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source: palm/trunk/SOURCE/boundary_conds.f90 @ 1355

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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 1354 2014-04-08 15:22:57Z heinze $
27	!
28	! 1353 2014-04-08 15:21:23Z heinze
29	! REAL constants provided with KIND-attribute
30	!
31	! 1320 2014-03-20 08:40:49Z raasch
32	! ONLY-attribute added to USE-statements,
33	! kind-parameters added to all INTEGER and REAL declaration statements,
34	! kinds are defined in new module kinds,
35	! revision history before 2012 removed,
36	! comment fields (!:) to be used for variable explanations added to
37	! all variable declaration statements
38	!
39	! 1257 2013-11-08 15:18:40Z raasch
40	! loop independent clauses added
41	!
42	! 1241 2013-10-30 11:36:58Z heinze
43	! Adjust ug and vg at each timestep in case of large_scale_forcing
44	!
45	! 1159 2013-05-21 11:58:22Z fricke
46	! Bugfix: Neumann boundary conditions for the velocity components at the
47	! outflow are in fact radiation boundary conditions using the maximum phase
48	! velocity that ensures numerical stability (CFL-condition).
49	! Hence, logical operator use_cmax is now used instead of bc_lr_dirneu/_neudir.
50	! Bugfix: In case of use_cmax at the outflow, u, v, w are replaced by
51	! u_p, v_p, w_p
52	!
53	! 1115 2013-03-26 18:16:16Z hoffmann
54	! boundary conditions of two-moment cloud scheme are restricted to Neumann-
55	! boundary-conditions
56	!
57	! 1113 2013-03-10 02:48:14Z raasch
58	! GPU-porting
59	! dummy argument "range" removed
60	! Bugfix: wrong index in loops of radiation boundary condition
61	!
62	! 1053 2012-11-13 17:11:03Z hoffmann
63	! boundary conditions for the two new prognostic equations (nr, qr) of the
64	! two-moment cloud scheme
65	!
66	! 1036 2012-10-22 13:43:42Z raasch
67	! code put under GPL (PALM 3.9)
68	!
69	! 996 2012-09-07 10:41:47Z raasch
70	! little reformatting
71	!
72	! 978 2012-08-09 08:28:32Z fricke
73	! Neumann boudnary conditions are added at the inflow boundary for the SGS-TKE.
74	! Outflow boundary conditions for the velocity components can be set to Neumann
75	! conditions or to radiation conditions with a horizontal averaged phase
76	! velocity.
77	!
78	! 875 2012-04-02 15:35:15Z gryschka
79	! Bugfix in case of dirichlet inflow bc at the right or north boundary
80	!
81	! Revision 1.1 1997/09/12 06:21:34 raasch
82	! Initial revision
83	!
84	!
85	! Description:
86	! ------------
87	! Boundary conditions for the prognostic quantities.
88	! One additional bottom boundary condition is applied for the TKE (=(u)*2)
89	! in prandtl_fluxes. The cyclic lateral boundary conditions are implicitly
90	! handled in routine exchange_horiz. Pressure boundary conditions are
91	! explicitly set in routines pres, poisfft, poismg and sor.
92	!------------------------------------------------------------------------------!
93
94	USE arrays_3d, &
95	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, &
96	dzu, e_p, nr_p, pt, pt_p, q, q_p, qr_p, sa, sa_p, &
97	u, ug, u_init, u_m_l, u_m_n, u_m_r, u_m_s, u_p, &
98	v, vg, v_init, v_m_l, v_m_n, v_m_r, v_m_s, v_p, &
99	w, w_p, w_m_l, w_m_n, w_m_r, w_m_s
100
101	USE control_parameters, &
102	ONLY: bc_pt_t_val, bc_q_t_val, constant_diffusion, &
103	cloud_physics, dt_3d, humidity, &
104	ibc_pt_b, ibc_pt_t, ibc_q_b, ibc_sa_t, ibc_uv_b, ibc_uv_t, &
105	icloud_scheme, inflow_l, inflow_n, inflow_r, inflow_s, &
106	intermediate_timestep_count, large_scale_forcing, ocean, &
107	outflow_l, outflow_n, outflow_r, outflow_s, passive_scalar, &
108	precipitation, tsc, use_cmax
109
110	USE grid_variables, &
111	ONLY: ddx, ddy, dx, dy
112
113	USE indices, &
114	ONLY: nx, nxl, nxlg, nxr, nxrg, ny, nyn, nyng, nys, nysg, &
115	nzb, nzb_s_inner, nzb_w_inner, nzt
116
117	USE kinds
118
119	USE pegrid
120
121
122	IMPLICIT NONE
123
124	INTEGER(iwp) :: i !:
125	INTEGER(iwp) :: j !:
126	INTEGER(iwp) :: k !:
127
128	REAL(wp) :: c_max !:
129	REAL(wp) :: denom !:
130
131
132	!
