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source: palm/trunk/SOURCE/boundary_conds.f90 @ 1407

Last change on this file since 1407 was 1399, checked in by heinze, 11 years ago
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[1113]	1	SUBROUTINE boundary_conds
[1]	2
[1036]	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	!
[1310]	17	! Copyright 1997-2014 Leibniz Universitaet Hannover
[1036]	18	!--------------------------------------------------------------------------------!
	19	!
[484]	20	! Current revisions:
[1]	21	! -----------------
[1354]	22	!
[1399]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: boundary_conds.f90 1399 2014-05-07 11:16:25Z raasch $
	27	!
[1399]	28	! 1398 2014-05-07 11:15:00Z heinze
	29	! Dirichlet-condition at the top for u and v changed to u_init and v_init also
	30	! for large_scale_forcing
	31	!
[1381]	32	! 1380 2014-04-28 12:40:45Z heinze
	33	! Adjust Dirichlet-condition at the top for pt in case of nudging
	34	!
[1362]	35	! 1361 2014-04-16 15:17:48Z hoffmann
	36	! Bottom and top boundary conditions of rain water content (qr) and
	37	! rain drop concentration (nr) changed to Dirichlet
	38	!
[1354]	39	! 1353 2014-04-08 15:21:23Z heinze
	40	! REAL constants provided with KIND-attribute
	41	!
[1321]	42	! 1320 2014-03-20 08:40:49Z raasch
[1320]	43	! ONLY-attribute added to USE-statements,
	44	! kind-parameters added to all INTEGER and REAL declaration statements,
	45	! kinds are defined in new module kinds,
	46	! revision history before 2012 removed,
	47	! comment fields (!:) to be used for variable explanations added to
	48	! all variable declaration statements
[1160]	49	!
[1258]	50	! 1257 2013-11-08 15:18:40Z raasch
	51	! loop independent clauses added
	52	!
[1242]	53	! 1241 2013-10-30 11:36:58Z heinze
	54	! Adjust ug and vg at each timestep in case of large_scale_forcing
	55	!
[1160]	56	! 1159 2013-05-21 11:58:22Z fricke
[1159]	57	! Bugfix: Neumann boundary conditions for the velocity components at the
	58	! outflow are in fact radiation boundary conditions using the maximum phase
	59	! velocity that ensures numerical stability (CFL-condition).
	60	! Hence, logical operator use_cmax is now used instead of bc_lr_dirneu/_neudir.
	61	! Bugfix: In case of use_cmax at the outflow, u, v, w are replaced by
	62	! u_p, v_p, w_p
[1116]	63	!
	64	! 1115 2013-03-26 18:16:16Z hoffmann
	65	! boundary conditions of two-moment cloud scheme are restricted to Neumann-
	66	! boundary-conditions
	67	!
[1114]	68	! 1113 2013-03-10 02:48:14Z raasch
	69	! GPU-porting
	70	! dummy argument "range" removed
	71	! Bugfix: wrong index in loops of radiation boundary condition
[1113]	72	!
[1054]	73	! 1053 2012-11-13 17:11:03Z hoffmann
	74	! boundary conditions for the two new prognostic equations (nr, qr) of the
	75	! two-moment cloud scheme
	76	!
[1037]	77	! 1036 2012-10-22 13:43:42Z raasch
	78	! code put under GPL (PALM 3.9)
	79	!
[997]	80	! 996 2012-09-07 10:41:47Z raasch
	81	! little reformatting
	82	!
[979]	83	! 978 2012-08-09 08:28:32Z fricke
	84	! Neumann boudnary conditions are added at the inflow boundary for the SGS-TKE.
	85	! Outflow boundary conditions for the velocity components can be set to Neumann
	86	! conditions or to radiation conditions with a horizontal averaged phase
	87	! velocity.
	88	!
[876]	89	! 875 2012-04-02 15:35:15Z gryschka
	90	! Bugfix in case of dirichlet inflow bc at the right or north boundary
	91	!
[1]	92	! Revision 1.1 1997/09/12 06:21:34 raasch
	93	! Initial revision
	94	!
	95	!
	96	! Description:
	97	! ------------
[1159]	98	! Boundary conditions for the prognostic quantities.
