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source: palm/trunk/SOURCE/boundary_conds.f90 @ 1396

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1	SUBROUTINE boundary_conds
2
3	!--------------------------------------------------------------------------------!
4	! This file is part of PALM.
5	!
6	! PALM is free software: you can redistribute it and/or modify it under the terms
7	! of the GNU General Public License as published by the Free Software Foundation,
8	! either version 3 of the License, or (at your option) any later 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 1997-2014 Leibniz Universitaet Hannover
18	!--------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: boundary_conds.f90 1381 2014-04-28 12:41:59Z raasch $
27	!
28	! 1380 2014-04-28 12:40:45Z heinze
29	! Adjust Dirichlet-condition at the top for pt in case of nudging
30	!
31	! 1361 2014-04-16 15:17:48Z hoffmann
32	! Bottom and top boundary conditions of rain water content (qr) and
33	! rain drop concentration (nr) changed to Dirichlet
34	!
35	! 1353 2014-04-08 15:21:23Z heinze
36	! REAL constants provided with KIND-attribute
37	!
38	! 1320 2014-03-20 08:40:49Z raasch
39	! ONLY-attribute added to USE-statements,
40	! kind-parameters added to all INTEGER and REAL declaration statements,
41	! kinds are defined in new module kinds,
42	! revision history before 2012 removed,
43	! comment fields (!:) to be used for variable explanations added to
44	! all variable declaration statements
45	!
46	! 1257 2013-11-08 15:18:40Z raasch
47	! loop independent clauses added
48	!
49	! 1241 2013-10-30 11:36:58Z heinze
50	! Adjust ug and vg at each timestep in case of large_scale_forcing
51	!
52	! 1159 2013-05-21 11:58:22Z fricke
53	! Bugfix: Neumann boundary conditions for the velocity components at the
54	! outflow are in fact radiation boundary conditions using the maximum phase
55	! velocity that ensures numerical stability (CFL-condition).
56	! Hence, logical operator use_cmax is now used instead of bc_lr_dirneu/_neudir.
57	! Bugfix: In case of use_cmax at the outflow, u, v, w are replaced by
58	! u_p, v_p, w_p
59	!
60	! 1115 2013-03-26 18:16:16Z hoffmann
61	! boundary conditions of two-moment cloud scheme are restricted to Neumann-
62	! boundary-conditions
63	!
64	! 1113 2013-03-10 02:48:14Z raasch
65	! GPU-porting
66	! dummy argument "range" removed
67	! Bugfix: wrong index in loops of radiation boundary condition
68	!
69	! 1053 2012-11-13 17:11:03Z hoffmann
70	! boundary conditions for the two new prognostic equations (nr, qr) of the
71	! two-moment cloud scheme
72	!
73	! 1036 2012-10-22 13:43:42Z raasch
74	! code put under GPL (PALM 3.9)
75	!
76	! 996 2012-09-07 10:41:47Z raasch
77	! little reformatting
78	!
79	! 978 2012-08-09 08:28:32Z fricke
80	! Neumann boudnary conditions are added at the inflow boundary for the SGS-TKE.
81	! Outflow boundary conditions for the velocity components can be set to Neumann
82	! conditions or to radiation conditions with a horizontal averaged phase
83	! velocity.
84	!
85	! 875 2012-04-02 15:35:15Z gryschka
86	! Bugfix in case of dirichlet inflow bc at the right or north boundary
87	!
88	! Revision 1.1 1997/09/12 06:21:34 raasch
89	! Initial revision
90	!
91	!
92	! Description:
93	! ------------
94	! Boundary conditions for the prognostic quantities.
95	! One additional bottom boundary condition is applied for the TKE (=(u)*2)
96	! in prandtl_fluxes. The cyclic lateral boundary conditions are implicitly
97	! handled in routine exchange_horiz. Pressure boundary conditions are
98	! explicitly set in routines pres, poisfft, poismg and sor.
99	!------------------------------------------------------------------------------!
100
101	USE arrays_3d, &
102	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, &
103	dzu, e_p, nr_p, pt, pt_p, q, q_p, qr_p, sa, sa_p, &
104	u, ug, u_init, u_m_l, u_m_n, u_m_r, u_m_s, u_p, &
105	v, vg, v_init, v_m_l, v_m_n, v_m_r, v_m_s, v_p, &
106	w, w_p, w_m_l, w_m_n, w_m_r, w_m_s,&
107	pt_init
108
109	USE control_parameters, &
110	ONLY: bc_pt_t_val, bc_q_t_val, constant_diffusion, &
111	cloud_physics, dt_3d, humidity, &
112	ibc_pt_b, ibc_pt_t, ibc_q_b, ibc_sa_t, ibc_uv_b, ibc_uv_t, &
113	icloud_scheme, inflow_l, inflow_n, inflow_r, inflow_s, &
114	intermediate_timestep_count, large_scale_forcing, ocean, &
115	outflow_l, outflow_n, outflow_r, outflow_s, passive_scalar, &
116	precipitation, tsc, use_cmax, &
117	nudging
118
119	USE grid_variables, &
120	ONLY: ddx, ddy, dx, dy
121
122	USE indices, &
123	ONLY: nx, nxl, nxlg, nxr, nxrg, ny, nyn, nyng, nys, nysg, &
124	nzb, nzb_s_inner, nzb_w_inner, nzt
125
126	USE kinds
127
128	USE pegrid
129
130
131	IMPLICIT NONE
132
133	INTEGER(iwp) :: i !:
134	INTEGER(iwp) :: j !:
135	INTEGER(iwp) :: k !:
136
137	REAL(wp) :: c_max !:
138	REAL(wp) :: denom !:
139
140
141	!
