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source: palm/trunk/SOURCE/boundary_conds.f90 @ 2723

Last change on this file since 2723 was 2718, checked in by maronga, 7 years ago
deleting of deprecated files; headers updated where needed
Property svn:keywords set to `Id`
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1	!> @file boundary_conds.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 1997-2018 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: boundary_conds.f90 2718 2018-01-02 08:49:38Z maronga $
27	! Corrected "Former revisions" section
28	!
29	! 2696 2017-12-14 17:12:51Z kanani
30	! Change in file header (GPL part)
31	! Adjust boundary conditions for e and diss in case of TKE-e closure (TG)
32	! Implementation of chemistry module (FK)
33	!
34	! 2569 2017-10-20 11:54:42Z kanani
35	! Removed redundant code for ibc_s_b=1 and ibc_q_b=1
36	!
37	! 2365 2017-08-21 14:59:59Z kanani
38	! Vertical grid nesting implemented: exclude setting vertical velocity to zero
39	! on fine grid (SadiqHuq)
40	!
41	! 2320 2017-07-21 12:47:43Z suehring
42	! Remove unused control parameter large_scale_forcing from only-list
43	!
44	! 2292 2017-06-20 09:51:42Z schwenkel
45	! Implementation of new microphysic scheme: cloud_scheme = 'morrison'
46	! includes two more prognostic equations for cloud drop concentration (nc)
47	! and cloud water content (qc).
48	!
49	! 2233 2017-05-30 18:08:54Z suehring
50	!
51	! 2232 2017-05-30 17:47:52Z suehring
52	! Set boundary conditions on topography top using flag method.
53	!
54	! 2118 2017-01-17 16:38:49Z raasch
55	! OpenACC directives removed
56	!
57	! 2000 2016-08-20 18:09:15Z knoop
58	! Forced header and separation lines into 80 columns
59	!
60	! 1992 2016-08-12 15:14:59Z suehring
61	! Adjustments for top boundary condition for passive scalar
62	!
63	! 1960 2016-07-12 16:34:24Z suehring
64	! Treat humidity and passive scalar separately
65	!
66	! 1823 2016-04-07 08:57:52Z hoffmann
67	! Initial version of purely vertical nesting introduced.
68	!
69	! 1822 2016-04-07 07:49:42Z hoffmann
70	! icloud_scheme removed. microphyisics_seifert added.
71	!
72	! 1764 2016-02-28 12:45:19Z raasch
73	! index bug for u_p at left outflow removed
74	!
75	! 1762 2016-02-25 12:31:13Z hellstea
76	! Introduction of nested domain feature
77	!
78	! 1742 2016-01-13 09:50:06Z raasch
79	! bugfix for outflow Neumann boundary conditions at bottom and top
80	!
81	! 1717 2015-11-11 15:09:47Z raasch
82	! Bugfix: index error in outflow conditions for left boundary
83	!
84	! 1682 2015-10-07 23:56:08Z knoop
85	! Code annotations made doxygen readable
86	!
87	! 1410 2014-05-23 12:16:18Z suehring
88	! Bugfix: set dirichlet boundary condition for passive_scalar at model domain
89	! top
90	!
91	! 1399 2014-05-07 11:16:25Z heinze
92	! Bugfix: set inflow boundary conditions also if no humidity or passive_scalar
93	! is used.
94	!
95	! 1398 2014-05-07 11:15:00Z heinze
96	! Dirichlet-condition at the top for u and v changed to u_init and v_init also
97	! for large_scale_forcing
98	!
99	! 1380 2014-04-28 12:40:45Z heinze
100	! Adjust Dirichlet-condition at the top for pt in case of nudging
101	!
102	! 1361 2014-04-16 15:17:48Z hoffmann
103	! Bottom and top boundary conditions of rain water content (qr) and
104	! rain drop concentration (nr) changed to Dirichlet
105	!
106	! 1353 2014-04-08 15:21:23Z heinze
107	! REAL constants provided with KIND-attribute
108	!
109	! 1320 2014-03-20 08:40:49Z raasch
110	! ONLY-attribute added to USE-statements,
111	! kind-parameters added to all INTEGER and REAL declaration statements,
112	! kinds are defined in new module kinds,
113	! revision history before 2012 removed,
114	! comment fields (!:) to be used for variable explanations added to
115	! all variable declaration statements
116	!
117	! 1257 2013-11-08 15:18:40Z raasch
118	! loop independent clauses added
119	!
120	! 1241 2013-10-30 11:36:58Z heinze
121	! Adjust ug and vg at each timestep in case of large_scale_forcing
122	!
123	! 1159 2013-05-21 11:58:22Z fricke
124	! Bugfix: Neumann boundary conditions for the velocity components at the
125	! outflow are in fact radiation boundary conditions using the maximum phase
126	! velocity that ensures numerical stability (CFL-condition).
127	! Hence, logical operator use_cmax is now used instead of bc_lr_dirneu/_neudir.
128	! Bugfix: In case of use_cmax at the outflow, u, v, w are replaced by
129	! u_p, v_p, w_p
130	!
131	! 1115 2013-03-26 18:16:16Z hoffmann
132	! boundary conditions of two-moment cloud scheme are restricted to Neumann-
133	! boundary-conditions
134	!
135	! 1113 2013-03-10 02:48:14Z raasch
136	! GPU-porting
137	! dummy argument "range" removed
138	! Bugfix: wrong index in loops of radiation boundary condition
139	!
140	! 1053 2012-11-13 17:11:03Z hoffmann
141	! boundary conditions for the two new prognostic equations (nr, qr) of the
142	! two-moment cloud scheme
143	!
144	! 1036 2012-10-22 13:43:42Z raasch
145	! code put under GPL (PALM 3.9)
146	!
147	! 996 2012-09-07 10:41:47Z raasch
148	! little reformatting
149	!
150	! 978 2012-08-09 08:28:32Z fricke
151	! Neumann boudnary conditions are added at the inflow boundary for the SGS-TKE.
152	! Outflow boundary conditions for the velocity components can be set to Neumann
153	! conditions or to radiation conditions with a horizontal averaged phase
154	! velocity.
155	!
156	! 875 2012-04-02 15:35:15Z gryschka
157	! Bugfix in case of dirichlet inflow bc at the right or north boundary
158	!
159	! Revision 1.1 1997/09/12 06:21:34 raasch
160	! Initial revision
161	!
162	!
163	! Description:
164	! ------------
165	!> Boundary conditions for the prognostic quantities.