[1]	99	! One additional bottom boundary condition is applied for the TKE (=(u)*2)
	100	! in prandtl_fluxes. The cyclic lateral boundary conditions are implicitly
	101	! handled in routine exchange_horiz. Pressure boundary conditions are
	102	! explicitly set in routines pres, poisfft, poismg and sor.
	103	!------------------------------------------------------------------------------!
	104
[1320]	105	USE arrays_3d, &
	106	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, &
	107	dzu, e_p, nr_p, pt, pt_p, q, q_p, qr_p, sa, sa_p, &
	108	u, ug, u_init, u_m_l, u_m_n, u_m_r, u_m_s, u_p, &
	109	v, vg, v_init, v_m_l, v_m_n, v_m_r, v_m_s, v_p, &
[1380]	110	w, w_p, w_m_l, w_m_n, w_m_r, w_m_s,&
	111	pt_init
[1320]	112
	113	USE control_parameters, &
	114	ONLY: bc_pt_t_val, bc_q_t_val, constant_diffusion, &
	115	cloud_physics, dt_3d, humidity, &
	116	ibc_pt_b, ibc_pt_t, ibc_q_b, ibc_sa_t, ibc_uv_b, ibc_uv_t, &
	117	icloud_scheme, inflow_l, inflow_n, inflow_r, inflow_s, &
	118	intermediate_timestep_count, large_scale_forcing, ocean, &
	119	outflow_l, outflow_n, outflow_r, outflow_s, passive_scalar, &
[1380]	120	precipitation, tsc, use_cmax, &
	121	nudging
[1320]	122
	123	USE grid_variables, &
	124	ONLY: ddx, ddy, dx, dy
	125
	126	USE indices, &
	127	ONLY: nx, nxl, nxlg, nxr, nxrg, ny, nyn, nyng, nys, nysg, &
	128	nzb, nzb_s_inner, nzb_w_inner, nzt
	129
	130	USE kinds
	131
[1]	132	USE pegrid
	133
[1320]	134
[1]	135	IMPLICIT NONE
	136
[1320]	137	INTEGER(iwp) :: i !:
	138	INTEGER(iwp) :: j !:
	139	INTEGER(iwp) :: k !:
[1]	140
[1320]	141	REAL(wp) :: c_max !:
	142	REAL(wp) :: denom !:
[1]	143
[73]	144
[1]	145	!
[1113]	146	!-- Bottom boundary
	147	IF ( ibc_uv_b == 1 ) THEN
	148	!$acc kernels present( u_p, v_p )
	149	u_p(nzb,:,:) = u_p(nzb+1,:,:)
	150	v_p(nzb,:,:) = v_p(nzb+1,:,:)
	151	!$acc end kernels
	152	ENDIF
	153
	154	!$acc kernels present( nzb_w_inner, w_p )
	155	DO i = nxlg, nxrg
	156	DO j = nysg, nyng
[1353]	157	w_p(nzb_w_inner(j,i),j,i) = 0.0_wp
[1113]	158	ENDDO
	159	ENDDO
	160	!$acc end kernels
	161
	162	!
	163	!-- Top boundary
	164	IF ( ibc_uv_t == 0 ) THEN
	165	!$acc kernels present( u_init, u_p, v_init, v_p )
	166	u_p(nzt+1,:,:) = u_init(nzt+1)
	167	v_p(nzt+1,:,:) = v_init(nzt+1)
	168	!$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	!$acc kernels present( w_p )
[1353]	176	w_p(nzt:nzt+1,:,:) = 0.0_wp ! nzt is not a prognostic level (but cf. pres)
[1113]	177	!$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	!$acc kernels present( nzb_s_inner, pt, pt_p )
[1257]	185	!$acc loop independent
[667]	186	DO i = nxlg, nxrg
[1257]	187	!$acc loop independent
[667]	188	DO j = nysg, nyng
[1113]	189	pt_p(nzb_s_inner(j,i),j,i) = pt(nzb_s_inner(j,i),j,i)
[1]	190	ENDDO
	191	ENDDO
[1113]	192	!$acc end kernels
	193	ELSEIF ( ibc_pt_b == 1 ) THEN
	194	!$acc kernels present( nzb_s_inner, pt_p )
[1257]	195	!$acc loop independent
[1113]	196	DO i = nxlg, nxrg
[1257]	197	!$acc loop independent
[1113]	198	DO j = nysg, nyng
	199	pt_p(nzb_s_inner(j,i),j,i) = pt_p(nzb_s_inner(j,i)+1,j,i)
	200	ENDDO
	201	ENDDO
	202	!$acc end kernels
	203	ENDIF
[1]	204
	205	!