142	!-- Bottom boundary
143	IF ( ibc_uv_b == 1 ) THEN
144	!$acc kernels present( u_p, v_p )
145	u_p(nzb,:,:) = u_p(nzb+1,:,:)
146	v_p(nzb,:,:) = v_p(nzb+1,:,:)
147	!$acc end kernels
148	ENDIF
149
150	!$acc kernels present( nzb_w_inner, w_p )
151	DO i = nxlg, nxrg
152	DO j = nysg, nyng
153	w_p(nzb_w_inner(j,i),j,i) = 0.0_wp
154	ENDDO
155	ENDDO
156	!$acc end kernels
157
158	!
159	!-- Top boundary
160	IF ( ibc_uv_t == 0 ) THEN
161	!$acc kernels present( u_init, u_p, v_init, v_p )
162	u_p(nzt+1,:,:) = u_init(nzt+1)
163	v_p(nzt+1,:,:) = v_init(nzt+1)
164	IF ( large_scale_forcing) THEN
165	u_p(nzt+1,:,:) = ug(nzt+1)
166	v_p(nzt+1,:,:) = vg(nzt+1)
167	END IF
168	!$acc end kernels
169	ELSE
170	!$acc kernels present( u_p, v_p )
171	u_p(nzt+1,:,:) = u_p(nzt,:,:)
172	v_p(nzt+1,:,:) = v_p(nzt,:,:)
173	!$acc end kernels
174	ENDIF
175	!$acc kernels present( w_p )
176	w_p(nzt:nzt+1,:,:) = 0.0_wp ! nzt is not a prognostic level (but cf. pres)
177	!$acc end kernels
178
179	!
180	!-- Temperature at bottom boundary.
181	!-- In case of coupled runs (ibc_pt_b = 2) the temperature is given by
182	!-- the sea surface temperature of the coupled ocean model.
183	IF ( ibc_pt_b == 0 ) THEN
184	!$acc kernels present( nzb_s_inner, pt, pt_p )
185	!$acc loop independent
186	DO i = nxlg, nxrg
187	!$acc loop independent
188	DO j = nysg, nyng
189	pt_p(nzb_s_inner(j,i),j,i) = pt(nzb_s_inner(j,i),j,i)
190	ENDDO
191	ENDDO
192	!$acc end kernels
193	ELSEIF ( ibc_pt_b == 1 ) THEN
194	!$acc kernels present( nzb_s_inner, pt_p )
195	!$acc loop independent
196	DO i = nxlg, nxrg
197	!$acc loop independent
198	DO j = nysg, nyng
199	pt_p(nzb_s_inner(j,i),j,i) = pt_p(nzb_s_inner(j,i)+1,j,i)
200	ENDDO
201	ENDDO
202	!$acc end kernels
203	ENDIF
204
205	!
206	!-- Temperature at top boundary
207	IF ( ibc_pt_t == 0 ) THEN
208	!$acc kernels present( pt, pt_p )
209	pt_p(nzt+1,:,:) = pt(nzt+1,:,:)
210	!
211	!-- In case of nudging adjust top boundary to pt which is
212	!-- read in from NUDGING-DATA
213	IF ( nudging ) THEN
214	pt_p(nzt+1,:,:) = pt_init(nzt+1)
215	ENDIF
216	!$acc end kernels
217	ELSEIF ( ibc_pt_t == 1 ) THEN
218	!$acc kernels present( pt_p )
219	pt_p(nzt+1,:,:) = pt_p(nzt,:,:)
220	!$acc end kernels
221	ELSEIF ( ibc_pt_t == 2 ) THEN
222	!$acc kernels present( dzu, pt_p )
223	pt_p(nzt+1,:,:) = pt_p(nzt,:,:) + bc_pt_t_val * dzu(nzt+1)
224	!$acc end kernels
225	ENDIF
226
227	!
228	!-- Boundary conditions for TKE
229	!-- Generally Neumann conditions with de/dz=0 are assumed
230	IF ( .NOT. constant_diffusion ) THEN
231	!$acc kernels present( e_p, nzb_s_inner )
232	!$acc loop independent
233	DO i = nxlg, nxrg
234	!$acc loop independent
235	DO j = nysg, nyng
236	e_p(nzb_s_inner(j,i),j,i) = e_p(nzb_s_inner(j,i)+1,j,i)
237	ENDDO
238	ENDDO
239	e_p(nzt+1,:,:) = e_p(nzt,:,:)
240	!$acc end kernels
241	ENDIF
242
243	!