133	!-- Bottom boundary
134	IF ( ibc_uv_b == 1 ) THEN
135	!$acc kernels present( u_p, v_p )
136	u_p(nzb,:,:) = u_p(nzb+1,:,:)
137	v_p(nzb,:,:) = v_p(nzb+1,:,:)
138	!$acc end kernels
139	ENDIF
140
141	!$acc kernels present( nzb_w_inner, w_p )
142	DO i = nxlg, nxrg
143	DO j = nysg, nyng
144	w_p(nzb_w_inner(j,i),j,i) = 0.0_wp
145	ENDDO
146	ENDDO
147	!$acc end kernels
148
149	!
150	!-- Top boundary
151	IF ( ibc_uv_t == 0 ) THEN
152	!$acc kernels present( u_init, u_p, v_init, v_p )
153	u_p(nzt+1,:,:) = u_init(nzt+1)
154	v_p(nzt+1,:,:) = v_init(nzt+1)
155	IF ( large_scale_forcing) THEN
156	u_p(nzt+1,:,:) = ug(nzt+1)
157	v_p(nzt+1,:,:) = vg(nzt+1)
158	END IF
159	!$acc end kernels
160	ELSE
161	!$acc kernels present( u_p, v_p )
162	u_p(nzt+1,:,:) = u_p(nzt,:,:)
163	v_p(nzt+1,:,:) = v_p(nzt,:,:)
164	!$acc end kernels
165	ENDIF
166	!$acc kernels present( w_p )
167	w_p(nzt:nzt+1,:,:) = 0.0_wp ! nzt is not a prognostic level (but cf. pres)
168	!$acc end kernels
169
170	!
171	!-- Temperature at bottom boundary.
172	!-- In case of coupled runs (ibc_pt_b = 2) the temperature is given by
173	!-- the sea surface temperature of the coupled ocean model.
174	IF ( ibc_pt_b == 0 ) THEN
175	!$acc kernels present( nzb_s_inner, pt, pt_p )
176	!$acc loop independent
177	DO i = nxlg, nxrg
178	!$acc loop independent
179	DO j = nysg, nyng
180	pt_p(nzb_s_inner(j,i),j,i) = pt(nzb_s_inner(j,i),j,i)
181	ENDDO
182	ENDDO
183	!$acc end kernels
184	ELSEIF ( ibc_pt_b == 1 ) THEN
185	!$acc kernels present( nzb_s_inner, pt_p )
186	!$acc loop independent
187	DO i = nxlg, nxrg
188	!$acc loop independent
189	DO j = nysg, nyng
190	pt_p(nzb_s_inner(j,i),j,i) = pt_p(nzb_s_inner(j,i)+1,j,i)
191	ENDDO
192	ENDDO
193	!$acc end kernels
194	ENDIF
195
196	!
197	!-- Temperature at top boundary
198	IF ( ibc_pt_t == 0 ) THEN
199	!$acc kernels present( pt, pt_p )
200	pt_p(nzt+1,:,:) = pt(nzt+1,:,:)
201	!$acc end kernels
202	ELSEIF ( ibc_pt_t == 1 ) THEN
203	!$acc kernels present( pt_p )
204	pt_p(nzt+1,:,:) = pt_p(nzt,:,:)
205	!$acc end kernels
206	ELSEIF ( ibc_pt_t == 2 ) THEN
207	!$acc kernels present( dzu, pt_p )
208	pt_p(nzt+1,:,:) = pt_p(nzt,:,:) + bc_pt_t_val * dzu(nzt+1)
209	!$acc end kernels
210	ENDIF
211
212	!
213	!-- Boundary conditions for TKE
214	!-- Generally Neumann conditions with de/dz=0 are assumed
215	IF ( .NOT. constant_diffusion ) THEN
216	!$acc kernels present( e_p, nzb_s_inner )
217	!$acc loop independent
218	DO i = nxlg, nxrg
219	!$acc loop independent
220	DO j = nysg, nyng
221	e_p(nzb_s_inner(j,i),j,i) = e_p(nzb_s_inner(j,i)+1,j,i)
222	ENDDO
223	ENDDO
224	e_p(nzt+1,:,:) = e_p(nzt,:,:)
225	!$acc end kernels
226	ENDIF
227
228	!
229	!-- Boundary conditions for salinity
230	IF ( ocean ) THEN
231	!
232	!-- Bottom boundary: Neumann condition because salinity flux is always
233	!-- given
234	DO i = nxlg, nxrg
235	DO j = nysg, nyng
236	sa_p(nzb_s_inner(j,i),j,i) = sa_p(nzb_s_inner(j,i)+1,j,i)
237	ENDDO
238	ENDDO
239
240	!
241	!-- Top boundary: Dirichlet or Neumann
242	IF ( ibc_sa_t == 0 ) THEN
243	sa_p(nzt+1,:,:) = sa(nzt+1,:,:)
244	ELSEIF ( ibc_sa_t == 1 ) THEN
245	sa_p(nzt+1,:,:) = sa_p(nzt,:,:)
246	ENDIF
247
248	ENDIF
249
250	!
