- average along the outflow boundary.
628	DO k = nzb+1, nzt+1
629	DO i = nxl, nxr
630
631	denom = u_m_s(k,0,i) - u_m_s(k,1,i)
632
633	IF ( denom /= 0.0_wp ) THEN
634	c_u(k,i) = -c_max * ( u(k,0,i) - u_m_s(k,0,i) ) / ( denom * tsc(2) )
635	IF ( c_u(k,i) < 0.0_wp ) THEN
636	c_u(k,i) = 0.0_wp
637	ELSEIF ( c_u(k,i) > c_max ) THEN
638	c_u(k,i) = c_max
639	ENDIF
640	ELSE
641	c_u(k,i) = c_max
642	ENDIF
643
644	denom = v_m_s(k,1,i) - v_m_s(k,2,i)
645
646	IF ( denom /= 0.0_wp ) THEN
647	c_v(k,i) = -c_max * ( v(k,1,i) - v_m_s(k,1,i) ) / ( denom * tsc(2) )
648	IF ( c_v(k,i) < 0.0_wp ) THEN
649	c_v(k,i) = 0.0_wp
650	ELSEIF ( c_v(k,i) > c_max ) THEN
651	c_v(k,i) = c_max
652	ENDIF
653	ELSE
654	c_v(k,i) = c_max
655	ENDIF
656
657	denom = w_m_s(k,0,i) - w_m_s(k,1,i)
658
659	IF ( denom /= 0.0_wp ) THEN
660	c_w(k,i) = -c_max * ( w(k,0,i) - w_m_s(k,0,i) ) / ( denom * tsc(2) )
661	IF ( c_w(k,i) < 0.0_wp ) THEN
662	c_w(k,i) = 0.0_wp
663	ELSEIF ( c_w(k,i) > c_max ) THEN
664	c_w(k,i) = c_max
665	ENDIF
666	ELSE
667	c_w(k,i) = c_max
668	ENDIF
669
670	c_u_m_l(k) = c_u_m_l(k) + c_u(k,i)
671	c_v_m_l(k) = c_v_m_l(k) + c_v(k,i)
672	c_w_m_l(k) = c_w_m_l(k) + c_w(k,i)
673
674	ENDDO
675	ENDDO
676
677	#if defined( __parallel )
678	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
679	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
680	MPI_SUM, comm1dx, ierr )
681	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
682	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
683	MPI_SUM, comm1dx, ierr )
684	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
685	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
686	MPI_SUM, comm1dx, ierr )
687	#else
688	c_u_m = c_u_m_l
689	c_v_m = c_v_m_l
690	c_w_m = c_w_m_l
691	#endif
692
693	c_u_m = c_u_m / (nx+1)
694	c_v_m = c_v_m / (nx+1)
695	c_w_m = c_w_m / (nx+1)
696
697	!
698	!-- Save old timelevels for the next timestep
699	IF ( intermediate_timestep_count == 1 ) THEN
700	u_m_s(:,:,:) = u(:,0:1,:)
701	v_m_s(:,:,:) = v(:,1:2,:)
702	w_m_s(:,:,:) = w(:,0:1,:)
703	ENDIF
704
705	!
706	!-- Calculate the new velocities
707	DO k = nzb+1, nzt+1
708	DO i = nxlg, nxrg
709	u_p(k,-1,i) = u(k,-1,i) - dt_3d * tsc(2) * c_u_m(k) * &
710	( u(k,-1,i) - u(k,0,i) ) * ddy
711
712	v_p(k,0,i) = v(k,0,i) - dt_3d * tsc(2) * c_v_m(k) * &
713	( v(k,0,i) - v(k,1,i) ) * ddy
714
715	w_p(k,-1,i) = w(k,-1,i) - dt_3d * tsc(2) * c_w_m(k) * &
716	( w(k,-1,i) - w(k,0,i) ) * ddy
717	ENDDO
718	ENDDO
719
720	!
721	!-- Bottom boundary at the outflow
722	IF ( ibc_uv_b == 0 ) THEN
723	u_p(nzb,-1,:) = 0.0_wp
724	v_p(nzb,0,:) = 0.0_wp
725	ELSE
726	u_p(nzb,-1,:) = u_p(nzb+1,-1,:)
727	v_p(nzb,0,:) = v_p(nzb+1,0,:)
728	ENDIF
729	w_p(nzb,-1,:) = 0.0_wp
730
731	!