244	!-- Boundary conditions for salinity
245	IF ( ocean ) THEN
246	!
247	!-- Bottom boundary: Neumann condition because salinity flux is always
248	!-- given
249	DO i = nxlg, nxrg
250	DO j = nysg, nyng
251	sa_p(nzb_s_inner(j,i),j,i) = sa_p(nzb_s_inner(j,i)+1,j,i)
252	ENDDO
253	ENDDO
254
255	!
256	!-- Top boundary: Dirichlet or Neumann
257	IF ( ibc_sa_t == 0 ) THEN
258	sa_p(nzt+1,:,:) = sa(nzt+1,:,:)
259	ELSEIF ( ibc_sa_t == 1 ) THEN
260	sa_p(nzt+1,:,:) = sa_p(nzt,:,:)
261	ENDIF
262
263	ENDIF
264
265	!
266	!-- Boundary conditions for total water content or scalar,
267	!-- bottom and top boundary (see also temperature)
268	IF ( humidity .OR. passive_scalar ) THEN
269	!
270	!-- Surface conditions for constant_humidity_flux
271	IF ( ibc_q_b == 0 ) THEN
272	DO i = nxlg, nxrg
273	DO j = nysg, nyng
274	q_p(nzb_s_inner(j,i),j,i) = q(nzb_s_inner(j,i),j,i)
275	ENDDO
276	ENDDO
277	ELSE
278	DO i = nxlg, nxrg
279	DO j = nysg, nyng
280	q_p(nzb_s_inner(j,i),j,i) = q_p(nzb_s_inner(j,i)+1,j,i)
281	ENDDO
282	ENDDO
283	ENDIF
284	!
285	!-- Top boundary
286	q_p(nzt+1,:,:) = q_p(nzt,:,:) + bc_q_t_val * dzu(nzt+1)
287
288	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. precipitation ) THEN
289	!
290	!-- Surface conditions rain water (Dirichlet)
291	DO i = nxlg, nxrg
292	DO j = nysg, nyng
293	qr_p(nzb_s_inner(j,i),j,i) = 0.0_wp
294	nr_p(nzb_s_inner(j,i),j,i) = 0.0_wp
295	ENDDO
296	ENDDO
297	!
298	!-- Top boundary condition for rain water (Dirichlet)
299	qr_p(nzt+1,:,:) = 0.0_wp
300	nr_p(nzt+1,:,:) = 0.0_wp
301
302	ENDIF
303	!
304	!-- In case of inflow at the south boundary the boundary for v is at nys
305	!-- and in case of inflow at the left boundary the boundary for u is at nxl.
306	!-- Since in prognostic_equations (cache optimized version) these levels are
307	!-- handled as a prognostic level, boundary values have to be restored here.
308	!-- For the SGS-TKE, Neumann boundary conditions are used at the inflow.
309	IF ( inflow_s ) THEN
310	v_p(:,nys,:) = v_p(:,nys-1,:)
311	IF ( .NOT. constant_diffusion ) e_p(:,nys-1,:) = e_p(:,nys,:)
312	ELSEIF ( inflow_n ) THEN
313	IF ( .NOT. constant_diffusion ) e_p(:,nyn+1,:) = e_p(:,nyn,:)
314	ELSEIF ( inflow_l ) THEN
315	u_p(:,:,nxl) = u_p(:,:,nxl-1)
316	IF ( .NOT. constant_diffusion ) e_p(:,:,nxl-1) = e_p(:,:,nxl)
317	ELSEIF ( inflow_r ) THEN
318	IF ( .NOT. constant_diffusion ) e_p(:,:,nxr+1) = e_p(:,:,nxr)
319	ENDIF
320
321	!