251	!-- Boundary conditions for total water content or scalar,
252	!-- bottom and top boundary (see also temperature)
253	IF ( humidity .OR. passive_scalar ) THEN
254	!
255	!-- Surface conditions for constant_humidity_flux
256	IF ( ibc_q_b == 0 ) THEN
257	DO i = nxlg, nxrg
258	DO j = nysg, nyng
259	q_p(nzb_s_inner(j,i),j,i) = q(nzb_s_inner(j,i),j,i)
260	ENDDO
261	ENDDO
262	ELSE
263	DO i = nxlg, nxrg
264	DO j = nysg, nyng
265	q_p(nzb_s_inner(j,i),j,i) = q_p(nzb_s_inner(j,i)+1,j,i)
266	ENDDO
267	ENDDO
268	ENDIF
269	!
270	!-- Top boundary
271	q_p(nzt+1,:,:) = q_p(nzt,:,:) + bc_q_t_val * dzu(nzt+1)
272
273	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
274	precipitation ) THEN
275	!
276	!-- Surface conditions rain water (Neumann)
277	DO i = nxlg, nxrg
278	DO j = nysg, nyng
279	qr_p(nzb_s_inner(j,i),j,i) = qr_p(nzb_s_inner(j,i)+1,j,i)
280	nr_p(nzb_s_inner(j,i),j,i) = nr_p(nzb_s_inner(j,i)+1,j,i)
281	ENDDO
282	ENDDO
283	!
284	!-- Top boundary condition for rain water (Neumann)
285	qr_p(nzt+1,:,:) = qr_p(nzt,:,:)
286	nr_p(nzt+1,:,:) = nr_p(nzt,:,:)
287
288	ENDIF
289	!
290	!-- In case of inflow at the south boundary the boundary for v is at nys
291	!-- and in case of inflow at the left boundary the boundary for u is at nxl.
292	!-- Since in prognostic_equations (cache optimized version) these levels are
293	!-- handled as a prognostic level, boundary values have to be restored here.
294	!-- For the SGS-TKE, Neumann boundary conditions are used at the inflow.
295	IF ( inflow_s ) THEN
296	v_p(:,nys,:) = v_p(:,nys-1,:)
297	IF ( .NOT. constant_diffusion ) e_p(:,nys-1,:) = e_p(:,nys,:)
298	ELSEIF ( inflow_n ) THEN
299	IF ( .NOT. constant_diffusion ) e_p(:,nyn+1,:) = e_p(:,nyn,:)
300	ELSEIF ( inflow_l ) THEN
301	u_p(:,:,nxl) = u_p(:,:,nxl-1)
302	IF ( .NOT. constant_diffusion ) e_p(:,:,nxl-1) = e_p(:,:,nxl)
303	ELSEIF ( inflow_r ) THEN
304	IF ( .NOT. constant_diffusion ) e_p(:,:,nxr+1) = e_p(:,:,nxr)
305	ENDIF
306
307	!
308	!-- Lateral boundary conditions for scalar quantities at the outflow
309	IF ( outflow_s ) THEN
310	pt_p(:,nys-1,:) = pt_p(:,nys,:)
311	IF ( .NOT. constant_diffusion ) e_p(:,nys-1,:) = e_p(:,nys,:)
312	IF ( humidity .OR. passive_scalar ) THEN
313	q_p(:,nys-1,:) = q_p(:,nys,:)
314	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
315	precipitation) THEN
316	qr_p(:,nys-1,:) = qr_p(:,nys,:)
317	nr_p(:,nys-1,:) = nr_p(:,nys,:)
318	ENDIF
319	ENDIF
320	ELSEIF ( outflow_n ) THEN
321	pt_p(:,nyn+1,:) = pt_p(:,nyn,:)
322	IF ( .NOT. constant_diffusion ) e_p(:,nyn+1,:) = e_p(:,nyn,:)
323	IF ( humidity .OR. passive_scalar ) THEN
324	q_p(:,nyn+1,:) = q_p(:,nyn,:)
325	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
326	precipitation ) THEN
327	qr_p(:,nyn+1,:) = qr_p(:,nyn,:)
328	nr_p(:,nyn+1,:) = nr_p(:,nyn,:)
329	ENDIF
330	ENDIF
331	ELSEIF ( outflow_l ) THEN
332	pt_p(:,:,nxl-1) = pt_p(:,:,nxl)
333	IF ( .NOT. constant_diffusion ) e_p(:,:,nxl-1) = e_p(:,:,nxl)
334	IF ( humidity .OR. passive_scalar ) THEN
335	q_p(:,:,nxl-1) = q_p(:,:,nxl)
336	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
337	precipitation ) THEN
338	qr_p(:,:,nxl-1) = qr_p(:,:,nxl)
339	nr_p(:,:,nxl-1) = nr_p(:,:,nxl)
340	ENDIF
341	ENDIF
342	ELSEIF ( outflow_r ) THEN
343	pt_p(:,:,nxr+1) = pt_p(:,:,nxr)
344	IF ( .NOT. constant_diffusion ) e_p(:,:,nxr+1) = e_p(:,:,nxr)
345	IF ( humidity .OR. passive_scalar ) THEN
346	q_p(:,:,nxr+1) = q_p(:,:,nxr)
347	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. precipitation ) THEN
348	qr_p(:,:,nxr+1) = qr_p(:,:,nxr)
349	nr_p(:,:,nxr+1) = nr_p(:,:,nxr)
350	ENDIF
351	ENDIF
352	ENDIF
353
354	ENDIF
355
356	!