732	!-- Top boundary at the outflow
733	IF ( ibc_uv_t == 0 ) THEN
734	u_p(nzt+1,-1,:) = u_init(nzt+1)
735	v_p(nzt+1,0,:) = v_init(nzt+1)
736	ELSE
737	u_p(nzt+1,-1,:) = u_p(nzt,-1,:)
738	v_p(nzt+1,0,:) = v_p(nzt,0,:)
739	ENDIF
740	w_p(nzt:nzt+1,-1,:) = 0.0_wp
741
742	ENDIF
743
744	ENDIF
745
746	IF ( outflow_n ) THEN
747
748	IF ( use_cmax ) THEN
749	u_p(:,ny+1,:) = u(:,ny,:)
750	v_p(:,ny+1,:) = v(:,ny,:)
751	w_p(:,ny+1,:) = w(:,ny,:)
752	ELSEIF ( .NOT. use_cmax ) THEN
753
754	c_max = dy / dt_3d
755
756	c_u_m_l = 0.0_wp
757	c_v_m_l = 0.0_wp
758	c_w_m_l = 0.0_wp
759
760	c_u_m = 0.0_wp
761	c_v_m = 0.0_wp
762	c_w_m = 0.0_wp
763
764	!
765	!-- Calculate the phase speeds for u, v, and w, first local and then
766	!-- average along the outflow boundary.
767	DO k = nzb+1, nzt+1
768	DO i = nxl, nxr
769
770	denom = u_m_n(k,ny,i) - u_m_n(k,ny-1,i)
771
772	IF ( denom /= 0.0_wp ) THEN
773	c_u(k,i) = -c_max * ( u(k,ny,i) - u_m_n(k,ny,i) ) / ( denom * tsc(2) )
774	IF ( c_u(k,i) < 0.0_wp ) THEN
775	c_u(k,i) = 0.0_wp
776	ELSEIF ( c_u(k,i) > c_max ) THEN
777	c_u(k,i) = c_max
778	ENDIF
779	ELSE
780	c_u(k,i) = c_max
781	ENDIF
782
783	denom = v_m_n(k,ny,i) - v_m_n(k,ny-1,i)
784
785	IF ( denom /= 0.0_wp ) THEN
786	c_v(k,i) = -c_max * ( v(k,ny,i) - v_m_n(k,ny,i) ) / ( denom * tsc(2) )
787	IF ( c_v(k,i) < 0.0_wp ) THEN
788	c_v(k,i) = 0.0_wp
789	ELSEIF ( c_v(k,i) > c_max ) THEN
790	c_v(k,i) = c_max
791	ENDIF
792	ELSE
793	c_v(k,i) = c_max
794	ENDIF
795
796	denom = w_m_n(k,ny,i) - w_m_n(k,ny-1,i)
797
798	IF ( denom /= 0.0_wp ) THEN
799	c_w(k,i) = -c_max * ( w(k,ny,i) - w_m_n(k,ny,i) ) / ( denom * tsc(2) )
800	IF ( c_w(k,i) < 0.0_wp ) THEN
801	c_w(k,i) = 0.0_wp
802	ELSEIF ( c_w(k,i) > c_max ) THEN
803	c_w(k,i) = c_max
804	ENDIF
805	ELSE
806	c_w(k,i) = c_max
807	ENDIF
808
809	c_u_m_l(k) = c_u_m_l(k) + c_u(k,i)
810	c_v_m_l(k) = c_v_m_l(k) + c_v(k,i)
811	c_w_m_l(k) = c_w_m_l(k) + c_w(k,i)
812
813	ENDDO
814	ENDDO
815
816	#if defined( __parallel )
817	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
818	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
819	MPI_SUM, comm1dx, ierr )
820	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
821	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
822	MPI_SUM, comm1dx, ierr )
823	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
824	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
825	MPI_SUM, comm1dx, ierr )
826	#else
827	c_u_m = c_u_m_l
828	c_v_m = c_v_m_l
829	c_w_m = c_w_m_l
830	#endif
831
832	c_u_m = c_u_m / (nx+1)
833	c_v_m = c_v_m / (nx+1)
834	c_w_m = c_w_m / (nx+1)
835
836	!
837	!-- Save old timelevels for the next timestep
838	IF ( intermediate_timestep_count == 1 ) THEN
839	u_m_n(:,:,:) = u(:,ny-1:ny,:)
840	v_m_n(:,:,:) = v(:,ny-1:ny,:)
841	w_m_n(:,:,:) = w(:,ny-1:ny,:)
842	ENDIF
843
844	!