322	!-- Lateral boundary conditions for scalar quantities at the outflow
323	IF ( outflow_s ) THEN
324	pt_p(:,nys-1,:) = pt_p(:,nys,:)
325	IF ( .NOT. constant_diffusion ) e_p(:,nys-1,:) = e_p(:,nys,:)
326	IF ( humidity .OR. passive_scalar ) THEN
327	q_p(:,nys-1,:) = q_p(:,nys,:)
328	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
329	precipitation) THEN
330	qr_p(:,nys-1,:) = qr_p(:,nys,:)
331	nr_p(:,nys-1,:) = nr_p(:,nys,:)
332	ENDIF
333	ENDIF
334	ELSEIF ( outflow_n ) THEN
335	pt_p(:,nyn+1,:) = pt_p(:,nyn,:)
336	IF ( .NOT. constant_diffusion ) e_p(:,nyn+1,:) = e_p(:,nyn,:)
337	IF ( humidity .OR. passive_scalar ) THEN
338	q_p(:,nyn+1,:) = q_p(:,nyn,:)
339	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
340	precipitation ) THEN
341	qr_p(:,nyn+1,:) = qr_p(:,nyn,:)
342	nr_p(:,nyn+1,:) = nr_p(:,nyn,:)
343	ENDIF
344	ENDIF
345	ELSEIF ( outflow_l ) THEN
346	pt_p(:,:,nxl-1) = pt_p(:,:,nxl)
347	IF ( .NOT. constant_diffusion ) e_p(:,:,nxl-1) = e_p(:,:,nxl)
348	IF ( humidity .OR. passive_scalar ) THEN
349	q_p(:,:,nxl-1) = q_p(:,:,nxl)
350	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
351	precipitation ) THEN
352	qr_p(:,:,nxl-1) = qr_p(:,:,nxl)
353	nr_p(:,:,nxl-1) = nr_p(:,:,nxl)
354	ENDIF
355	ENDIF
356	ELSEIF ( outflow_r ) THEN
357	pt_p(:,:,nxr+1) = pt_p(:,:,nxr)
358	IF ( .NOT. constant_diffusion ) e_p(:,:,nxr+1) = e_p(:,:,nxr)
359	IF ( humidity .OR. passive_scalar ) THEN
360	q_p(:,:,nxr+1) = q_p(:,:,nxr)
361	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. precipitation ) THEN
362	qr_p(:,:,nxr+1) = qr_p(:,:,nxr)
363	nr_p(:,:,nxr+1) = nr_p(:,:,nxr)
364	ENDIF
365	ENDIF
366	ENDIF
367
368	ENDIF
369
370	!
371	!-- Radiation boundary conditions for the velocities at the respective outflow.
372	!-- The phase velocity is either assumed to the maximum phase velocity that
373	!-- ensures numerical stability (CFL-condition) or calculated after
374	!-- Orlanski(1976) and averaged along the outflow boundary.
375	IF ( outflow_s ) THEN
376
377	IF ( use_cmax ) THEN
378	u_p(:,-1,:) = u(:,0,:)
379	v_p(:,0,:) = v(:,1,:)
380	w_p(:,-1,:) = w(:,0,:)
381	ELSEIF ( .NOT. use_cmax ) THEN
382
383	c_max = dy / dt_3d
384
385	c_u_m_l = 0.0_wp
386	c_v_m_l = 0.0_wp
387	c_w_m_l = 0.0_wp
388
389	c_u_m = 0.0_wp
390	c_v_m = 0.0_wp
391	c_w_m = 0.0_wp
392
393	!
394	!-- Calculate the phase speeds for u, v, and w, first local and then
395	!-- average along the outflow boundary.
396	DO k = nzb+1, nzt+1
397	DO i = nxl, nxr
398
399	denom = u_m_s(k,0,i) - u_m_s(k,1,i)
400
401	IF ( denom /= 0.0_wp ) THEN
402	c_u(k,i) = -c_max * ( u(k,0,i) - u_m_s(k,0,i) ) / ( denom * tsc(2) )
403	IF ( c_u(k,i) < 0.0_wp ) THEN
404	c_u(k,i) = 0.0_wp
405	ELSEIF ( c_u(k,i) > c_max ) THEN
406	c_u(k,i) = c_max
407	ENDIF
408	ELSE
409	c_u(k,i) = c_max
410	ENDIF
411
412	denom = v_m_s(k,1,i) - v_m_s(k,2,i)
413
414	IF ( denom /= 0.0_wp ) THEN
415	c_v(k,i) = -c_max * ( v(k,1,i) - v_m_s(k,1,i) ) / ( denom * tsc(2) )
416	IF ( c_v(k,i) < 0.0_wp ) THEN
417	c_v(k,i) = 0.0_wp
418	ELSEIF ( c_v(k,i) > c_max ) THEN
419	c_v(k,i) = c_max
420	ENDIF
421	ELSE
422	c_v(k,i) = c_max
423	ENDIF
424
425	denom = w_m_s(k,0,i) - w_m_s(k,1,i)
426
427	IF ( denom /= 0.0_wp ) THEN
428	c_w(k,i) = -c_max * ( w(k,0,i) - w_m_s(k,0,i) ) / ( denom * tsc(2) )
429	IF ( c_w(k,i) < 0.0_wp ) THEN
430	c_w(k,i) = 0.0_wp
431	ELSEIF ( c_w(k,i) > c_max ) THEN
432	c_w(k,i) = c_max
433	ENDIF
434	ELSE
435	c_w(k,i) = c_max
436	ENDIF
437
438	c_u_m_l(k) = c_u_m_l(k) + c_u(k,i)
439	c_v_m_l(k) = c_v_m_l(k) + c_v(k,i)
440	c_w_m_l(k) = c_w_m_l(k) + c_w(k,i)
441
442	ENDDO
443	ENDDO
444
445	#if defined( __parallel )
446	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
447	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
448	MPI_SUM, comm1dx, ierr )
449	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
450	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
451	MPI_SUM, comm1dx, ierr )
452	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
453	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
454	MPI_SUM, comm1dx, ierr )
455	#else
456	c_u_m = c_u_m_l
457	c_v_m = c_v_m_l
458	c_w_m = c_w_m_l
459	#endif
460
461	c_u_m = c_u_m / (nx+1)
462	c_v_m = c_v_m / (nx+1)
463	c_w_m = c_w_m / (nx+1)
464
465	!