357	!-- Radiation boundary conditions for the velocities at the respective outflow.
358	!-- The phase velocity is either assumed to the maximum phase velocity that
359	!-- ensures numerical stability (CFL-condition) or calculated after
360	!-- Orlanski(1976) and averaged along the outflow boundary.
361	IF ( outflow_s ) THEN
362
363	IF ( use_cmax ) THEN
364	u_p(:,-1,:) = u(:,0,:)
365	v_p(:,0,:) = v(:,1,:)
366	w_p(:,-1,:) = w(:,0,:)
367	ELSEIF ( .NOT. use_cmax ) THEN
368
369	c_max = dy / dt_3d
370
371	c_u_m_l = 0.0_wp
372	c_v_m_l = 0.0_wp
373	c_w_m_l = 0.0_wp
374
375	c_u_m = 0.0_wp
376	c_v_m = 0.0_wp
377	c_w_m = 0.0_wp
378
379	!
380	!-- Calculate the phase speeds for u, v, and w, first local and then
381	!-- average along the outflow boundary.
382	DO k = nzb+1, nzt+1
383	DO i = nxl, nxr
384
385	denom = u_m_s(k,0,i) - u_m_s(k,1,i)
386
387	IF ( denom /= 0.0_wp ) THEN
388	c_u(k,i) = -c_max * ( u(k,0,i) - u_m_s(k,0,i) ) / ( denom * tsc(2) )
389	IF ( c_u(k,i) < 0.0_wp ) THEN
390	c_u(k,i) = 0.0_wp
391	ELSEIF ( c_u(k,i) > c_max ) THEN
392	c_u(k,i) = c_max
393	ENDIF
394	ELSE
395	c_u(k,i) = c_max
396	ENDIF
397
398	denom = v_m_s(k,1,i) - v_m_s(k,2,i)
399
400	IF ( denom /= 0.0_wp ) THEN
401	c_v(k,i) = -c_max * ( v(k,1,i) - v_m_s(k,1,i) ) / ( denom * tsc(2) )
402	IF ( c_v(k,i) < 0.0_wp ) THEN
403	c_v(k,i) = 0.0_wp
404	ELSEIF ( c_v(k,i) > c_max ) THEN
405	c_v(k,i) = c_max
406	ENDIF
407	ELSE
408	c_v(k,i) = c_max
409	ENDIF
410
411	denom = w_m_s(k,0,i) - w_m_s(k,1,i)
412
413	IF ( denom /= 0.0_wp ) THEN
414	c_w(k,i) = -c_max * ( w(k,0,i) - w_m_s(k,0,i) ) / ( denom * tsc(2) )
415	IF ( c_w(k,i) < 0.0_wp ) THEN
416	c_w(k,i) = 0.0_wp
417	ELSEIF ( c_w(k,i) > c_max ) THEN
418	c_w(k,i) = c_max
419	ENDIF
420	ELSE
421	c_w(k,i) = c_max
422	ENDIF
423
424	c_u_m_l(k) = c_u_m_l(k) + c_u(k,i)
425	c_v_m_l(k) = c_v_m_l(k) + c_v(k,i)
426	c_w_m_l(k) = c_w_m_l(k) + c_w(k,i)
427
428	ENDDO
429	ENDDO
430
431	#if defined( __parallel )
432	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
433	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
434	MPI_SUM, comm1dx, ierr )
435	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
436	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
437	MPI_SUM, comm1dx, ierr )
438	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
439	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
440	MPI_SUM, comm1dx, ierr )
441	#else
442	c_u_m = c_u_m_l
443	c_v_m = c_v_m_l
444	c_w_m = c_w_m_l
445	#endif
446
447	c_u_m = c_u_m / (nx+1)
448	c_v_m = c_v_m / (nx+1)
449	c_w_m = c_w_m / (nx+1)
450
451	!
452	!-- Save old timelevels for the next timestep
453	IF ( intermediate_timestep_count == 1 ) THEN
454	u_m_s(:,:,:) = u(:,0:1,:)
455	v_m_s(:,:,:) = v(:,1:2,:)
456	w_m_s(:,:,:) = w(:,0:1,:)
457	ENDIF
458
459	!