166	!> One additional bottom boundary condition is applied for the TKE (=(u)*2)
167	!> in prandtl_fluxes. The cyclic lateral boundary conditions are implicitly
168	!> handled in routine exchange_horiz. Pressure boundary conditions are
169	!> explicitly set in routines pres, poisfft, poismg and sor.
170	!------------------------------------------------------------------------------!
171	SUBROUTINE boundary_conds
172
173
174	USE arrays_3d, &
175	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, &
176	diss_p, dzu, e_p, nc_p, nr_p, pt, pt_p, q, q_p, qc_p, qr_p, s, &
177	s_p, sa, sa_p, u, ug, u_init, u_m_l, u_m_n, u_m_r, u_m_s, u_p, &
178	v, vg, v_init, v_m_l, v_m_n, v_m_r, v_m_s, v_p, &
179	w, w_p, w_m_l, w_m_n, w_m_r, w_m_s, pt_init
180
181	#if defined( __chem )
182	USE chemistry_model_mod, &
183	ONLY: chem_boundary_conds
184	#endif
185
186	USE control_parameters, &
187	ONLY: air_chemistry, bc_pt_t_val, bc_q_t_val, bc_s_t_val, &
188	constant_diffusion, cloud_physics, coupling_mode, dt_3d, &
189	force_bound_l, force_bound_s, forcing, humidity, &
190	ibc_pt_b, ibc_pt_t, ibc_q_b, ibc_q_t, ibc_s_b, ibc_s_t, &
191	ibc_sa_t, ibc_uv_b, ibc_uv_t, inflow_l, inflow_n, inflow_r, &
192	inflow_s, intermediate_timestep_count, &
193	microphysics_morrison, microphysics_seifert, nest_domain, &
194	nest_bound_l, nest_bound_s, nudging, ocean, outflow_l, &
195	outflow_n, outflow_r, outflow_s, passive_scalar, rans_tke_e, &
196	tsc, use_cmax
197
198	USE grid_variables, &
199	ONLY: ddx, ddy, dx, dy
200
201	USE indices, &
202	ONLY: nx, nxl, nxlg, nxr, nxrg, ny, nyn, nyng, nys, nysg, &
203	nzb, nzt, wall_flags_0
204
205	USE kinds
206
207	USE pegrid
208
209	USE pmc_interface, &
210	ONLY : nesting_mode
211
212	USE surface_mod, &
213	ONLY : bc_h
214
215	IMPLICIT NONE
216
217	INTEGER(iwp) :: i !< grid index x direction
218	INTEGER(iwp) :: j !< grid index y direction
219	INTEGER(iwp) :: k !< grid index z direction
220	INTEGER(iwp) :: kb !< variable to set respective boundary value, depends on facing.
221	INTEGER(iwp) :: l !< running index boundary type, for up- and downward-facing walls
222	INTEGER(iwp) :: m !< running index surface elements
223
224	REAL(wp) :: c_max !<
225	REAL(wp) :: denom !<
226
227
228	!
229	!-- Bottom boundary
230	IF ( ibc_uv_b == 1 ) THEN
231	u_p(nzb,:,:) = u_p(nzb+1,:,:)
232	v_p(nzb,:,:) = v_p(nzb+1,:,:)
233	ENDIF
234	!
235	!-- Set zero vertical velocity at topography top (l=0), or bottom (l=1) in case
236	!-- of downward-facing surfaces.
237	DO l = 0, 1
238	!
239	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
240	!-- for downward-facing surfaces at topography bottom (k+1).
241	kb = MERGE( -1, 1, l == 0 )
242	!$OMP PARALLEL DO PRIVATE( i, j, k )
243	DO m = 1, bc_h(l)%ns
244	i = bc_h(l)%i(m)
245	j = bc_h(l)%j(m)
246	k = bc_h(l)%k(m)
247	w_p(k+kb,j,i) = 0.0_wp
248	ENDDO
249	ENDDO
250
251	!
252	!-- Top boundary. A nested domain ( ibc_uv_t = 3 ) does not require settings.
253	IF ( ibc_uv_t == 0 ) THEN
254	u_p(nzt+1,:,:) = u_init(nzt+1)
255	v_p(nzt+1,:,:) = v_init(nzt+1)
256	ELSEIF ( ibc_uv_t == 1 ) THEN
257	u_p(nzt+1,:,:) = u_p(nzt,:,:)
258	v_p(nzt+1,:,:) = v_p(nzt,:,:)
259	ENDIF
260
261	!
262	!-- Vertical nesting: Vertical velocity not zero at the top of the fine grid
263	IF ( .NOT. nest_domain .AND. &
264	TRIM(coupling_mode) /= 'vnested_fine' ) THEN
265	w_p(nzt:nzt+1,:,:) = 0.0_wp !< nzt is not a prognostic level (but cf. pres)
266	ENDIF
267
268	!
269	!-- Temperature at bottom and top boundary.
270	!-- In case of coupled runs (ibc_pt_b = 2) the temperature is given by
271	!-- the sea surface temperature of the coupled ocean model.
272	!-- Dirichlet
273	IF ( ibc_pt_b == 0 ) THEN
274	DO l = 0, 1
275	!
276	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
277	!-- for downward-facing surfaces at topography bottom (k+1).
278	kb = MERGE( -1, 1, l == 0 )
279	!$OMP PARALLEL DO PRIVATE( i, j, k )
280	DO m = 1, bc_h(l)%ns
281	i = bc_h(l)%i(m)
282	j = bc_h(l)%j(m)
283	k = bc_h(l)%k(m)
284	pt_p(k+kb,j,i) = pt(k+kb,j,i)
285	ENDDO
286	ENDDO
287	!
288	!-- Neumann, zero-gradient
289	ELSEIF ( ibc_pt_b == 1 ) THEN
290	DO l = 0, 1
291	!
292	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
293	!-- for downward-facing surfaces at topography bottom (k+1).
294	kb = MERGE( -1, 1, l == 0 )
295	!$OMP PARALLEL DO PRIVATE( i, j, k )
296	DO m = 1, bc_h(l)%ns
297	i = bc_h(l)%i(m)
298	j = bc_h(l)%j(m)
299	k = bc_h(l)%k(m)
300	pt_p(k+kb,j,i) = pt_p(k,j,i)
301	ENDDO
302	ENDDO
303	ENDIF
304
305	!
306	!-- Temperature at top boundary
307	IF ( ibc_pt_t == 0 ) THEN
308	pt_p(nzt+1,:,:) = pt(nzt+1,:,:)
309	!