845	!-- Calculate the new velocities
846	DO k = nzb+1, nzt+1
847	DO i = nxlg, nxrg
848	u_p(k,ny+1,i) = u(k,ny+1,i) - dt_3d * tsc(2) * c_u_m(k) * &
849	( u(k,ny+1,i) - u(k,ny,i) ) * ddy
850
851	v_p(k,ny+1,i) = v(k,ny+1,i) - dt_3d * tsc(2) * c_v_m(k) * &
852	( v(k,ny+1,i) - v(k,ny,i) ) * ddy
853
854	w_p(k,ny+1,i) = w(k,ny+1,i) - dt_3d * tsc(2) * c_w_m(k) * &
855	( w(k,ny+1,i) - w(k,ny,i) ) * ddy
856	ENDDO
857	ENDDO
858
859	!
860	!-- Bottom boundary at the outflow
861	IF ( ibc_uv_b == 0 ) THEN
862	u_p(nzb,ny+1,:) = 0.0_wp
863	v_p(nzb,ny+1,:) = 0.0_wp
864	ELSE
865	u_p(nzb,ny+1,:) = u_p(nzb+1,ny+1,:)
866	v_p(nzb,ny+1,:) = v_p(nzb+1,ny+1,:)
867	ENDIF
868	w_p(nzb,ny+1,:) = 0.0_wp
869
870	!
871	!-- Top boundary at the outflow
872	IF ( ibc_uv_t == 0 ) THEN
873	u_p(nzt+1,ny+1,:) = u_init(nzt+1)
874	v_p(nzt+1,ny+1,:) = v_init(nzt+1)
875	ELSE
876	u_p(nzt+1,ny+1,:) = u_p(nzt,nyn+1,:)
877	v_p(nzt+1,ny+1,:) = v_p(nzt,nyn+1,:)
878	ENDIF
879	w_p(nzt:nzt+1,ny+1,:) = 0.0_wp
880
881	ENDIF
882
883	ENDIF
884
885	IF ( outflow_l ) THEN
886
887	IF ( use_cmax ) THEN
888	u_p(:,:,0) = u(:,:,1)
889	v_p(:,:,-1) = v(:,:,0)
890	w_p(:,:,-1) = w(:,:,0)
891	ELSEIF ( .NOT. use_cmax ) THEN
892
893	c_max = dx / dt_3d
894
895	c_u_m_l = 0.0_wp
896	c_v_m_l = 0.0_wp
897	c_w_m_l = 0.0_wp
898
899	c_u_m = 0.0_wp
900	c_v_m = 0.0_wp
901	c_w_m = 0.0_wp
902
903	!
904	!-- Calculate the phase speeds for u, v, and w, first local and then
905	!-- average along the outflow boundary.
906	DO k = nzb+1, nzt+1
907	DO j = nys, nyn
908
909	denom = u_m_l(k,j,1) - u_m_l(k,j,2)
910
911	IF ( denom /= 0.0_wp ) THEN
912	c_u(k,j) = -c_max * ( u(k,j,1) - u_m_l(k,j,1) ) / ( denom * tsc(2) )
913	IF ( c_u(k,j) < 0.0_wp ) THEN
914	c_u(k,j) = 0.0_wp
915	ELSEIF ( c_u(k,j) > c_max ) THEN
916	c_u(k,j) = c_max
917	ENDIF
918	ELSE
919	c_u(k,j) = c_max
920	ENDIF
921
922	denom = v_m_l(k,j,0) - v_m_l(k,j,1)
923
924	IF ( denom /= 0.0_wp ) THEN
925	c_v(k,j) = -c_max * ( v(k,j,0) - v_m_l(k,j,0) ) / ( denom * tsc(2) )
926	IF ( c_v(k,j) < 0.0_wp ) THEN
927	c_v(k,j) = 0.0_wp
928	ELSEIF ( c_v(k,j) > c_max ) THEN
929	c_v(k,j) = c_max
930	ENDIF
931	ELSE
932	c_v(k,j) = c_max
933	ENDIF
934
935	denom = w_m_l(k,j,0) - w_m_l(k,j,1)
936
937	IF ( denom /= 0.0_wp ) THEN
938	c_w(k,j) = -c_max * ( w(k,j,0) - w_m_l(k,j,0) ) / ( denom * tsc(2) )
939	IF ( c_w(k,j) < 0.0_wp ) THEN
940	c_w(k,j) = 0.0_wp
941	ELSEIF ( c_w(k,j) > c_max ) THEN
942	c_w(k,j) = c_max
943	ENDIF
944	ELSE
945	c_w(k,j) = c_max
946	ENDIF
947
948	c_u_m_l(k) = c_u_m_l(k) + c_u(k,j)
949	c_v_m_l(k) = c_v_m_l(k) + c_v(k,j)
950	c_w_m_l(k) = c_w_m_l(k) + c_w(k,j)
951
952	ENDDO
953	ENDDO
954
955	#if defined( __parallel )
956	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
957	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
958	MPI_SUM, comm1dy, ierr )
959	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
960	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
961	MPI_SUM, comm1dy, ierr )
962	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
963	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
964	MPI_SUM, comm1dy, ierr )
965	#else
966	c_u_m = c_u_m_l
967	c_v_m = c_v_m_l
968	c_w_m = c_w_m_l
969	#endif
970
971	c_u_m = c_u_m / (ny+1)
972	c_v_m = c_v_m / (ny+1)
973	c_w_m = c_w_m / (ny+1)
974
975	!