[1113]	206	!-- Temperature at top boundary
	207	IF ( ibc_pt_t == 0 ) THEN
	208	!$acc kernels present( pt, pt_p )
	209	pt_p(nzt+1,:,:) = pt(nzt+1,:,:)
[1380]	210	!
	211	!-- In case of nudging adjust top boundary to pt which is
	212	!-- read in from NUDGING-DATA
	213	IF ( nudging ) THEN
	214	pt_p(nzt+1,:,:) = pt_init(nzt+1)
	215	ENDIF
[1113]	216	!$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
[1]	226
	227	!
[1113]	228	!-- Boundary conditions for TKE
	229	!-- Generally Neumann conditions with de/dz=0 are assumed
	230	IF ( .NOT. constant_diffusion ) THEN
	231	!$acc kernels present( e_p, nzb_s_inner )
[1257]	232	!$acc loop independent
[1113]	233	DO i = nxlg, nxrg
[1257]	234	!$acc loop independent
[1113]	235	DO j = nysg, nyng
	236	e_p(nzb_s_inner(j,i),j,i) = e_p(nzb_s_inner(j,i)+1,j,i)
[73]	237	ENDDO
[1113]	238	ENDDO
	239	e_p(nzt+1,:,:) = e_p(nzt,:,:)
	240	!$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)
[1]	252	ENDDO
[1113]	253	ENDDO
[1]	254
	255	!
[1113]	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,:,:)
[1]	261	ENDIF
	262
[1113]	263	ENDIF
	264
[1]	265	!
[1113]	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
[667]	272	DO i = nxlg, nxrg
	273	DO j = nysg, nyng
[1113]	274	q_p(nzb_s_inner(j,i),j,i) = q(nzb_s_inner(j,i),j,i)
[1]	275	ENDDO
	276	ENDDO
[1113]	277	ELSE
[667]	278	DO i = nxlg, nxrg
	279	DO j = nysg, nyng
[1113]	280	q_p(nzb_s_inner(j,i),j,i) = q_p(nzb_s_inner(j,i)+1,j,i)
[95]	281	ENDDO
	282	ENDDO
[1113]	283	ENDIF
[95]	284	!
[1113]	285	!-- Top boundary
	286	q_p(nzt+1,:,:) = q_p(nzt,:,:) + bc_q_t_val * dzu(nzt+1)
[95]	287
[1361]	288	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. precipitation ) THEN
[1113]	289	!
[1361]	290	!-- Surface conditions rain water (Dirichlet)
[1115]	291	DO i = nxlg, nxrg
	292	DO j = nysg, nyng
[1361]	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
[73]	295	ENDDO
[1115]	296	ENDDO
[1]	297	!
[1361]	298	!-- Top boundary condition for rain water (Dirichlet)
	299	qr_p(nzt+1,:,:) = 0.0_wp
	300	nr_p(nzt+1,:,:) = 0.0_wp
[1115]	301
[1]	302	ENDIF
	303	!
[875]	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.
[978]	308	!-- For the SGS-TKE, Neumann boundary conditions are used at the inflow.
[1]	309	IF ( inflow_s ) THEN
[73]	310	v_p(:,nys,:) = v_p(:,nys-1,:)
[978]	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,:)
[1]	314	ELSEIF ( inflow_l ) THEN
[73]	315	u_p(:,:,nxl) = u_p(:,:,nxl-1)
[978]	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)
[1]	319	ENDIF
	320
	321	!