310	!-- In case of nudging adjust top boundary to pt which is
311	!-- read in from NUDGING-DATA
312	IF ( nudging ) THEN
313	pt_p(nzt+1,:,:) = pt_init(nzt+1)
314	ENDIF
315	ELSEIF ( ibc_pt_t == 1 ) THEN
316	pt_p(nzt+1,:,:) = pt_p(nzt,:,:)
317	ELSEIF ( ibc_pt_t == 2 ) THEN
318	pt_p(nzt+1,:,:) = pt_p(nzt,:,:) + bc_pt_t_val * dzu(nzt+1)
319	ENDIF
320
321	!
322	!-- Boundary conditions for TKE
323	!-- Generally Neumann conditions with de/dz=0 are assumed
324	IF ( .NOT. constant_diffusion ) THEN
325
326	IF ( .NOT. rans_tke_e ) THEN
327	DO l = 0, 1
328	!
329	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
330	!-- for downward-facing surfaces at topography bottom (k+1).
331	kb = MERGE( -1, 1, l == 0 )
332	!$OMP PARALLEL DO PRIVATE( i, j, k )
333	DO m = 1, bc_h(l)%ns
334	i = bc_h(l)%i(m)
335	j = bc_h(l)%j(m)
336	k = bc_h(l)%k(m)
337	e_p(k+kb,j,i) = e_p(k,j,i)
338	ENDDO
339	ENDDO
340	ENDIF
341
342	IF ( .NOT. nest_domain ) THEN
343	e_p(nzt+1,:,:) = e_p(nzt,:,:)
344	ENDIF
345	ENDIF
346
347	!
348	!-- Boundary conditions for TKE dissipation rate
349	IF ( rans_tke_e .AND. .NOT. nest_domain ) THEN
350	diss_p(nzt+1,:,:) = diss_p(nzt,:,:)
351	ENDIF
352
353	!
354	!-- Boundary conditions for salinity
355	IF ( ocean ) THEN
356	!
357	!-- Bottom boundary: Neumann condition because salinity flux is always
358	!-- given.
359	DO l = 0, 1
360	!
361	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
362	!-- for downward-facing surfaces at topography bottom (k+1).
363	kb = MERGE( -1, 1, l == 0 )
364	!$OMP PARALLEL DO PRIVATE( i, j, k )
365	DO m = 1, bc_h(l)%ns
366	i = bc_h(l)%i(m)
367	j = bc_h(l)%j(m)
368	k = bc_h(l)%k(m)
369	sa_p(k+kb,j,i) = sa_p(k,j,i)
370	ENDDO
371	ENDDO
372	!
373	!-- Top boundary: Dirichlet or Neumann
374	IF ( ibc_sa_t == 0 ) THEN
375	sa_p(nzt+1,:,:) = sa(nzt+1,:,:)
376	ELSEIF ( ibc_sa_t == 1 ) THEN
377	sa_p(nzt+1,:,:) = sa_p(nzt,:,:)
378	ENDIF
379
380	ENDIF
381
382	!
383	!-- Boundary conditions for total water content,
384	!-- bottom and top boundary (see also temperature)
385	IF ( humidity ) THEN
386	!
387	!-- Surface conditions for constant_humidity_flux
388	!-- Run loop over all non-natural and natural walls. Note, in wall-datatype
389	!-- the k coordinate belongs to the atmospheric grid point, therefore, set
390	!-- q_p at k-1
391	IF ( ibc_q_b == 0 ) THEN
392
393	DO l = 0, 1
394	!
395	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
396	!-- for downward-facing surfaces at topography bottom (k+1).
397	kb = MERGE( -1, 1, l == 0 )
398	!$OMP PARALLEL DO PRIVATE( i, j, k )
399	DO m = 1, bc_h(l)%ns
400	i = bc_h(l)%i(m)
401	j = bc_h(l)%j(m)
402	k = bc_h(l)%k(m)
403	q_p(k+kb,j,i) = q(k+kb,j,i)
404	ENDDO
405	ENDDO
406
407	ELSE
408
409	DO l = 0, 1
410	!
411	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
412	!-- for downward-facing surfaces at topography bottom (k+1).
413	kb = MERGE( -1, 1, l == 0 )
414	!$OMP PARALLEL DO PRIVATE( i, j, k )
415	DO m = 1, bc_h(l)%ns
416	i = bc_h(l)%i(m)
417	j = bc_h(l)%j(m)
418	k = bc_h(l)%k(m)
419	q_p(k+kb,j,i) = q_p(k,j,i)
420	ENDDO
421	ENDDO
422	ENDIF
423	!
424	!-- Top boundary
425	IF ( ibc_q_t == 0 ) THEN
426	q_p(nzt+1,:,:) = q(nzt+1,:,:)
427	ELSEIF ( ibc_q_t == 1 ) THEN
428	q_p(nzt+1,:,:) = q_p(nzt,:,:) + bc_q_t_val * dzu(nzt+1)
429	ENDIF
430
431	IF ( cloud_physics .AND. microphysics_morrison ) THEN
432	!
433	!-- Surface conditions cloud water (Dirichlet)
434	!-- Run loop over all non-natural and natural walls. Note, in wall-datatype
435	!-- the k coordinate belongs to the atmospheric grid point, therefore, set
436	!-- qr_p and nr_p at k-1
437	!$OMP PARALLEL DO PRIVATE( i, j, k )
438	DO m = 1, bc_h(0)%ns
439	i = bc_h(0)%i(m)
440	j = bc_h(0)%j(m)
441	k = bc_h(0)%k(m)
442	qc_p(k-1,j,i) = 0.0_wp
443	nc_p(k-1,j,i) = 0.0_wp
444	ENDDO
445	!
446	!-- Top boundary condition for cloud water (Dirichlet)
447	qc_p(nzt+1,:,:) = 0.0_wp
448	nc_p(nzt+1,:,:) = 0.0_wp
449
450	ENDIF
451
452	IF ( cloud_physics .AND. microphysics_seifert ) THEN
453	!
454	!-- Surface conditions rain water (Dirichlet)
455	!-- Run loop over all non-natural and natural walls. Note, in wall-datatype
456	!-- the k coordinate belongs to the atmospheric grid point, therefore, set
457	!-- qr_p and nr_p at k-1
458	!$OMP PARALLEL DO PRIVATE( i, j, k )
459	DO m = 1, bc_h(0)%ns
460	i = bc_h(0)%i(m)
461	j = bc_h(0)%j(m)
462	k = bc_h(0)%k(m)
463	qr_p(k-1,j,i) = 0.0_wp
464	nr_p(k-1,j,i) = 0.0_wp
465	ENDDO
466	!
467	!-- Top boundary condition for rain water (Dirichlet)
468	qr_p(nzt+1,:,:) = 0.0_wp
469	nr_p(nzt+1,:,:) = 0.0_wp
470
471	ENDIF
472	ENDIF
473	!