466	!-- Save old timelevels for the next timestep
467	IF ( intermediate_timestep_count == 1 ) THEN
468	u_m_s(:,:,:) = u(:,0:1,:)
469	v_m_s(:,:,:) = v(:,1:2,:)
470	w_m_s(:,:,:) = w(:,0:1,:)
471	ENDIF
472
473	!
474	!-- Calculate the new velocities
475	DO k = nzb+1, nzt+1
476	DO i = nxlg, nxrg
477	u_p(k,-1,i) = u(k,-1,i) - dt_3d * tsc(2) * c_u_m(k) * &
478	( u(k,-1,i) - u(k,0,i) ) * ddy
479
480	v_p(k,0,i) = v(k,0,i) - dt_3d * tsc(2) * c_v_m(k) * &
481	( v(k,0,i) - v(k,1,i) ) * ddy
482
483	w_p(k,-1,i) = w(k,-1,i) - dt_3d * tsc(2) * c_w_m(k) * &
484	( w(k,-1,i) - w(k,0,i) ) * ddy
485	ENDDO
486	ENDDO
487
488	!
489	!-- Bottom boundary at the outflow
490	IF ( ibc_uv_b == 0 ) THEN
491	u_p(nzb,-1,:) = 0.0_wp
492	v_p(nzb,0,:) = 0.0_wp
493	ELSE
494	u_p(nzb,-1,:) = u_p(nzb+1,-1,:)
495	v_p(nzb,0,:) = v_p(nzb+1,0,:)
496	ENDIF
497	w_p(nzb,-1,:) = 0.0_wp
498
499	!
500	!-- Top boundary at the outflow
501	IF ( ibc_uv_t == 0 ) THEN
502	u_p(nzt+1,-1,:) = u_init(nzt+1)
503	v_p(nzt+1,0,:) = v_init(nzt+1)
504	ELSE
505	u_p(nzt+1,-1,:) = u(nzt,-1,:)
506	v_p(nzt+1,0,:) = v(nzt,0,:)
507	ENDIF
508	w_p(nzt:nzt+1,-1,:) = 0.0_wp
509
510	ENDIF
511
512	ENDIF
513
514	IF ( outflow_n ) THEN
515
516	IF ( use_cmax ) THEN
517	u_p(:,ny+1,:) = u(:,ny,:)
518	v_p(:,ny+1,:) = v(:,ny,:)
519	w_p(:,ny+1,:) = w(:,ny,:)
520	ELSEIF ( .NOT. use_cmax ) THEN
521
522	c_max = dy / dt_3d
523
524	c_u_m_l = 0.0_wp
525	c_v_m_l = 0.0_wp
526	c_w_m_l = 0.0_wp
527
528	c_u_m = 0.0_wp
529	c_v_m = 0.0_wp
530	c_w_m = 0.0_wp
531
532	!
533	!-- Calculate the phase speeds for u, v, and w, first local and then
534	!-- average along the outflow boundary.
535	DO k = nzb+1, nzt+1
536	DO i = nxl, nxr
537
538	denom = u_m_n(k,ny,i) - u_m_n(k,ny-1,i)
539
540	IF ( denom /= 0.0_wp ) THEN
541	c_u(k,i) = -c_max * ( u(k,ny,i) - u_m_n(k,ny,i) ) / ( denom * tsc(2) )
542	IF ( c_u(k,i) < 0.0_wp ) THEN
543	c_u(k,i) = 0.0_wp
544	ELSEIF ( c_u(k,i) > c_max ) THEN
545	c_u(k,i) = c_max
546	ENDIF
547	ELSE
548	c_u(k,i) = c_max
549	ENDIF
550
551	denom = v_m_n(k,ny,i) - v_m_n(k,ny-1,i)
552
553	IF ( denom /= 0.0_wp ) THEN
554	c_v(k,i) = -c_max * ( v(k,ny,i) - v_m_n(k,ny,i) ) / ( denom * tsc(2) )
555	IF ( c_v(k,i) < 0.0_wp ) THEN
556	c_v(k,i) = 0.0_wp
557	ELSEIF ( c_v(k,i) > c_max ) THEN
558	c_v(k,i) = c_max
559	ENDIF
560	ELSE
561	c_v(k,i) = c_max
562	ENDIF
563
564	denom = w_m_n(k,ny,i) - w_m_n(k,ny-1,i)
565
566	IF ( denom /= 0.0_wp ) THEN
567	c_w(k,i) = -c_max * ( w(k,ny,i) - w_m_n(k,ny,i) ) / ( denom * tsc(2) )
568	IF ( c_w(k,i) < 0.0_wp ) THEN
569	c_w(k,i) = 0.0_wp
570	ELSEIF ( c_w(k,i) > c_max ) THEN
571	c_w(k,i) = c_max
572	ENDIF
573	ELSE
574	c_w(k,i) = c_max
575	ENDIF
576
577	c_u_m_l(k) = c_u_m_l(k) + c_u(k,i)
578	c_v_m_l(k) = c_v_m_l(k) + c_v(k,i)
579	c_w_m_l(k) = c_w_m_l(k) + c_w(k,i)
580
581	ENDDO
582	ENDDO
583
584	#if defined( __parallel )
585	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
586	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
587	MPI_SUM, comm1dx, ierr )
588	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
589	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
590	MPI_SUM, comm1dx, ierr )
591	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
592	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
593	MPI_SUM, comm1dx, ierr )
594	#else
595	c_u_m = c_u_m_l
596	c_v_m = c_v_m_l
597	c_w_m = c_w_m_l
598	#endif
599
600	c_u_m = c_u_m / (nx+1)
601	c_v_m = c_v_m / (nx+1)
602	c_w_m = c_w_m / (nx+1)
603
604	!