976	!-- Save old timelevels for the next timestep
977	IF ( intermediate_timestep_count == 1 ) THEN
978	u_m_l(:,:,:) = u(:,:,1:2)
979	v_m_l(:,:,:) = v(:,:,0:1)
980	w_m_l(:,:,:) = w(:,:,0:1)
981	ENDIF
982
983	!
984	!-- Calculate the new velocities
985	DO k = nzb+1, nzt+1
986	DO j = nysg, nyng
987	u_p(k,j,0) = u(k,j,0) - dt_3d * tsc(2) * c_u_m(k) * &
988	( u(k,j,0) - u(k,j,1) ) * ddx
989
990	v_p(k,j,-1) = v(k,j,-1) - dt_3d * tsc(2) * c_v_m(k) * &
991	( v(k,j,-1) - v(k,j,0) ) * ddx
992
993	w_p(k,j,-1) = w(k,j,-1) - dt_3d * tsc(2) * c_w_m(k) * &
994	( w(k,j,-1) - w(k,j,0) ) * ddx
995	ENDDO
996	ENDDO
997
998	!
999	!-- Bottom boundary at the outflow
1000	IF ( ibc_uv_b == 0 ) THEN
1001	u_p(nzb,:,0) = 0.0_wp
1002	v_p(nzb,:,-1) = 0.0_wp
1003	ELSE
1004	u_p(nzb,:,0) = u_p(nzb+1,:,0)
1005	v_p(nzb,:,-1) = v_p(nzb+1,:,-1)
1006	ENDIF
1007	w_p(nzb,:,-1) = 0.0_wp
1008
1009	!
1010	!-- Top boundary at the outflow
1011	IF ( ibc_uv_t == 0 ) THEN
1012	u_p(nzt+1,:,0) = u_init(nzt+1)
1013	v_p(nzt+1,:,-1) = v_init(nzt+1)
1014	ELSE
1015	u_p(nzt+1,:,0) = u_p(nzt,:,0)
1016	v_p(nzt+1,:,-1) = v_p(nzt,:,-1)
1017	ENDIF
1018	w_p(nzt:nzt+1,:,-1) = 0.0_wp
1019
1020	ENDIF
1021
1022	ENDIF
1023
1024	IF ( outflow_r ) THEN
1025
1026	IF ( use_cmax ) THEN
1027	u_p(:,:,nx+1) = u(:,:,nx)
1028	v_p(:,:,nx+1) = v(:,:,nx)
1029	w_p(:,:,nx+1) = w(:,:,nx)
1030	ELSEIF ( .NOT. use_cmax ) THEN
1031
1032	c_max = dx / dt_3d
1033
1034	c_u_m_l = 0.0_wp
1035	c_v_m_l = 0.0_wp
1036	c_w_m_l = 0.0_wp
1037
1038	c_u_m = 0.0_wp
1039	c_v_m = 0.0_wp
1040	c_w_m = 0.0_wp
1041
1042	!
1043	!-- Calculate the phase speeds for u, v, and w, first local and then
1044	!-- average along the outflow boundary.