474	!-- Boundary conditions for scalar,
475	!-- bottom and top boundary (see also temperature)
476	IF ( passive_scalar ) THEN
477	!
478	!-- Surface conditions for constant_humidity_flux
479	!-- Run loop over all non-natural and natural walls. Note, in wall-datatype
480	!-- the k coordinate belongs to the atmospheric grid point, therefore, set
481	!-- s_p at k-1
482	IF ( ibc_s_b == 0 ) THEN
483
484	DO l = 0, 1
485	!
486	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
487	!-- for downward-facing surfaces at topography bottom (k+1).
488	kb = MERGE( -1, 1, l == 0 )
489	!$OMP PARALLEL DO PRIVATE( i, j, k )
490	DO m = 1, bc_h(l)%ns
491	i = bc_h(l)%i(m)
492	j = bc_h(l)%j(m)
493	k = bc_h(l)%k(m)
494	s_p(k+kb,j,i) = s(k+kb,j,i)
495	ENDDO
496	ENDDO
497
498	ELSE
499
500	DO l = 0, 1
501	!
502	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
503	!-- for downward-facing surfaces at topography bottom (k+1).
504	kb = MERGE( -1, 1, l == 0 )
505	!$OMP PARALLEL DO PRIVATE( i, j, k )
506	DO m = 1, bc_h(l)%ns
507	i = bc_h(l)%i(m)
508	j = bc_h(l)%j(m)
509	k = bc_h(l)%k(m)
510	s_p(k+kb,j,i) = s_p(k,j,i)
511	ENDDO
512	ENDDO
513	ENDIF
514	!
515	!-- Top boundary condition
516	IF ( ibc_s_t == 0 ) THEN
517	s_p(nzt+1,:,:) = s(nzt+1,:,:)
518	ELSEIF ( ibc_s_t == 1 ) THEN
519	s_p(nzt+1,:,:) = s_p(nzt,:,:)
520	ELSEIF ( ibc_s_t == 2 ) THEN
521	s_p(nzt+1,:,:) = s_p(nzt,:,:) + bc_s_t_val * dzu(nzt+1)
522	ENDIF
523
524	ENDIF
525	!
526	!-- Top/bottom boundary conditions for chemical species
527	#if defined( __chem )
528	IF ( air_chemistry ) CALL chem_boundary_conds( 'set_bc_bottomtop' )
529	#endif
530	!
531	!-- In case of inflow or nest boundary at the south boundary the boundary for v
532	!-- is at nys and in case of inflow or nest boundary at the left boundary the
533	!-- boundary for u is at nxl. Since in prognostic_equations (cache optimized
534	!-- version) these levels are handled as a prognostic level, boundary values
535	!-- have to be restored here.
536	!-- For the SGS-TKE, Neumann boundary conditions are used at the inflow.
537	IF ( inflow_s ) THEN
538	v_p(:,nys,:) = v_p(:,nys-1,:)
539	IF ( .NOT. constant_diffusion ) e_p(:,nys-1,:) = e_p(:,nys,:)
540	ELSEIF ( inflow_n ) THEN
541	IF ( .NOT. constant_diffusion ) e_p(:,nyn+1,:) = e_p(:,nyn,:)
542	ELSEIF ( inflow_l ) THEN
543	u_p(:,:,nxl) = u_p(:,:,nxl-1)
544	IF ( .NOT. constant_diffusion ) e_p(:,:,nxl-1) = e_p(:,:,nxl)
545	ELSEIF ( inflow_r ) THEN
546	IF ( .NOT. constant_diffusion ) e_p(:,:,nxr+1) = e_p(:,:,nxr)
547	ENDIF
548
549	!
550	!-- The same restoration for u at i=nxl and v at j=nys as above must be made
551	!-- in case of nest boundaries. This must not be done in case of vertical nesting
552	!-- mode as in that case the lateral boundaries are actually cyclic.
553	IF ( nesting_mode /= 'vertical' .OR. forcing ) THEN
554	IF ( nest_bound_s .OR. force_bound_s ) THEN
555	v_p(:,nys,:) = v_p(:,nys-1,:)
556	ENDIF
557	IF ( nest_bound_l .OR. force_bound_l ) THEN
558	u_p(:,:,nxl) = u_p(:,:,nxl-1)
559	ENDIF
560	ENDIF
561
562	!
563	!-- Lateral boundary conditions for scalar quantities at the outflow
564	IF ( outflow_s ) THEN
565	pt_p(:,nys-1,:) = pt_p(:,nys,:)
566	IF ( .NOT. constant_diffusion ) e_p(:,nys-1,:) = e_p(:,nys,:)
567	IF ( rans_tke_e ) diss_p(:,nys-1,:) = diss_p(:,nys,:)
568	IF ( humidity ) THEN
569	q_p(:,nys-1,:) = q_p(:,nys,:)
570	IF ( cloud_physics .AND. microphysics_morrison ) THEN
571	qc_p(:,nys-1,:) = qc_p(:,nys,:)
572	nc_p(:,nys-1,:) = nc_p(:,nys,:)
573	ENDIF
574	IF ( cloud_physics .AND. microphysics_seifert ) THEN
575	qr_p(:,nys-1,:) = qr_p(:,nys,:)
576	nr_p(:,nys-1,:) = nr_p(:,nys,:)
577	ENDIF
578	ENDIF
579	IF ( passive_scalar ) s_p(:,nys-1,:) = s_p(:,nys,:)
580	ELSEIF ( outflow_n ) THEN
581	pt_p(:,nyn+1,:) = pt_p(:,nyn,:)
582	IF ( .NOT. constant_diffusion ) e_p(:,nyn+1,:) = e_p(:,nyn,:)
583	IF ( rans_tke_e ) diss_p(:,nyn+1,:) = diss_p(:,nyn,:)
584	IF ( humidity ) THEN
585	q_p(:,nyn+1,:) = q_p(:,nyn,:)
586	IF ( cloud_physics .AND. microphysics_morrison ) THEN
587	qc_p(:,nyn+1,:) = qc_p(:,nyn,:)
588	nc_p(:,nyn+1,:) = nc_p(:,nyn,:)
589	ENDIF
590	IF ( cloud_physics .AND. microphysics_seifert ) THEN
591	qr_p(:,nyn+1,:) = qr_p(:,nyn,:)
592	nr_p(:,nyn+1,:) = nr_p(:,nyn,:)
593	ENDIF