605	!-- Save old timelevels for the next timestep
606	IF ( intermediate_timestep_count == 1 ) THEN
607	u_m_n(:,:,:) = u(:,ny-1:ny,:)
608	v_m_n(:,:,:) = v(:,ny-1:ny,:)
609	w_m_n(:,:,:) = w(:,ny-1:ny,:)
610	ENDIF
611
612	!
613	!-- Calculate the new velocities
614	DO k = nzb+1, nzt+1
615	DO i = nxlg, nxrg
616	u_p(k,ny+1,i) = u(k,ny+1,i) - dt_3d * tsc(2) * c_u_m(k) * &
617	( u(k,ny+1,i) - u(k,ny,i) ) * ddy
618
619	v_p(k,ny+1,i) = v(k,ny+1,i) - dt_3d * tsc(2) * c_v_m(k) * &
620	( v(k,ny+1,i) - v(k,ny,i) ) * ddy
621
622	w_p(k,ny+1,i) = w(k,ny+1,i) - dt_3d * tsc(2) * c_w_m(k) * &
623	( w(k,ny+1,i) - w(k,ny,i) ) * ddy
624	ENDDO
625	ENDDO
626
627	!
628	!-- Bottom boundary at the outflow
629	IF ( ibc_uv_b == 0 ) THEN
630	u_p(nzb,ny+1,:) = 0.0_wp
631	v_p(nzb,ny+1,:) = 0.0_wp
632	ELSE
633	u_p(nzb,ny+1,:) = u_p(nzb+1,ny+1,:)
634	v_p(nzb,ny+1,:) = v_p(nzb+1,ny+1,:)
635	ENDIF
636	w_p(nzb,ny+1,:) = 0.0_wp
637
638	!
639	!-- Top boundary at the outflow
640	IF ( ibc_uv_t == 0 ) THEN
641	u_p(nzt+1,ny+1,:) = u_init(nzt+1)
642	v_p(nzt+1,ny+1,:) = v_init(nzt+1)
643	ELSE
644	u_p(nzt+1,ny+1,:) = u_p(nzt,nyn+1,:)
645	v_p(nzt+1,ny+1,:) = v_p(nzt,nyn+1,:)
646	ENDIF
647	w_p(nzt:nzt+1,ny+1,:) = 0.0_wp
648
649	ENDIF
650
651	ENDIF
652
653	IF ( outflow_l ) THEN
654
655	IF ( use_cmax ) THEN
656	u_p(:,:,-1) = u(:,:,0)
657	v_p(:,:,0) = v(:,:,1)
658	w_p(:,:,-1) = w(:,:,0)
659	ELSEIF ( .NOT. use_cmax ) THEN
660
661	c_max = dx / dt_3d
662
663	c_u_m_l = 0.0_wp
664	c_v_m_l = 0.0_wp
665	c_w_m_l = 0.0_wp
666
667	c_u_m = 0.0_wp
668	c_v_m = 0.0_wp
669	c_w_m = 0.0_wp
670
671	!
672	!-- Calculate the phase speeds for u, v, and w, first local and then
673	!-- average along the outflow boundary.