460	!-- Calculate the new velocities
461	DO k = nzb+1, nzt+1
462	DO i = nxlg, nxrg
463	u_p(k,-1,i) = u(k,-1,i) - dt_3d * tsc(2) * c_u_m(k) * &
464	( u(k,-1,i) - u(k,0,i) ) * ddy
465
466	v_p(k,0,i) = v(k,0,i) - dt_3d * tsc(2) * c_v_m(k) * &
467	( v(k,0,i) - v(k,1,i) ) * ddy
468
469	w_p(k,-1,i) = w(k,-1,i) - dt_3d * tsc(2) * c_w_m(k) * &
470	( w(k,-1,i) - w(k,0,i) ) * ddy
471	ENDDO
472	ENDDO
473
474	!
475	!-- Bottom boundary at the outflow
476	IF ( ibc_uv_b == 0 ) THEN
477	u_p(nzb,-1,:) = 0.0_wp
478	v_p(nzb,0,:) = 0.0_wp
479	ELSE
480	u_p(nzb,-1,:) = u_p(nzb+1,-1,:)
481	v_p(nzb,0,:) = v_p(nzb+1,0,:)
482	ENDIF
483	w_p(nzb,-1,:) = 0.0_wp
484
485	!
486	!-- Top boundary at the outflow
487	IF ( ibc_uv_t == 0 ) THEN
488	u_p(nzt+1,-1,:) = u_init(nzt+1)
489	v_p(nzt+1,0,:) = v_init(nzt+1)
490	ELSE
491	u_p(nzt+1,-1,:) = u(nzt,-1,:)
492	v_p(nzt+1,0,:) = v(nzt,0,:)
493	ENDIF
494	w_p(nzt:nzt+1,-1,:) = 0.0_wp
495
496	ENDIF
497
498	ENDIF
499
500	IF ( outflow_n ) THEN
501
502	IF ( use_cmax ) THEN
503	u_p(:,ny+1,:) = u(:,ny,:)
504	v_p(:,ny+1,:) = v(:,ny,:)
505	w_p(:,ny+1,:) = w(:,ny,:)
506	ELSEIF ( .NOT. use_cmax ) THEN
507
508	c_max = dy / dt_3d
509
510	c_u_m_l = 0.0_wp
511	c_v_m_l = 0.0_wp
512	c_w_m_l = 0.0_wp
513
514	c_u_m = 0.0_wp
515	c_v_m = 0.0_wp
516	c_w_m = 0.0_wp
517
518	!
519	!-- Calculate the phase speeds for u, v, and w, first local and then
520	!-- average along the outflow boundary.
521	DO k = nzb+1, nzt+1
522	DO i = nxl, nxr
523
524	denom = u_m_n(k,ny,i) - u_m_n(k,ny-1,i)
525
526	IF ( denom /= 0.0_wp ) THEN
527	c_u(k,i) = -c_max * ( u(k,ny,i) - u_m_n(k,ny,i) ) / ( denom * tsc(2) )
528	IF ( c_u(k,i) < 0.0_wp ) THEN
529	c_u(k,i) = 0.0_wp
530	ELSEIF ( c_u(k,i) > c_max ) THEN
531	c_u(k,i) = c_max
532	ENDIF
533	ELSE
534	c_u(k,i) = c_max
535	ENDIF
536
537	denom = v_m_n(k,ny,i) - v_m_n(k,ny-1,i)
538
539	IF ( denom /= 0.0_wp ) THEN
540	c_v(k,i) = -c_max * ( v(k,ny,i) - v_m_n(k,ny,i) ) / ( denom * tsc(2) )
541	IF ( c_v(k,i) < 0.0_wp ) THEN
542	c_v(k,i) = 0.0_wp
543	ELSEIF ( c_v(k,i) > c_max ) THEN
544	c_v(k,i) = c_max
545	ENDIF
546	ELSE
547	c_v(k,i) = c_max
548	ENDIF
549
550	denom = w_m_n(k,ny,i) - w_m_n(k,ny-1,i)
551
552	IF ( denom /= 0.0_wp ) THEN
553	c_w(k,i) = -c_max * ( w(k,ny,i) - w_m_n(k,ny,i) ) / ( denom * tsc(2) )
554	IF ( c_w(k,i) < 0.0_wp ) THEN
555	c_w(k,i) = 0.0_wp
556	ELSEIF ( c_w(k,i) > c_max ) THEN
557	c_w(k,i) = c_max
558	ENDIF
559	ELSE
560	c_w(k,i) = c_max
561	ENDIF
562
563	c_u_m_l(k) = c_u_m_l(k) + c_u(k,i)
564	c_v_m_l(k) = c_v_m_l(k) + c_v(k,i)
565	c_w_m_l(k) = c_w_m_l(k) + c_w(k,i)
566
567	ENDDO
568	ENDDO
569
570	#if defined( __parallel )
571	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
572	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
573	MPI_SUM, comm1dx, ierr )
574	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
575	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
576	MPI_SUM, comm1dx, ierr )
577	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
578	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
579	MPI_SUM, comm1dx, ierr )
580	#else
581	c_u_m = c_u_m_l
582	c_v_m = c_v_m_l
583	c_w_m = c_w_m_l
584	#endif
585
586	c_u_m = c_u_m / (nx+1)
587	c_v_m = c_v_m / (nx+1)
588	c_w_m = c_w_m / (nx+1)
589
590	!