594	ENDIF
595	IF ( passive_scalar ) s_p(:,nyn+1,:) = s_p(:,nyn,:)
596	ELSEIF ( outflow_l ) THEN
597	pt_p(:,:,nxl-1) = pt_p(:,:,nxl)
598	IF ( .NOT. constant_diffusion ) e_p(:,:,nxl-1) = e_p(:,:,nxl)
599	IF ( rans_tke_e ) diss_p(:,:,nxl-1) = diss_p(:,:,nxl)
600	IF ( humidity ) THEN
601	q_p(:,:,nxl-1) = q_p(:,:,nxl)
602	IF ( cloud_physics .AND. microphysics_morrison ) THEN
603	qc_p(:,:,nxl-1) = qc_p(:,:,nxl)
604	nc_p(:,:,nxl-1) = nc_p(:,:,nxl)
605	ENDIF
606	IF ( cloud_physics .AND. microphysics_seifert ) THEN
607	qr_p(:,:,nxl-1) = qr_p(:,:,nxl)
608	nr_p(:,:,nxl-1) = nr_p(:,:,nxl)
609	ENDIF
610	ENDIF
611	IF ( passive_scalar ) s_p(:,:,nxl-1) = s_p(:,:,nxl)
612	ELSEIF ( outflow_r ) THEN
613	pt_p(:,:,nxr+1) = pt_p(:,:,nxr)
614	IF ( .NOT. constant_diffusion ) e_p(:,:,nxr+1) = e_p(:,:,nxr)
615	IF ( rans_tke_e ) diss_p(:,:,nxr+1) = diss_p(:,:,nxr)
616	IF ( humidity ) THEN
617	q_p(:,:,nxr+1) = q_p(:,:,nxr)
618	IF ( cloud_physics .AND. microphysics_morrison ) THEN
619	qc_p(:,:,nxr+1) = qc_p(:,:,nxr)
620	nc_p(:,:,nxr+1) = nc_p(:,:,nxr)
621	ENDIF
622	IF ( cloud_physics .AND. microphysics_seifert ) THEN
623	qr_p(:,:,nxr+1) = qr_p(:,:,nxr)
624	nr_p(:,:,nxr+1) = nr_p(:,:,nxr)
625	ENDIF
626	ENDIF
627	IF ( passive_scalar ) s_p(:,:,nxr+1) = s_p(:,:,nxr)
628	ENDIF
629
630	!
631	!-- Lateral boundary conditions for chemical species
632	#if defined( __chem )
633	IF ( air_chemistry ) CALL chem_boundary_conds( 'set_bc_lateral' )
634	#endif
635
636
637	!
638	!-- Radiation boundary conditions for the velocities at the respective outflow.
639	!-- The phase velocity is either assumed to the maximum phase velocity that
640	!-- ensures numerical stability (CFL-condition) or calculated after
641	!-- Orlanski(1976) and averaged along the outflow boundary.
642	IF ( outflow_s ) THEN
643
644	IF ( use_cmax ) THEN
645	u_p(:,-1,:) = u(:,0,:)
646	v_p(:,0,:) = v(:,1,:)
647	w_p(:,-1,:) = w(:,0,:)
648	ELSEIF ( .NOT. use_cmax ) THEN
649
650	c_max = dy / dt_3d
651
652	c_u_m_l = 0.0_wp
653	c_v_m_l = 0.0_wp
654	c_w_m_l = 0.0_wp
655
656	c_u_m = 0.0_wp
657	c_v_m = 0.0_wp
658	c_w_m = 0.0_wp
659
660	!
661	!-- Calculate the phase speeds for u, v, and w, first local and then
662	!-- average along the outflow boundary.
663	DO k = nzb+1, nzt+1
664	DO i = nxl, nxr
665
666	denom = u_m_s(k,0,i) - u_m_s(k,1,i)
667
668	IF ( denom /= 0.0_wp ) THEN
669	c_u(k,i) = -c_max * ( u(k,0,i) - u_m_s(k,0,i) ) / ( denom * tsc(2) )
670	IF ( c_u(k,i) < 0.0_wp ) THEN
671	c_u(k,i) = 0.0_wp
672	ELSEIF ( c_u(k,i) > c_max ) THEN
673	c_u(k,i) = c_max
674	ENDIF
675	ELSE
676	c_u(k,i) = c_max
677	ENDIF
678
679	denom = v_m_s(k,1,i) - v_m_s(k,2,i)
680
681	IF ( denom /= 0.0_wp ) THEN
682	c_v(k,i) = -c_max * ( v(k,1,i) - v_m_s(k,1,i) ) / ( denom * tsc(2) )
683	IF ( c_v(k,i) < 0.0_wp ) THEN
684	c_v(k,i) = 0.0_wp
685	ELSEIF ( c_v(k,i) > c_max ) THEN
686	c_v(k,i) = c_max
687	ENDIF
688	ELSE
689	c_v(k,i) = c_max
690	ENDIF
691
692	denom = w_m_s(k,0,i) - w_m_s(k,1,i)
693
694	IF ( denom /= 0.0_wp ) THEN
695	c_w(k,i) = -c_max * ( w(k,0,i) - w_m_s(k,0,i) ) / ( denom * tsc(2) )
696	IF ( c_w(k,i) < 0.0_wp ) THEN
697	c_w(k,i) = 0.0_wp
698	ELSEIF ( c_w(k,i) > c_max ) THEN
699	c_w(k,i) = c_max
700	ENDIF
701	ELSE
702	c_w(k,i) = c_max
703	ENDIF
704
705	c_u_m_l(k) = c_u_m_l(k) + c_u(k,i)
706	c_v_m_l(k) = c_v_m_l(k) + c_v(k,i)
707	c_w_m_l(k) = c_w_m_l(k) + c_w(k,i)
708
709	ENDDO
710	ENDDO
711
712	#if defined( __parallel )
713	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
714	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
715	MPI_SUM, comm1dx, ierr )
716	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
717	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
718	MPI_SUM, comm1dx, ierr )
719	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
720	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
721	MPI_SUM, comm1dx, ierr )
722	#else
723	c_u_m = c_u_m_l
724	c_v_m = c_v_m_l
725	c_w_m = c_w_m_l
726	#endif
727
728	c_u_m = c_u_m / (nx+1)
729	c_v_m = c_v_m / (nx+1)
730	c_w_m = c_w_m / (nx+1)
731
732	!
733	!-- Save old timelevels for the next timestep
734	IF ( intermediate_timestep_count == 1 ) THEN
735	u_m_s(:,:,:) = u(:,0:1,:)
736	v_m_s(:,:,:) = v(:,1:2,:)
737	w_m_s(:,:,:) = w(:,0:1,:)
738	ENDIF
739
740	!