	322	!-- Lateral boundary conditions for scalar quantities at the outflow
	323	IF ( outflow_s ) THEN
[73]	324	pt_p(:,nys-1,:) = pt_p(:,nys,:)
	325	IF ( .NOT. constant_diffusion ) e_p(:,nys-1,:) = e_p(:,nys,:)
[1115]	326	IF ( humidity .OR. passive_scalar ) THEN
[1053]	327	q_p(:,nys-1,:) = q_p(:,nys,:)
[1320]	328	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
[1115]	329	precipitation) THEN
[1053]	330	qr_p(:,nys-1,:) = qr_p(:,nys,:)
	331	nr_p(:,nys-1,:) = nr_p(:,nys,:)
	332	ENDIF
	333	ENDIF
[1]	334	ELSEIF ( outflow_n ) THEN
[73]	335	pt_p(:,nyn+1,:) = pt_p(:,nyn,:)
	336	IF ( .NOT. constant_diffusion ) e_p(:,nyn+1,:) = e_p(:,nyn,:)
[1115]	337	IF ( humidity .OR. passive_scalar ) THEN
[1053]	338	q_p(:,nyn+1,:) = q_p(:,nyn,:)
[1320]	339	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
[1115]	340	precipitation ) THEN
[1053]	341	qr_p(:,nyn+1,:) = qr_p(:,nyn,:)
	342	nr_p(:,nyn+1,:) = nr_p(:,nyn,:)
	343	ENDIF
	344	ENDIF
[1]	345	ELSEIF ( outflow_l ) THEN
[73]	346	pt_p(:,:,nxl-1) = pt_p(:,:,nxl)
	347	IF ( .NOT. constant_diffusion ) e_p(:,:,nxl-1) = e_p(:,:,nxl)
[1115]	348	IF ( humidity .OR. passive_scalar ) THEN
[1053]	349	q_p(:,:,nxl-1) = q_p(:,:,nxl)
[1320]	350	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
[1115]	351	precipitation ) THEN
[1053]	352	qr_p(:,:,nxl-1) = qr_p(:,:,nxl)
	353	nr_p(:,:,nxl-1) = nr_p(:,:,nxl)
	354	ENDIF
	355	ENDIF
[1]	356	ELSEIF ( outflow_r ) THEN
[73]	357	pt_p(:,:,nxr+1) = pt_p(:,:,nxr)
	358	IF ( .NOT. constant_diffusion ) e_p(:,:,nxr+1) = e_p(:,:,nxr)
[1053]	359	IF ( humidity .OR. passive_scalar ) THEN
	360	q_p(:,:,nxr+1) = q_p(:,:,nxr)
[1115]	361	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. precipitation ) THEN
[1053]	362	qr_p(:,:,nxr+1) = qr_p(:,:,nxr)
	363	nr_p(:,:,nxr+1) = nr_p(:,:,nxr)
	364	ENDIF
	365	ENDIF
[1]	366	ENDIF
	367
	368	ENDIF
	369
	370	!
[1159]	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.
[106]	375	IF ( outflow_s ) THEN
[75]	376
[1159]	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
[75]	382
[978]	383	c_max = dy / dt_3d
[75]	384
[1353]	385	c_u_m_l = 0.0_wp
	386	c_v_m_l = 0.0_wp
	387	c_w_m_l = 0.0_wp
[978]	388
[1353]	389	c_u_m = 0.0_wp
	390	c_v_m = 0.0_wp
	391	c_w_m = 0.0_wp
[978]	392
[75]	393	!
[996]	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
[75]	398
[106]	399	denom = u_m_s(k,0,i) - u_m_s(k,1,i)
	400
[1353]	401	IF ( denom /= 0.0_wp ) THEN
[996]	402	c_u(k,i) = -c_max * ( u(k,0,i) - u_m_s(k,0,i) ) / ( denom * tsc(2) )
[1353]	403	IF ( c_u(k,i) < 0.0_wp ) THEN
	404	c_u(k,i) = 0.0_wp
[106]	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
[75]	410	ENDIF
	411
[106]	412	denom = v_m_s(k,1,i) - v_m_s(k,2,i)
	413
[1353]	414	IF ( denom /= 0.0_wp ) THEN
[996]	415	c_v(k,i) = -c_max * ( v(k,1,i) - v_m_s(k,1,i) ) / ( denom * tsc(2) )
[1353]	416	IF ( c_v(k,i) < 0.0_wp ) THEN
	417	c_v(k,i) = 0.0_wp
[106]	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
[75]	423	ENDIF
	424
[106]	425	denom = w_m_s(k,0,i) - w_m_s(k,1,i)
[75]	426
[1353]	427	IF ( denom /= 0.0_wp ) THEN
[996]	428	c_w(k,i) = -c_max * ( w(k,0,i) - w_m_s(k,0,i) ) / ( denom * tsc(2) )
[1353]	429	IF ( c_w(k,i) < 0.0_wp ) THEN
	430	c_w(k,i) = 0.0_wp
[106]	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
[75]	436	ENDIF
[106]	437
[978]	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)
[106]	441
[978]	442	ENDDO
	443	ENDDO
[75]	444
[978]	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
[75]	465	!