1045	DO k = nzb+1, nzt+1
1046	DO j = nys, nyn
1047
1048	denom = u_m_r(k,j,nx) - u_m_r(k,j,nx-1)
1049
1050	IF ( denom /= 0.0_wp ) THEN
1051	c_u(k,j) = -c_max * ( u(k,j,nx) - u_m_r(k,j,nx) ) / ( denom * tsc(2) )
1052	IF ( c_u(k,j) < 0.0_wp ) THEN
1053	c_u(k,j) = 0.0_wp
1054	ELSEIF ( c_u(k,j) > c_max ) THEN
1055	c_u(k,j) = c_max
1056	ENDIF
1057	ELSE
1058	c_u(k,j) = c_max
1059	ENDIF
1060
1061	denom = v_m_r(k,j,nx) - v_m_r(k,j,nx-1)
1062
1063	IF ( denom /= 0.0_wp ) THEN
1064	c_v(k,j) = -c_max * ( v(k,j,nx) - v_m_r(k,j,nx) ) / ( denom * tsc(2) )
1065	IF ( c_v(k,j) < 0.0_wp ) THEN
1066	c_v(k,j) = 0.0_wp
1067	ELSEIF ( c_v(k,j) > c_max ) THEN
1068	c_v(k,j) = c_max
1069	ENDIF
1070	ELSE
1071	c_v(k,j) = c_max
1072	ENDIF
1073
1074	denom = w_m_r(k,j,nx) - w_m_r(k,j,nx-1)
1075
1076	IF ( denom /= 0.0_wp ) THEN
1077	c_w(k,j) = -c_max * ( w(k,j,nx) - w_m_r(k,j,nx) ) / ( denom * tsc(2) )
1078	IF ( c_w(k,j) < 0.0_wp ) THEN
1079	c_w(k,j) = 0.0_wp
1080	ELSEIF ( c_w(k,j) > c_max ) THEN
1081	c_w(k,j) = c_max
1082	ENDIF
1083	ELSE
1084	c_w(k,j) = c_max
1085	ENDIF
1086
1087	c_u_m_l(k) = c_u_m_l(k) + c_u(k,j)
1088	c_v_m_l(k) = c_v_m_l(k) + c_v(k,j)
1089	c_w_m_l(k) = c_w_m_l(k) + c_w(k,j)
1090
1091	ENDDO
1092	ENDDO
1093
1094	#if defined( __parallel )
1095	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
1096	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
1097	MPI_SUM, comm1dy, ierr )
1098	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
1099	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
1100	MPI_SUM, comm1dy, ierr )
1101	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
1102	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
1103	MPI_SUM, comm1dy, ierr )
1104	#else
1105	c_u_m = c_u_m_l
1106	c_v_m = c_v_m_l
1107	c_w_m = c_w_m_l
1108	#endif
1109
1110	c_u_m = c_u_m / (ny+1)
1111	c_v_m = c_v_m / (ny+1)
1112	c_w_m = c_w_m / (ny+1)
1113
1114	!
1115	!-- Save old timelevels for the next timestep
1116	IF ( intermediate_timestep_count == 1 ) THEN
1117	u_m_r(:,:,:) = u(:,:,nx-1:nx)
1118	v_m_r(:,:,:) = v(:,:,nx-1:nx)
1119	w_m_r(:,:,:) = w(:,:,nx-1:nx)
1120	ENDIF
1121
1122	!
1123	!-- Calculate the new velocities
1124	DO k = nzb+1, nzt+1
1125	DO j = nysg, nyng
1126	u_p(k,j,nx+1) = u(k,j,nx+1) - dt_3d * tsc(2) * c_u_m(k) * &
1127	( u(k,j,nx+1) - u(k,j,nx) ) * ddx
1128
1129	v_p(k,j,nx+1) = v(k,j,nx+1) - dt_3d * tsc(2) * c_v_m(k) * &
1130	( v(k,j,nx+1) - v(k,j,nx) ) * ddx
1131
1132	w_p(k,j,nx+1) = w(k,j,nx+1) - dt_3d * tsc(2) * c_w_m(k) * &
1133	( w(k,j,nx+1) - w(k,j,nx) ) * ddx
1134	ENDDO
1135	ENDDO
1136
1137	!
1138	!-- Bottom boundary at the outflow
1139	IF ( ibc_uv_b == 0 ) THEN
1140	u_p(nzb,:,nx+1) = 0.0_wp
1141	v_p(nzb,:,nx+1) = 0.0_wp
1142	ELSE
1143	u_p(nzb,:,nx+1) = u_p(nzb+1,:,nx+1)
1144	v_p(nzb,:,nx+1) = v_p(nzb+1,:,nx+1)
1145	ENDIF
1146	w_p(nzb,:,nx+1) = 0.0_wp
1147
1148	!
1149	!-- Top boundary at the outflow
1150	IF ( ibc_uv_t == 0 ) THEN
1151	u_p(nzt+1,:,nx+1) = u_init(nzt+1)
1152	v_p(nzt+1,:,nx+1) = v_init(nzt+1)
1153	ELSE
1154	u_p(nzt+1,:,nx+1) = u_p(nzt,:,nx+1)
1155	v_p(nzt+1,:,nx+1) = v_p(nzt,:,nx+1)
1156	ENDIF
1157	w_p(nzt:nzt+1,:,nx+1) = 0.0_wp
1158
1159	ENDIF
1160
1161	ENDIF
1162
1163	END SUBROUTINE boundary_conds

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