741	!-- Calculate the new velocities
742	DO k = nzb+1, nzt+1
743	DO i = nxlg, nxrg
744	u_p(k,-1,i) = u(k,-1,i) - dt_3d * tsc(2) * c_u_m(k) * &
745	( u(k,-1,i) - u(k,0,i) ) * ddy
746
747	v_p(k,0,i) = v(k,0,i) - dt_3d * tsc(2) * c_v_m(k) * &
748	( v(k,0,i) - v(k,1,i) ) * ddy
749
750	w_p(k,-1,i) = w(k,-1,i) - dt_3d * tsc(2) * c_w_m(k) * &
751	( w(k,-1,i) - w(k,0,i) ) * ddy
752	ENDDO
753	ENDDO
754
755	!
756	!-- Bottom boundary at the outflow
757	IF ( ibc_uv_b == 0 ) THEN
758	u_p(nzb,-1,:) = 0.0_wp
759	v_p(nzb,0,:) = 0.0_wp
760	ELSE
761	u_p(nzb,-1,:) = u_p(nzb+1,-1,:)
762	v_p(nzb,0,:) = v_p(nzb+1,0,:)
763	ENDIF
764	w_p(nzb,-1,:) = 0.0_wp
765
766	!
767	!-- Top boundary at the outflow
768	IF ( ibc_uv_t == 0 ) THEN
769	u_p(nzt+1,-1,:) = u_init(nzt+1)
770	v_p(nzt+1,0,:) = v_init(nzt+1)
771	ELSE
772	u_p(nzt+1,-1,:) = u_p(nzt,-1,:)
773	v_p(nzt+1,0,:) = v_p(nzt,0,:)
774	ENDIF
775	w_p(nzt:nzt+1,-1,:) = 0.0_wp
776
777	ENDIF
778
779	ENDIF
780
781	IF ( outflow_n ) THEN
782
783	IF ( use_cmax ) THEN
784	u_p(:,ny+1,:) = u(:,ny,:)
785	v_p(:,ny+1,:) = v(:,ny,:)
786	w_p(:,ny+1,:) = w(:,ny,:)
787	ELSEIF ( .NOT. use_cmax ) THEN
788
789	c_max = dy / dt_3d
790
791	c_u_m_l = 0.0_wp
792	c_v_m_l = 0.0_wp
793	c_w_m_l = 0.0_wp
794
795	c_u_m = 0.0_wp
796	c_v_m = 0.0_wp
797	c_w_m = 0.0_wp
798
799	!
800	!-- Calculate the phase speeds for u, v, and w, first local and then
801	!-- average along the outflow boundary.
802	DO k = nzb+1, nzt+1
803	DO i = nxl, nxr
804
805	denom = u_m_n(k,ny,i) - u_m_n(k,ny-1,i)
806
807	IF ( denom /= 0.0_wp ) THEN
808	c_u(k,i) = -c_max * ( u(k,ny,i) - u_m_n(k,ny,i) ) / ( denom * tsc(2) )
809	IF ( c_u(k,i) < 0.0_wp ) THEN
810	c_u(k,i) = 0.0_wp
811	ELSEIF ( c_u(k,i) > c_max ) THEN
812	c_u(k,i) = c_max
813	ENDIF
814	ELSE
815	c_u(k,i) = c_max
816	ENDIF
817
818	denom = v_m_n(k,ny,i) - v_m_n(k,ny-1,i)
819
820	IF ( denom /= 0.0_wp ) THEN
821	c_v(k,i) = -c_max * ( v(k,ny,i) - v_m_n(k,ny,i) ) / ( denom * tsc(2) )
822	IF ( c_v(k,i) < 0.0_wp ) THEN
823	c_v(k,i) = 0.0_wp
824	ELSEIF ( c_v(k,i) > c_max ) THEN
825	c_v(k,i) = c_max
826	ENDIF
827	ELSE
828	c_v(k,i) = c_max
829	ENDIF
830
831	denom = w_m_n(k,ny,i) - w_m_n(k,ny-1,i)
832
833	IF ( denom /= 0.0_wp ) THEN
834	c_w(k,i) = -c_max * ( w(k,ny,i) - w_m_n(k,ny,i) ) / ( denom * tsc(2) )
835	IF ( c_w(k,i) < 0.0_wp ) THEN
836	c_w(k,i) = 0.0_wp
837	ELSEIF ( c_w(k,i) > c_max ) THEN
838	c_w(k,i) = c_max
839	ENDIF
840	ELSE
841	c_w(k,i) = c_max
842	ENDIF
843
844	c_u_m_l(k) = c_u_m_l(k) + c_u(k,i)
845	c_v_m_l(k) = c_v_m_l(k) + c_v(k,i)
846	c_w_m_l(k) = c_w_m_l(k) + c_w(k,i)
847
848	ENDDO
849	ENDDO
850
851	#if defined( __parallel )
852	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
853	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
854	MPI_SUM, comm1dx, ierr )
855	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
856	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
857	MPI_SUM, comm1dx, ierr )
858	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
859	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
860	MPI_SUM, comm1dx, ierr )
861	#else
862	c_u_m = c_u_m_l
863	c_v_m = c_v_m_l
864	c_w_m = c_w_m_l
865	#endif
866
867	c_u_m = c_u_m / (nx+1)
868	c_v_m = c_v_m / (nx+1)
869	c_w_m = c_w_m / (nx+1)
870
871	!
872	!-- Save old timelevels for the next timestep
873	IF ( intermediate_timestep_count == 1 ) THEN
874	u_m_n(:,:,:) = u(:,ny-1:ny,:)
875	v_m_n(:,:,:) = v(:,ny-1:ny,:)
876	w_m_n(:,:,:) = w(:,ny-1:ny,:)
877	ENDIF
878
879	!
880	!-- Calculate the new velocities
881	DO k = nzb+1, nzt+1
882	DO i = nxlg, nxrg
883	u_p(k,ny+1,i) = u(k,ny+1,i) - dt_3d * tsc(2) * c_u_m(k) * &
884	( u(k,ny+1,i) - u(k,ny,i) ) * ddy
885
886	v_p(k,ny+1,i) = v(k,ny+1,i) - dt_3d * tsc(2) * c_v_m(k) * &
887	( v(k,ny+1,i) - v(k,ny,i) ) * ddy
888
889	w_p(k,ny+1,i) = w(k,ny+1,i) - dt_3d * tsc(2) * c_w_m(k) * &
890	( w(k,ny+1,i) - w(k,ny,i) ) * ddy
891	ENDDO
892	ENDDO
893
894	!