[978]	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
[996]	475	DO k = nzb+1, nzt+1
	476	DO i = nxlg, nxrg
[978]	477	u_p(k,-1,i) = u(k,-1,i) - dt_3d * tsc(2) * c_u_m(k) * &
[75]	478	( u(k,-1,i) - u(k,0,i) ) * ddy
	479
[978]	480	v_p(k,0,i) = v(k,0,i) - dt_3d * tsc(2) * c_v_m(k) * &
[106]	481	( v(k,0,i) - v(k,1,i) ) * ddy
[75]	482
[978]	483	w_p(k,-1,i) = w(k,-1,i) - dt_3d * tsc(2) * c_w_m(k) * &
[75]	484	( w(k,-1,i) - w(k,0,i) ) * ddy
[978]	485	ENDDO
[75]	486	ENDDO
	487
	488	!
[978]	489	!-- Bottom boundary at the outflow
	490	IF ( ibc_uv_b == 0 ) THEN
[1353]	491	u_p(nzb,-1,:) = 0.0_wp
	492	v_p(nzb,0,:) = 0.0_wp
[978]	493	ELSE
	494	u_p(nzb,-1,:) = u_p(nzb+1,-1,:)
	495	v_p(nzb,0,:) = v_p(nzb+1,0,:)
	496	ENDIF
[1353]	497	w_p(nzb,-1,:) = 0.0_wp
[73]	498
[75]	499	!
[978]	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
[1353]	508	w_p(nzt:nzt+1,-1,:) = 0.0_wp
[978]	509
[75]	510	ENDIF
[73]	511
[75]	512	ENDIF
[73]	513
[106]	514	IF ( outflow_n ) THEN
[73]	515
[1159]	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
[75]	521
[978]	522	c_max = dy / dt_3d
[75]	523
[1353]	524	c_u_m_l = 0.0_wp
	525	c_v_m_l = 0.0_wp
	526	c_w_m_l = 0.0_wp
[978]	527
[1353]	528	c_u_m = 0.0_wp
	529	c_v_m = 0.0_wp
	530	c_w_m = 0.0_wp
[978]	531
[1]	532	!
[996]	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
[73]	537
[106]	538	denom = u_m_n(k,ny,i) - u_m_n(k,ny-1,i)
	539
[1353]	540	IF ( denom /= 0.0_wp ) THEN
[996]	541	c_u(k,i) = -c_max * ( u(k,ny,i) - u_m_n(k,ny,i) ) / ( denom * tsc(2) )
[1353]	542	IF ( c_u(k,i) < 0.0_wp ) THEN
	543	c_u(k,i) = 0.0_wp
[106]	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
[73]	549	ENDIF
	550
[106]	551	denom = v_m_n(k,ny,i) - v_m_n(k,ny-1,i)
[73]	552
[1353]	553	IF ( denom /= 0.0_wp ) THEN
[996]	554	c_v(k,i) = -c_max * ( v(k,ny,i) - v_m_n(k,ny,i) ) / ( denom * tsc(2) )
[1353]	555	IF ( c_v(k,i) < 0.0_wp ) THEN
	556	c_v(k,i) = 0.0_wp
[106]	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
[73]	562	ENDIF
	563
[106]	564	denom = w_m_n(k,ny,i) - w_m_n(k,ny-1,i)
[73]	565
[1353]	566	IF ( denom /= 0.0_wp ) THEN
[996]	567	c_w(k,i) = -c_max * ( w(k,ny,i) - w_m_n(k,ny,i) ) / ( denom * tsc(2) )
[1353]	568	IF ( c_w(k,i) < 0.0_wp ) THEN
	569	c_w(k,i) = 0.0_wp
[106]	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
[73]	575	ENDIF
[106]	576
[978]	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)
[106]	580
[978]	581	ENDDO
	582	ENDDO
[73]	583
[978]	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
[73]	604	!