674	DO k = nzb+1, nzt+1
675	DO j = nys, nyn
676
677	denom = u_m_l(k,j,1) - u_m_l(k,j,2)
678
679	IF ( denom /= 0.0_wp ) THEN
680	c_u(k,j) = -c_max * ( u(k,j,1) - u_m_l(k,j,1) ) / ( denom * tsc(2) )
681	IF ( c_u(k,j) < 0.0_wp ) THEN
682	c_u(k,j) = 0.0_wp
683	ELSEIF ( c_u(k,j) > c_max ) THEN
684	c_u(k,j) = c_max
685	ENDIF
686	ELSE
687	c_u(k,j) = c_max
688	ENDIF
689
690	denom = v_m_l(k,j,0) - v_m_l(k,j,1)
691
692	IF ( denom /= 0.0_wp ) THEN
693	c_v(k,j) = -c_max * ( v(k,j,0) - v_m_l(k,j,0) ) / ( denom * tsc(2) )
694	IF ( c_v(k,j) < 0.0_wp ) THEN
695	c_v(k,j) = 0.0_wp
696	ELSEIF ( c_v(k,j) > c_max ) THEN
697	c_v(k,j) = c_max
698	ENDIF
699	ELSE
700	c_v(k,j) = c_max
701	ENDIF
702
703	denom = w_m_l(k,j,0) - w_m_l(k,j,1)
704
705	IF ( denom /= 0.0_wp ) THEN
706	c_w(k,j) = -c_max * ( w(k,j,0) - w_m_l(k,j,0) ) / ( denom * tsc(2) )
707	IF ( c_w(k,j) < 0.0_wp ) THEN
708	c_w(k,j) = 0.0_wp
709	ELSEIF ( c_w(k,j) > c_max ) THEN
710	c_w(k,j) = c_max
711	ENDIF
712	ELSE
713	c_w(k,j) = c_max
714	ENDIF
715
716	c_u_m_l(k) = c_u_m_l(k) + c_u(k,j)
717	c_v_m_l(k) = c_v_m_l(k) + c_v(k,j)
718	c_w_m_l(k) = c_w_m_l(k) + c_w(k,j)
719
720	ENDDO
721	ENDDO
722
723	#if defined( __parallel )
724	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
725	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
726	MPI_SUM, comm1dy, ierr )
727	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
728	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
729	MPI_SUM, comm1dy, ierr )
730	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
731	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
732	MPI_SUM, comm1dy, ierr )
733	#else
734	c_u_m = c_u_m_l
735	c_v_m = c_v_m_l
736	c_w_m = c_w_m_l
737	#endif
738
739	c_u_m = c_u_m / (ny+1)
740	c_v_m = c_v_m / (ny+1)
741	c_w_m = c_w_m / (ny+1)
742
743	!
744	!-- Save old timelevels for the next timestep
745	IF ( intermediate_timestep_count == 1 ) THEN
746	u_m_l(:,:,:) = u(:,:,1:2)
747	v_m_l(:,:,:) = v(:,:,0:1)
748	w_m_l(:,:,:) = w(:,:,0:1)
749	ENDIF
750
751	!
752	!-- Calculate the new velocities
753	DO k = nzb+1, nzt+1
754	DO j = nysg, nyng
755	u_p(k,j,0) = u(k,j,0) - dt_3d * tsc(2) * c_u_m(k) * &
756	( u(k,j,0) - u(k,j,1) ) * ddx
757
758	v_p(k,j,-1) = v(k,j,-1) - dt_3d * tsc(2) * c_v_m(k) * &
759	( v(k,j,-1) - v(k,j,0) ) * ddx
760
761	w_p(k,j,-1) = w(k,j,-1) - dt_3d * tsc(2) * c_w_m(k) * &
762	( w(k,j,-1) - w(k,j,0) ) * ddx
763	ENDDO
764	ENDDO
765
766	!
767	!-- Bottom boundary at the outflow
768	IF ( ibc_uv_b == 0 ) THEN
769	u_p(nzb,:,0) = 0.0_wp
770	v_p(nzb,:,-1) = 0.0_wp
771	ELSE
772	u_p(nzb,:,0) = u_p(nzb+1,:,0)
773	v_p(nzb,:,-1) = v_p(nzb+1,:,-1)
774	ENDIF
775	w_p(nzb,:,-1) = 0.0_wp
776
777	!
778	!-- Top boundary at the outflow
779	IF ( ibc_uv_t == 0 ) THEN
780	u_p(nzt+1,:,-1) = u_init(nzt+1)
781	v_p(nzt+1,:,-1) = v_init(nzt+1)
782	ELSE
783	u_p(nzt+1,:,-1) = u_p(nzt,:,-1)
784	v_p(nzt+1,:,-1) = v_p(nzt,:,-1)
785	ENDIF
786	w_p(nzt:nzt+1,:,-1) = 0.0_wp
787
788	ENDIF
789
790	ENDIF
791
792	IF ( outflow_r ) THEN
793
794	IF ( use_cmax ) THEN
795	u_p(:,:,nx+1) = u(:,:,nx)
796	v_p(:,:,nx+1) = v(:,:,nx)
797	w_p(:,:,nx+1) = w(:,:,nx)
798	ELSEIF ( .NOT. use_cmax ) THEN
799
800	c_max = dx / dt_3d
801
802	c_u_m_l = 0.0_wp
803	c_v_m_l = 0.0_wp
804	c_w_m_l = 0.0_wp
805
806	c_u_m = 0.0_wp
807	c_v_m = 0.0_wp
808	c_w_m = 0.0_wp
809
810	!
811	!-- Calculate the phase speeds for u, v, and w, first local and then
812	!-- average along the outflow boundary.