591	!-- Save old timelevels for the next timestep
592	IF ( intermediate_timestep_count == 1 ) THEN
593	u_m_n(:,:,:) = u(:,ny-1:ny,:)
594	v_m_n(:,:,:) = v(:,ny-1:ny,:)
595	w_m_n(:,:,:) = w(:,ny-1:ny,:)
596	ENDIF
597
598	!
599	!-- Calculate the new velocities
600	DO k = nzb+1, nzt+1
601	DO i = nxlg, nxrg
602	u_p(k,ny+1,i) = u(k,ny+1,i) - dt_3d * tsc(2) * c_u_m(k) * &
603	( u(k,ny+1,i) - u(k,ny,i) ) * ddy
604
605	v_p(k,ny+1,i) = v(k,ny+1,i) - dt_3d * tsc(2) * c_v_m(k) * &
606	( v(k,ny+1,i) - v(k,ny,i) ) * ddy
607
608	w_p(k,ny+1,i) = w(k,ny+1,i) - dt_3d * tsc(2) * c_w_m(k) * &
609	( w(k,ny+1,i) - w(k,ny,i) ) * ddy
610	ENDDO
611	ENDDO
612
613	!
614	!-- Bottom boundary at the outflow
615	IF ( ibc_uv_b == 0 ) THEN
616	u_p(nzb,ny+1,:) = 0.0_wp
617	v_p(nzb,ny+1,:) = 0.0_wp
618	ELSE
619	u_p(nzb,ny+1,:) = u_p(nzb+1,ny+1,:)
620	v_p(nzb,ny+1,:) = v_p(nzb+1,ny+1,:)
621	ENDIF
622	w_p(nzb,ny+1,:) = 0.0_wp
623
624	!
625	!-- Top boundary at the outflow
626	IF ( ibc_uv_t == 0 ) THEN
627	u_p(nzt+1,ny+1,:) = u_init(nzt+1)
628	v_p(nzt+1,ny+1,:) = v_init(nzt+1)
629	ELSE
630	u_p(nzt+1,ny+1,:) = u_p(nzt,nyn+1,:)
631	v_p(nzt+1,ny+1,:) = v_p(nzt,nyn+1,:)
632	ENDIF
633	w_p(nzt:nzt+1,ny+1,:) = 0.0_wp
634
635	ENDIF
636
637	ENDIF
638
639	IF ( outflow_l ) THEN
640
641	IF ( use_cmax ) THEN
642	u_p(:,:,-1) = u(:,:,0)
643	v_p(:,:,0) = v(:,:,1)
644	w_p(:,:,-1) = w(:,:,0)
645	ELSEIF ( .NOT. use_cmax ) THEN
646
647	c_max = dx / dt_3d
648
649	c_u_m_l = 0.0_wp
650	c_v_m_l = 0.0_wp
651	c_w_m_l = 0.0_wp
652
653	c_u_m = 0.0_wp
654	c_v_m = 0.0_wp
655	c_w_m = 0.0_wp
656
657	!
658	!-- Calculate the phase speeds for u, v, and w, first local and then
659	!-- average along the outflow boundary.