[978]	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
[73]	611
[978]	612	!
	613	!-- Calculate the new velocities
[996]	614	DO k = nzb+1, nzt+1
	615	DO i = nxlg, nxrg
[978]	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
[73]	618
[978]	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
[73]	621
[978]	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
[1]	625	ENDDO
	626
	627	!
[978]	628	!-- Bottom boundary at the outflow
	629	IF ( ibc_uv_b == 0 ) THEN
[1353]	630	u_p(nzb,ny+1,:) = 0.0_wp
	631	v_p(nzb,ny+1,:) = 0.0_wp
[978]	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
[1353]	636	w_p(nzb,ny+1,:) = 0.0_wp
[73]	637
	638	!
[978]	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
[1353]	647	w_p(nzt:nzt+1,ny+1,:) = 0.0_wp
[978]	648
[1]	649	ENDIF
	650
[75]	651	ENDIF
	652
[106]	653	IF ( outflow_l ) THEN
[75]	654
[1159]	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
[75]	660
[978]	661	c_max = dx / dt_3d
[75]	662
[1353]	663	c_u_m_l = 0.0_wp
	664	c_v_m_l = 0.0_wp
	665	c_w_m_l = 0.0_wp
[978]	666
[1353]	667	c_u_m = 0.0_wp
	668	c_v_m = 0.0_wp
	669	c_w_m = 0.0_wp
[978]	670
[1]	671	!
[996]	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
[75]	676
[106]	677	denom = u_m_l(k,j,1) - u_m_l(k,j,2)
	678
[1353]	679	IF ( denom /= 0.0_wp ) THEN
[996]	680	c_u(k,j) = -c_max * ( u(k,j,1) - u_m_l(k,j,1) ) / ( denom * tsc(2) )
[1353]	681	IF ( c_u(k,j) < 0.0_wp ) THEN
	682	c_u(k,j) = 0.0_wp
[107]	683	ELSEIF ( c_u(k,j) > c_max ) THEN
	684	c_u(k,j) = c_max
[106]	685	ENDIF
	686	ELSE
[107]	687	c_u(k,j) = c_max
[75]	688	ENDIF
	689
[106]	690	denom = v_m_l(k,j,0) - v_m_l(k,j,1)
[75]	691
[1353]	692	IF ( denom /= 0.0_wp ) THEN
[996]	693	c_v(k,j) = -c_max * ( v(k,j,0) - v_m_l(k,j,0) ) / ( denom * tsc(2) )
[1353]	694	IF ( c_v(k,j) < 0.0_wp ) THEN
	695	c_v(k,j) = 0.0_wp
[106]	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
[75]	701	ENDIF
	702
[106]	703	denom = w_m_l(k,j,0) - w_m_l(k,j,1)
[75]	704
[1353]	705	IF ( denom /= 0.0_wp ) THEN
[996]	706	c_w(k,j) = -c_max * ( w(k,j,0) - w_m_l(k,j,0) ) / ( denom * tsc(2) )
[1353]	707	IF ( c_w(k,j) < 0.0_wp ) THEN
	708	c_w(k,j) = 0.0_wp
[106]	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
[75]	714	ENDIF
[106]	715
[978]	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)
[106]	719
[978]	720	ENDDO
	721	ENDDO
[75]	722
[978]	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
[73]	743	!
[978]	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
[996]	753	DO k = nzb+1, nzt+1
[1113]	754	DO j = nysg, nyng
[978]	755	u_p(k,j,0) = u(k,j,0) - dt_3d * tsc(2) * c_u_m(k) * &
[106]	756	( u(k,j,0) - u(k,j,1) ) * ddx
[75]	757
[978]	758	v_p(k,j,-1) = v(k,j,-1) - dt_3d * tsc(2) * c_v_m(k) * &
[75]	759	( v(k,j,-1) - v(k,j,0) ) * ddx
	760
[978]	761	w_p(k,j,-1) = w(k,j,-1) - dt_3d * tsc(2) * c_w_m(k) * &
[75]	762	( w(k,j,-1) - w(k,j,0) ) * ddx
[978]	763	ENDDO
[75]	764	ENDDO
	765
	766	!