813	DO k = nzb+1, nzt+1
814	DO j = nys, nyn
815
816	denom = u_m_r(k,j,nx) - u_m_r(k,j,nx-1)
817
818	IF ( denom /= 0.0_wp ) THEN
819	c_u(k,j) = -c_max * ( u(k,j,nx) - u_m_r(k,j,nx) ) / ( denom * tsc(2) )
820	IF ( c_u(k,j) < 0.0_wp ) THEN
821	c_u(k,j) = 0.0_wp
822	ELSEIF ( c_u(k,j) > c_max ) THEN
823	c_u(k,j) = c_max
824	ENDIF
825	ELSE
826	c_u(k,j) = c_max
827	ENDIF
828
829	denom = v_m_r(k,j,nx) - v_m_r(k,j,nx-1)
830
831	IF ( denom /= 0.0_wp ) THEN
832	c_v(k,j) = -c_max * ( v(k,j,nx) - v_m_r(k,j,nx) ) / ( denom * tsc(2) )
833	IF ( c_v(k,j) < 0.0_wp ) THEN
834	c_v(k,j) = 0.0_wp
835	ELSEIF ( c_v(k,j) > c_max ) THEN
836	c_v(k,j) = c_max
837	ENDIF
838	ELSE
839	c_v(k,j) = c_max
840	ENDIF
841
842	denom = w_m_r(k,j,nx) - w_m_r(k,j,nx-1)
843
844	IF ( denom /= 0.0_wp ) THEN
845	c_w(k,j) = -c_max * ( w(k,j,nx) - w_m_r(k,j,nx) ) / ( denom * tsc(2) )
846	IF ( c_w(k,j) < 0.0_wp ) THEN
847	c_w(k,j) = 0.0_wp
848	ELSEIF ( c_w(k,j) > c_max ) THEN
849	c_w(k,j) = c_max
850	ENDIF
851	ELSE
852	c_w(k,j) = c_max
853	ENDIF
854
855	c_u_m_l(k) = c_u_m_l(k) + c_u(k,j)
856	c_v_m_l(k) = c_v_m_l(k) + c_v(k,j)
857	c_w_m_l(k) = c_w_m_l(k) + c_w(k,j)
858
859	ENDDO
860	ENDDO
861
862	#if defined( __parallel )
863	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
864	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
865	MPI_SUM, comm1dy, ierr )
866	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
867	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
868	MPI_SUM, comm1dy, ierr )
869	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
870	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
871	MPI_SUM, comm1dy, ierr )
872	#else
873	c_u_m = c_u_m_l
874	c_v_m = c_v_m_l
875	c_w_m = c_w_m_l
876	#endif
877
878	c_u_m = c_u_m / (ny+1)
879	c_v_m = c_v_m / (ny+1)
880	c_w_m = c_w_m / (ny+1)
881
882	!
883	!-- Save old timelevels for the next timestep
884	IF ( intermediate_timestep_count == 1 ) THEN
885	u_m_r(:,:,:) = u(:,:,nx-1:nx)
886	v_m_r(:,:,:) = v(:,:,nx-1:nx)
887	w_m_r(:,:,:) = w(:,:,nx-1:nx)
888	ENDIF
889
890	!
891	!-- Calculate the new velocities
892	DO k = nzb+1, nzt+1
893	DO j = nysg, nyng
894	u_p(k,j,nx+1) = u(k,j,nx+1) - dt_3d * tsc(2) * c_u_m(k) * &
895	( u(k,j,nx+1) - u(k,j,nx) ) * ddx
896
897	v_p(k,j,nx+1) = v(k,j,nx+1) - dt_3d * tsc(2) * c_v_m(k) * &
898	( v(k,j,nx+1) - v(k,j,nx) ) * ddx
899
900	w_p(k,j,nx+1) = w(k,j,nx+1) - dt_3d * tsc(2) * c_w_m(k) * &
901	( w(k,j,nx+1) - w(k,j,nx) ) * ddx
902	ENDDO
903	ENDDO
904
905	!
906	!-- Bottom boundary at the outflow
907	IF ( ibc_uv_b == 0 ) THEN
908	u_p(nzb,:,nx+1) = 0.0_wp
909	v_p(nzb,:,nx+1) = 0.0_wp
910	ELSE
911	u_p(nzb,:,nx+1) = u_p(nzb+1,:,nx+1)
912	v_p(nzb,:,nx+1) = v_p(nzb+1,:,nx+1)
913	ENDIF
914	w_p(nzb,:,nx+1) = 0.0_wp
915
916	!
917	!-- Top boundary at the outflow
918	IF ( ibc_uv_t == 0 ) THEN
919	u_p(nzt+1,:,nx+1) = u_init(nzt+1)
920	v_p(nzt+1,:,nx+1) = v_init(nzt+1)
921	ELSE
922	u_p(nzt+1,:,nx+1) = u_p(nzt,:,nx+1)
923	v_p(nzt+1,:,nx+1) = v_p(nzt,:,nx+1)
924	ENDIF
925	w(nzt:nzt+1,:,nx+1) = 0.0_wp
926
927	ENDIF
928
929	ENDIF
930
931	END SUBROUTINE boundary_conds

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