660	DO k = nzb+1, nzt+1
661	DO j = nys, nyn
662
663	denom = u_m_l(k,j,1) - u_m_l(k,j,2)
664
665	IF ( denom /= 0.0_wp ) THEN
666	c_u(k,j) = -c_max * ( u(k,j,1) - u_m_l(k,j,1) ) / ( denom * tsc(2) )
667	IF ( c_u(k,j) < 0.0_wp ) THEN
668	c_u(k,j) = 0.0_wp
669	ELSEIF ( c_u(k,j) > c_max ) THEN
670	c_u(k,j) = c_max
671	ENDIF
672	ELSE
673	c_u(k,j) = c_max
674	ENDIF
675
676	denom = v_m_l(k,j,0) - v_m_l(k,j,1)
677
678	IF ( denom /= 0.0_wp ) THEN
679	c_v(k,j) = -c_max * ( v(k,j,0) - v_m_l(k,j,0) ) / ( denom * tsc(2) )
680	IF ( c_v(k,j) < 0.0_wp ) THEN
681	c_v(k,j) = 0.0_wp
682	ELSEIF ( c_v(k,j) > c_max ) THEN
683	c_v(k,j) = c_max
684	ENDIF
685	ELSE
686	c_v(k,j) = c_max
687	ENDIF
688
689	denom = w_m_l(k,j,0) - w_m_l(k,j,1)
690
691	IF ( denom /= 0.0_wp ) THEN
692	c_w(k,j) = -c_max * ( w(k,j,0) - w_m_l(k,j,0) ) / ( denom * tsc(2) )
693	IF ( c_w(k,j) < 0.0_wp ) THEN
694	c_w(k,j) = 0.0_wp
695	ELSEIF ( c_w(k,j) > c_max ) THEN
696	c_w(k,j) = c_max
697	ENDIF
698	ELSE
699	c_w(k,j) = c_max
700	ENDIF
701
702	c_u_m_l(k) = c_u_m_l(k) + c_u(k,j)
703	c_v_m_l(k) = c_v_m_l(k) + c_v(k,j)
704	c_w_m_l(k) = c_w_m_l(k) + c_w(k,j)
705
706	ENDDO
707	ENDDO
708
709	#if defined( __parallel )
710	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
711	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
712	MPI_SUM, comm1dy, ierr )
713	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
714	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
715	MPI_SUM, comm1dy, ierr )
716	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
717	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
718	MPI_SUM, comm1dy, ierr )
719	#else
720	c_u_m = c_u_m_l
721	c_v_m = c_v_m_l
722	c_w_m = c_w_m_l
723	#endif
724
725	c_u_m = c_u_m / (ny+1)
726	c_v_m = c_v_m / (ny+1)
727	c_w_m = c_w_m / (ny+1)
728
729	!
730	!-- Save old timelevels for the next timestep
731	IF ( intermediate_timestep_count == 1 ) THEN
732	u_m_l(:,:,:) = u(:,:,1:2)
733	v_m_l(:,:,:) = v(:,:,0:1)
734	w_m_l(:,:,:) = w(:,:,0:1)
735	ENDIF
736
737	!
738	!-- Calculate the new velocities
739	DO k = nzb+1, nzt+1
740	DO j = nysg, nyng
741	u_p(k,j,0) = u(k,j,0) - dt_3d * tsc(2) * c_u_m(k) * &
742	( u(k,j,0) - u(k,j,1) ) * ddx
743
744	v_p(k,j,-1) = v(k,j,-1) - dt_3d * tsc(2) * c_v_m(k) * &
745	( v(k,j,-1) - v(k,j,0) ) * ddx
746
747	w_p(k,j,-1) = w(k,j,-1) - dt_3d * tsc(2) * c_w_m(k) * &
748	( w(k,j,-1) - w(k,j,0) ) * ddx
749	ENDDO
750	ENDDO
751
752	!
753	!-- Bottom boundary at the outflow
754	IF ( ibc_uv_b == 0 ) THEN
755	u_p(nzb,:,0) = 0.0_wp
756	v_p(nzb,:,-1) = 0.0_wp
757	ELSE
758	u_p(nzb,:,0) = u_p(nzb+1,:,0)
759	v_p(nzb,:,-1) = v_p(nzb+1,:,-1)
760	ENDIF
761	w_p(nzb,:,-1) = 0.0_wp
762
763	!
764	!-- Top boundary at the outflow
765	IF ( ibc_uv_t == 0 ) THEN
766	u_p(nzt+1,:,-1) = u_init(nzt+1)
767	v_p(nzt+1,:,-1) = v_init(nzt+1)
768	ELSE
769	u_p(nzt+1,:,-1) = u_p(nzt,:,-1)
770	v_p(nzt+1,:,-1) = v_p(nzt,:,-1)
771	ENDIF
772	w_p(nzt:nzt+1,:,-1) = 0.0_wp
773
774	ENDIF
775
776	ENDIF
777
778	IF ( outflow_r ) THEN
779
780	IF ( use_cmax ) THEN
781	u_p(:,:,nx+1) = u(:,:,nx)
782	v_p(:,:,nx+1) = v(:,:,nx)
783	w_p(:,:,nx+1) = w(:,:,nx)
784	ELSEIF ( .NOT. use_cmax ) THEN
785
786	c_max = dx / dt_3d
787
788	c_u_m_l = 0.0_wp
789	c_v_m_l = 0.0_wp
790	c_w_m_l = 0.0_wp
791
792	c_u_m = 0.0_wp
793	c_v_m = 0.0_wp
794	c_w_m = 0.0_wp
795
796	!
797	!-- Calculate the phase speeds for u, v, and w, first local and then
798	!-- average along the outflow boundary.