895	!-- Bottom boundary at the outflow
896	IF ( ibc_uv_b == 0 ) THEN
897	u_p(nzb,ny+1,:) = 0.0_wp
898	v_p(nzb,ny+1,:) = 0.0_wp
899	ELSE
900	u_p(nzb,ny+1,:) = u_p(nzb+1,ny+1,:)
901	v_p(nzb,ny+1,:) = v_p(nzb+1,ny+1,:)
902	ENDIF
903	w_p(nzb,ny+1,:) = 0.0_wp
904
905	!
906	!-- Top boundary at the outflow
907	IF ( ibc_uv_t == 0 ) THEN
908	u_p(nzt+1,ny+1,:) = u_init(nzt+1)
909	v_p(nzt+1,ny+1,:) = v_init(nzt+1)
910	ELSE
911	u_p(nzt+1,ny+1,:) = u_p(nzt,nyn+1,:)
912	v_p(nzt+1,ny+1,:) = v_p(nzt,nyn+1,:)
913	ENDIF
914	w_p(nzt:nzt+1,ny+1,:) = 0.0_wp
915
916	ENDIF
917
918	ENDIF
919
920	IF ( outflow_l ) THEN
921
922	IF ( use_cmax ) THEN
923	u_p(:,:,0) = u(:,:,1)
924	v_p(:,:,-1) = v(:,:,0)
925	w_p(:,:,-1) = w(:,:,0)
926	ELSEIF ( .NOT. use_cmax ) THEN
927
928	c_max = dx / dt_3d
929
930	c_u_m_l = 0.0_wp
931	c_v_m_l = 0.0_wp
932	c_w_m_l = 0.0_wp
933
934	c_u_m = 0.0_wp
935	c_v_m = 0.0_wp
936	c_w_m = 0.0_wp
937
938	!
939	!-- Calculate the phase speeds for u, v, and w, first local and then
940	!-- average along the outflow boundary.
941	DO k = nzb+1, nzt+1
942	DO j = nys, nyn
943
944	denom = u_m_l(k,j,1) - u_m_l(k,j,2)
945
946	IF ( denom /= 0.0_wp ) THEN
947	c_u(k,j) = -c_max * ( u(k,j,1) - u_m_l(k,j,1) ) / ( denom * tsc(2) )
948	IF ( c_u(k,j) < 0.0_wp ) THEN
949	c_u(k,j) = 0.0_wp
950	ELSEIF ( c_u(k,j) > c_max ) THEN
951	c_u(k,j) = c_max
952	ENDIF
953	ELSE
954	c_u(k,j) = c_max
955	ENDIF
956
957	denom = v_m_l(k,j,0) - v_m_l(k,j,1)
958
959	IF ( denom /= 0.0_wp ) THEN
960	c_v(k,j) = -c_max * ( v(k,j,0) - v_m_l(k,j,0) ) / ( denom * tsc(2) )
961	IF ( c_v(k,j) < 0.0_wp ) THEN
962	c_v(k,j) = 0.0_wp
963	ELSEIF ( c_v(k,j) > c_max ) THEN
964	c_v(k,j) = c_max
965	ENDIF
966	ELSE
967	c_v(k,j) = c_max
968	ENDIF
969
970	denom = w_m_l(k,j,0) - w_m_l(k,j,1)
971
972	IF ( denom /= 0.0_wp ) THEN
973	c_w(k,j) = -c_max * ( w(k,j,0) - w_m_l(k,j,0) ) / ( denom * tsc(2) )
974	IF ( c_w(k,j) < 0.0_wp ) THEN
975	c_w(k,j) = 0.0_wp
976	ELSEIF ( c_w(k,j) > c_max ) THEN
977	c_w(k,j) = c_max
978	ENDIF
979	ELSE
980	c_w(k,j) = c_max
981	ENDIF
982
983	c_u_m_l(k) = c_u_m_l(k) + c_u(k,j)
984	c_v_m_l(k) = c_v_m_l(k) + c_v(k,j)
985	c_w_m_l(k) = c_w_m_l(k) + c_w(k,j)
986
987	ENDDO
988	ENDDO
989
990	#if defined( __parallel )
991	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
992	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
993	MPI_SUM, comm1dy, ierr )
994	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
995	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
996	MPI_SUM, comm1dy, ierr )
997	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
998	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
999	MPI_SUM, comm1dy, ierr )
1000	#else
1001	c_u_m = c_u_m_l
1002	c_v_m = c_v_m_l
1003	c_w_m = c_w_m_l
1004	#endif
1005
1006	c_u_m = c_u_m / (ny+1)
1007	c_v_m = c_v_m / (ny+1)
1008	c_w_m = c_w_m / (ny+1)
1009
1010	!
1011	!-- Save old timelevels for the next timestep
1012	IF ( intermediate_timestep_count == 1 ) THEN
1013	u_m_l(:,:,:) = u(:,:,1:2)
1014	v_m_l(:,:,:) = v(:,:,0:1)
1015	w_m_l(:,:,:) = w(:,:,0:1)
1016	ENDIF
1017
1018	!
1019	!-- Calculate the new velocities
1020	DO k = nzb+1, nzt+1
1021	DO j = nysg, nyng
1022	u_p(k,j,0) = u(k,j,0) - dt_3d * tsc(2) * c_u_m(k) * &
1023	( u(k,j,0) - u(k,j,1) ) * ddx
1024
1025	v_p(k,j,-1) = v(k,j,-1) - dt_3d * tsc(2) * c_v_m(k) * &
1026	( v(k,j,-1) - v(k,j,0) ) * ddx
1027
1028	w_p(k,j,-1) = w(k,j,-1) - dt_3d * tsc(2) * c_w_m(k) * &
1029	( w(k,j,-1) - w(k,j,0) ) * ddx
1030	ENDDO
1031	ENDDO
1032
1033	!
1034	!-- Bottom boundary at the outflow
1035	IF ( ibc_uv_b == 0 ) THEN
1036	u_p(nzb,:,0) = 0.0_wp
1037	v_p(nzb,:,-1) = 0.0_wp
1038	ELSE
1039	u_p(nzb,:,0) = u_p(nzb+1,:,0)
1040	v_p(nzb,:,-1) = v_p(nzb+1,:,-1)
1041	ENDIF
1042	w_p(nzb,:,-1) = 0.0_wp
1043
1044	!