[978]	767	!-- Bottom boundary at the outflow
	768	IF ( ibc_uv_b == 0 ) THEN
[1353]	769	u_p(nzb,:,0) = 0.0_wp
	770	v_p(nzb,:,-1) = 0.0_wp
[978]	771	ELSE
	772	u_p(nzb,:,0) = u_p(nzb+1,:,0)
	773	v_p(nzb,:,-1) = v_p(nzb+1,:,-1)
	774	ENDIF
[1353]	775	w_p(nzb,:,-1) = 0.0_wp
[1]	776
[75]	777	!
[978]	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
[1353]	786	w_p(nzt:nzt+1,:,-1) = 0.0_wp
[978]	787
[75]	788	ENDIF
[73]	789
[75]	790	ENDIF
[73]	791
[106]	792	IF ( outflow_r ) THEN
[73]	793
[1159]	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
[75]	799
[978]	800	c_max = dx / dt_3d
[75]	801
[1353]	802	c_u_m_l = 0.0_wp
	803	c_v_m_l = 0.0_wp
	804	c_w_m_l = 0.0_wp
[978]	805
[1353]	806	c_u_m = 0.0_wp
	807	c_v_m = 0.0_wp
	808	c_w_m = 0.0_wp
[978]	809
[1]	810	!
[996]	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
[73]	815
[106]	816	denom = u_m_r(k,j,nx) - u_m_r(k,j,nx-1)
	817
[1353]	818	IF ( denom /= 0.0_wp ) THEN
[996]	819	c_u(k,j) = -c_max * ( u(k,j,nx) - u_m_r(k,j,nx) ) / ( denom * tsc(2) )
[1353]	820	IF ( c_u(k,j) < 0.0_wp ) THEN
	821	c_u(k,j) = 0.0_wp
[106]	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
[73]	827	ENDIF
	828
[106]	829	denom = v_m_r(k,j,nx) - v_m_r(k,j,nx-1)
[73]	830
[1353]	831	IF ( denom /= 0.0_wp ) THEN
[996]	832	c_v(k,j) = -c_max * ( v(k,j,nx) - v_m_r(k,j,nx) ) / ( denom * tsc(2) )
[1353]	833	IF ( c_v(k,j) < 0.0_wp ) THEN
	834	c_v(k,j) = 0.0_wp
[106]	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
[73]	840	ENDIF
	841
[106]	842	denom = w_m_r(k,j,nx) - w_m_r(k,j,nx-1)
[73]	843
[1353]	844	IF ( denom /= 0.0_wp ) THEN
[996]	845	c_w(k,j) = -c_max * ( w(k,j,nx) - w_m_r(k,j,nx) ) / ( denom * tsc(2) )
[1353]	846	IF ( c_w(k,j) < 0.0_wp ) THEN
	847	c_w(k,j) = 0.0_wp
[106]	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
[73]	853	ENDIF
[106]	854
[978]	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)
[106]	858
[978]	859	ENDDO
	860	ENDDO
[73]	861
[978]	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
[73]	882	!
[978]	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
[73]	889
[978]	890	!
	891	!-- Calculate the new velocities
[996]	892	DO k = nzb+1, nzt+1
[1113]	893	DO j = nysg, nyng
[978]	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
[73]	896
[978]	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
[73]	899
[978]	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
[73]	903	ENDDO
	904
	905	!
[978]	906	!-- Bottom boundary at the outflow
	907	IF ( ibc_uv_b == 0 ) THEN
[1353]	908	u_p(nzb,:,nx+1) = 0.0_wp
	909	v_p(nzb,:,nx+1) = 0.0_wp
[978]	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
[1353]	914	w_p(nzb,:,nx+1) = 0.0_wp
[73]	915
	916	!
[978]	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
[1353]	925	w(nzt:nzt+1,:,nx+1) = 0.0_wp
[978]	926
[1]	927	ENDIF
	928
	929	ENDIF
	930
	931	END SUBROUTINE boundary_conds

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