799	DO k = nzb+1, nzt+1
800	DO j = nys, nyn
801
802	denom = u_m_r(k,j,nx) - u_m_r(k,j,nx-1)
803
804	IF ( denom /= 0.0_wp ) THEN
805	c_u(k,j) = -c_max * ( u(k,j,nx) - u_m_r(k,j,nx) ) / ( denom * tsc(2) )
806	IF ( c_u(k,j) < 0.0_wp ) THEN
807	c_u(k,j) = 0.0_wp
808	ELSEIF ( c_u(k,j) > c_max ) THEN
809	c_u(k,j) = c_max
810	ENDIF
811	ELSE
812	c_u(k,j) = c_max
813	ENDIF
814
815	denom = v_m_r(k,j,nx) - v_m_r(k,j,nx-1)
816
817	IF ( denom /= 0.0_wp ) THEN
818	c_v(k,j) = -c_max * ( v(k,j,nx) - v_m_r(k,j,nx) ) / ( denom * tsc(2) )
819	IF ( c_v(k,j) < 0.0_wp ) THEN
820	c_v(k,j) = 0.0_wp
821	ELSEIF ( c_v(k,j) > c_max ) THEN
822	c_v(k,j) = c_max
823	ENDIF
824	ELSE
825	c_v(k,j) = c_max
826	ENDIF
827
828	denom = w_m_r(k,j,nx) - w_m_r(k,j,nx-1)
829
830	IF ( denom /= 0.0_wp ) THEN
831	c_w(k,j) = -c_max * ( w(k,j,nx) - w_m_r(k,j,nx) ) / ( denom * tsc(2) )
832	IF ( c_w(k,j) < 0.0_wp ) THEN
833	c_w(k,j) = 0.0_wp
834	ELSEIF ( c_w(k,j) > c_max ) THEN
835	c_w(k,j) = c_max
836	ENDIF
837	ELSE
838	c_w(k,j) = c_max
839	ENDIF
840
841	c_u_m_l(k) = c_u_m_l(k) + c_u(k,j)
842	c_v_m_l(k) = c_v_m_l(k) + c_v(k,j)
843	c_w_m_l(k) = c_w_m_l(k) + c_w(k,j)
844
845	ENDDO
846	ENDDO
847
848	#if defined( __parallel )
849	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
850	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
851	MPI_SUM, comm1dy, ierr )
852	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
853	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
854	MPI_SUM, comm1dy, ierr )
855	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
856	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
857	MPI_SUM, comm1dy, ierr )
858	#else
859	c_u_m = c_u_m_l
860	c_v_m = c_v_m_l
861	c_w_m = c_w_m_l
862	#endif
863
864	c_u_m = c_u_m / (ny+1)
865	c_v_m = c_v_m / (ny+1)
866	c_w_m = c_w_m / (ny+1)
867
868	!
869	!-- Save old timelevels for the next timestep
870	IF ( intermediate_timestep_count == 1 ) THEN
871	u_m_r(:,:,:) = u(:,:,nx-1:nx)
872	v_m_r(:,:,:) = v(:,:,nx-1:nx)
873	w_m_r(:,:,:) = w(:,:,nx-1:nx)
874	ENDIF
875
876	!
877	!-- Calculate the new velocities
878	DO k = nzb+1, nzt+1
879	DO j = nysg, nyng
880	u_p(k,j,nx+1) = u(k,j,nx+1) - dt_3d * tsc(2) * c_u_m(k) * &
881	( u(k,j,nx+1) - u(k,j,nx) ) * ddx
882
883	v_p(k,j,nx+1) = v(k,j,nx+1) - dt_3d * tsc(2) * c_v_m(k) * &
884	( v(k,j,nx+1) - v(k,j,nx) ) * ddx
885
886	w_p(k,j,nx+1) = w(k,j,nx+1) - dt_3d * tsc(2) * c_w_m(k) * &
887	( w(k,j,nx+1) - w(k,j,nx) ) * ddx
888	ENDDO
889	ENDDO
890
891	!
892	!-- Bottom boundary at the outflow
893	IF ( ibc_uv_b == 0 ) THEN
894	u_p(nzb,:,nx+1) = 0.0_wp
895	v_p(nzb,:,nx+1) = 0.0_wp
896	ELSE
897	u_p(nzb,:,nx+1) = u_p(nzb+1,:,nx+1)
898	v_p(nzb,:,nx+1) = v_p(nzb+1,:,nx+1)
899	ENDIF
900	w_p(nzb,:,nx+1) = 0.0_wp
901
902	!
903	!-- Top boundary at the outflow
904	IF ( ibc_uv_t == 0 ) THEN
905	u_p(nzt+1,:,nx+1) = u_init(nzt+1)
906	v_p(nzt+1,:,nx+1) = v_init(nzt+1)
907	ELSE
908	u_p(nzt+1,:,nx+1) = u_p(nzt,:,nx+1)
909	v_p(nzt+1,:,nx+1) = v_p(nzt,:,nx+1)
910	ENDIF
911	w(nzt:nzt+1,:,nx+1) = 0.0_wp
912
913	ENDIF
914
915	ENDIF
916
917	END SUBROUTINE boundary_conds

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