1045	!-- Top boundary at the outflow
1046	IF ( ibc_uv_t == 0 ) THEN
1047	u_p(nzt+1,:,0) = u_init(nzt+1)
1048	v_p(nzt+1,:,-1) = v_init(nzt+1)
1049	ELSE
1050	u_p(nzt+1,:,0) = u_p(nzt,:,0)
1051	v_p(nzt+1,:,-1) = v_p(nzt,:,-1)
1052	ENDIF
1053	w_p(nzt:nzt+1,:,-1) = 0.0_wp
1054
1055	ENDIF
1056
1057	ENDIF
1058
1059	IF ( outflow_r ) THEN
1060
1061	IF ( use_cmax ) THEN
1062	u_p(:,:,nx+1) = u(:,:,nx)
1063	v_p(:,:,nx+1) = v(:,:,nx)
1064	w_p(:,:,nx+1) = w(:,:,nx)
1065	ELSEIF ( .NOT. use_cmax ) THEN
1066
1067	c_max = dx / dt_3d
1068
1069	c_u_m_l = 0.0_wp
1070	c_v_m_l = 0.0_wp
1071	c_w_m_l = 0.0_wp
1072
1073	c_u_m = 0.0_wp
1074	c_v_m = 0.0_wp
1075	c_w_m = 0.0_wp
1076
1077	!
1078	!-- Calculate the phase speeds for u, v, and w, first local and then
1079	!-- average along the outflow boundary.
1080	DO k = nzb+1, nzt+1
1081	DO j = nys, nyn
1082
1083	denom = u_m_r(k,j,nx) - u_m_r(k,j,nx-1)
1084
1085	IF ( denom /= 0.0_wp ) THEN
1086	c_u(k,j) = -c_max * ( u(k,j,nx) - u_m_r(k,j,nx) ) / ( denom * tsc(2) )
1087	IF ( c_u(k,j) < 0.0_wp ) THEN
1088	c_u(k,j) = 0.0_wp
1089	ELSEIF ( c_u(k,j) > c_max ) THEN
1090	c_u(k,j) = c_max
1091	ENDIF
1092	ELSE
1093	c_u(k,j) = c_max
1094	ENDIF
1095
1096	denom = v_m_r(k,j,nx) - v_m_r(k,j,nx-1)
1097
1098	IF ( denom /= 0.0_wp ) THEN
1099	c_v(k,j) = -c_max * ( v(k,j,nx) - v_m_r(k,j,nx) ) / ( denom * tsc(2) )
1100	IF ( c_v(k,j) < 0.0_wp ) THEN
1101	c_v(k,j) = 0.0_wp
1102	ELSEIF ( c_v(k,j) > c_max ) THEN
1103	c_v(k,j) = c_max
1104	ENDIF
1105	ELSE
1106	c_v(k,j) = c_max
1107	ENDIF
1108
1109	denom = w_m_r(k,j,nx) - w_m_r(k,j,nx-1)
1110
1111	IF ( denom /= 0.0_wp ) THEN
1112	c_w(k,j) = -c_max * ( w(k,j,nx) - w_m_r(k,j,nx) ) / ( denom * tsc(2) )
1113	IF ( c_w(k,j) < 0.0_wp ) THEN
1114	c_w(k,j) = 0.0_wp
1115	ELSEIF ( c_w(k,j) > c_max ) THEN
1116	c_w(k,j) = c_max
1117	ENDIF
1118	ELSE
1119	c_w(k,j) = c_max
1120	ENDIF
1121
1122	c_u_m_l(k) = c_u_m_l(k) + c_u(k,j)
1123	c_v_m_l(k) = c_v_m_l(k) + c_v(k,j)
1124	c_w_m_l(k) = c_w_m_l(k) + c_w(k,j)
1125
1126	ENDDO
1127	ENDDO
1128
1129	#if defined( __parallel )
1130	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
1131	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
1132	MPI_SUM, comm1dy, ierr )
1133	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
1134	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
1135	MPI_SUM, comm1dy, ierr )
1136	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
1137	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
1138	MPI_SUM, comm1dy, ierr )
1139	#else
1140	c_u_m = c_u_m_l
1141	c_v_m = c_v_m_l
1142	c_w_m = c_w_m_l
1143	#endif
1144
1145	c_u_m = c_u_m / (ny+1)
1146	c_v_m = c_v_m / (ny+1)
1147	c_w_m = c_w_m / (ny+1)
1148
1149	!
1150	!-- Save old timelevels for the next timestep
1151	IF ( intermediate_timestep_count == 1 ) THEN
1152	u_m_r(:,:,:) = u(:,:,nx-1:nx)
1153	v_m_r(:,:,:) = v(:,:,nx-1:nx)
1154	w_m_r(:,:,:) = w(:,:,nx-1:nx)
1155	ENDIF
1156
1157	!
1158	!-- Calculate the new velocities
1159	DO k = nzb+1, nzt+1
1160	DO j = nysg, nyng
1161	u_p(k,j,nx+1) = u(k,j,nx+1) - dt_3d * tsc(2) * c_u_m(k) * &
1162	( u(k,j,nx+1) - u(k,j,nx) ) * ddx
1163
1164	v_p(k,j,nx+1) = v(k,j,nx+1) - dt_3d * tsc(2) * c_v_m(k) * &
1165	( v(k,j,nx+1) - v(k,j,nx) ) * ddx
1166
1167	w_p(k,j,nx+1) = w(k,j,nx+1) - dt_3d * tsc(2) * c_w_m(k) * &
1168	( w(k,j,nx+1) - w(k,j,nx) ) * ddx
1169	ENDDO
1170	ENDDO
1171
1172	!
1173	!-- Bottom boundary at the outflow
1174	IF ( ibc_uv_b == 0 ) THEN
1175	u_p(nzb,:,nx+1) = 0.0_wp
1176	v_p(nzb,:,nx+1) = 0.0_wp
1177	ELSE
1178	u_p(nzb,:,nx+1) = u_p(nzb+1,:,nx+1)
1179	v_p(nzb,:,nx+1) = v_p(nzb+1,:,nx+1)
1180	ENDIF
1181	w_p(nzb,:,nx+1) = 0.0_wp
1182
1183	!
1184	!-- Top boundary at the outflow
1185	IF ( ibc_uv_t == 0 ) THEN
1186	u_p(nzt+1,:,nx+1) = u_init(nzt+1)
1187	v_p(nzt+1,:,nx+1) = v_init(nzt+1)
1188	ELSE
1189	u_p(nzt+1,:,nx+1) = u_p(nzt,:,nx+1)
1190	v_p(nzt+1,:,nx+1) = v_p(nzt,:,nx+1)
1191	ENDIF
1192	w_p(nzt:nzt+1,:,nx+1) = 0.0_wp
1193
1194	ENDIF
1195
1196	ENDIF
1197
1198	END SUBROUTINE boundary_conds

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