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source: palm/trunk/SOURCE/boundary_conds.f90 @ 1380

Last change on this file since 1380 was 1380, checked in by heinze, 11 years ago
Upper boundary conditions for pt and q in case of nudging adjusted
Property svn:keywords set to `Id`
File size: 31.0 KB

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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	! -----------------
[1380]	22	! Adjust Dirichlet-condition at the top for pt in case of nudging
[1354]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: boundary_conds.f90 1380 2014-04-28 12:40:45Z heinze $
	27	!
[1362]	28	! 1361 2014-04-16 15:17:48Z hoffmann
	29	! Bottom and top boundary conditions of rain water content (qr) and
	30	! rain drop concentration (nr) changed to Dirichlet
	31	!
[1354]	32	! 1353 2014-04-08 15:21:23Z heinze
	33	! REAL constants provided with KIND-attribute
	34	!
[1321]	35	! 1320 2014-03-20 08:40:49Z raasch
[1320]	36	! ONLY-attribute added to USE-statements,
	37	! kind-parameters added to all INTEGER and REAL declaration statements,
	38	! kinds are defined in new module kinds,
	39	! revision history before 2012 removed,
	40	! comment fields (!:) to be used for variable explanations added to
	41	! all variable declaration statements
[1160]	42	!
[1258]	43	! 1257 2013-11-08 15:18:40Z raasch
	44	! loop independent clauses added
	45	!
[1242]	46	! 1241 2013-10-30 11:36:58Z heinze
	47	! Adjust ug and vg at each timestep in case of large_scale_forcing
	48	!
[1160]	49	! 1159 2013-05-21 11:58:22Z fricke
[1159]	50	! Bugfix: Neumann boundary conditions for the velocity components at the
	51	! outflow are in fact radiation boundary conditions using the maximum phase
	52	! velocity that ensures numerical stability (CFL-condition).
	53	! Hence, logical operator use_cmax is now used instead of bc_lr_dirneu/_neudir.
	54	! Bugfix: In case of use_cmax at the outflow, u, v, w are replaced by
	55	! u_p, v_p, w_p
[1116]	56	!
	57	! 1115 2013-03-26 18:16:16Z hoffmann
	58	! boundary conditions of two-moment cloud scheme are restricted to Neumann-
	59	! boundary-conditions
	60	!
[1114]	61	! 1113 2013-03-10 02:48:14Z raasch
	62	! GPU-porting
	63	! dummy argument "range" removed
	64	! Bugfix: wrong index in loops of radiation boundary condition
[1113]	65	!
[1054]	66	! 1053 2012-11-13 17:11:03Z hoffmann
	67	! boundary conditions for the two new prognostic equations (nr, qr) of the
	68	! two-moment cloud scheme
	69	!
[1037]	70	! 1036 2012-10-22 13:43:42Z raasch
	71	! code put under GPL (PALM 3.9)
	72	!
[997]	73	! 996 2012-09-07 10:41:47Z raasch
	74	! little reformatting
	75	!
[979]	76	! 978 2012-08-09 08:28:32Z fricke
	77	! Neumann boudnary conditions are added at the inflow boundary for the SGS-TKE.
	78	! Outflow boundary conditions for the velocity components can be set to Neumann
	79	! conditions or to radiation conditions with a horizontal averaged phase
	80	! velocity.
	81	!
[876]	82	! 875 2012-04-02 15:35:15Z gryschka
	83	! Bugfix in case of dirichlet inflow bc at the right or north boundary
	84	!
[1]	85	! Revision 1.1 1997/09/12 06:21:34 raasch
	86	! Initial revision
	87	!
	88	!
	89	! Description:
	90	! ------------
[1159]	91	! Boundary conditions for the prognostic quantities.
[1]	92	! One additional bottom boundary condition is applied for the TKE (=(u)*2)
	93	! in prandtl_fluxes. The cyclic lateral boundary conditions are implicitly
	94	! handled in routine exchange_horiz. Pressure boundary conditions are
	95	! explicitly set in routines pres, poisfft, poismg and sor.
	96	!------------------------------------------------------------------------------!
	97
[1320]	98	USE arrays_3d, &
	99	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, &
	100	dzu, e_p, nr_p, pt, pt_p, q, q_p, qr_p, sa, sa_p, &
	101	u, ug, u_init, u_m_l, u_m_n, u_m_r, u_m_s, u_p, &
	102	v, vg, v_init, v_m_l, v_m_n, v_m_r, v_m_s, v_p, &
[1380]	103	w, w_p, w_m_l, w_m_n, w_m_r, w_m_s,&
	104	pt_init
[1320]	105
	106	USE control_parameters, &
	107	ONLY: bc_pt_t_val, bc_q_t_val, constant_diffusion, &
	108	cloud_physics, dt_3d, humidity, &
	109	ibc_pt_b, ibc_pt_t, ibc_q_b, ibc_sa_t, ibc_uv_b, ibc_uv_t, &
	110	icloud_scheme, inflow_l, inflow_n, inflow_r, inflow_s, &
	111	intermediate_timestep_count, large_scale_forcing, ocean, &
	112	outflow_l, outflow_n, outflow_r, outflow_s, passive_scalar, &
[1380]	113	precipitation, tsc, use_cmax, &
	114	nudging
[1320]	115
	116	USE grid_variables, &
	117	ONLY: ddx, ddy, dx, dy
	118
	119	USE indices, &
	120	ONLY: nx, nxl, nxlg, nxr, nxrg, ny, nyn, nyng, nys, nysg, &
	121	nzb, nzb_s_inner, nzb_w_inner, nzt
	122
	123	USE kinds
	124
[1]	125	USE pegrid
	126
[1320]	127
[1]	128	IMPLICIT NONE
	129
[1320]	130	INTEGER(iwp) :: i !:
	131	INTEGER(iwp) :: j !:
	132	INTEGER(iwp) :: k !:
[1]	133
[1320]	134	REAL(wp) :: c_max !:
	135	REAL(wp) :: denom !:
[1]	136
[73]	137
[1]	138	!
[1113]	139	!-- Bottom boundary
	140	IF ( ibc_uv_b == 1 ) THEN
	141	!$acc kernels present( u_p, v_p )
	142	u_p(nzb,:,:) = u_p(nzb+1,:,:)
	143	v_p(nzb,:,:) = v_p(nzb+1,:,:)
	144	!$acc end kernels
	145	ENDIF
	146
	147	!$acc kernels present( nzb_w_inner, w_p )
	148	DO i = nxlg, nxrg
	149	DO j = nysg, nyng
[1353]	150	w_p(nzb_w_inner(j,i),j,i) = 0.0_wp
[1113]	151	ENDDO
	152	ENDDO
	153	!$acc end kernels
	154
	155	!
	156	!-- Top boundary
	157	IF ( ibc_uv_t == 0 ) THEN
	158	!$acc kernels present( u_init, u_p, v_init, v_p )
	159	u_p(nzt+1,:,:) = u_init(nzt+1)
	160	v_p(nzt+1,:,:) = v_init(nzt+1)
[1241]	161	IF ( large_scale_forcing) THEN
	162	u_p(nzt+1,:,:) = ug(nzt+1)
	163	v_p(nzt+1,:,:) = vg(nzt+1)
	164	END IF
[1113]	165	!$acc end kernels
	166	ELSE
	167	!$acc kernels present( u_p, v_p )
	168	u_p(nzt+1,:,:) = u_p(nzt,:,:)
	169	v_p(nzt+1,:,:) = v_p(nzt,:,:)
	170	!$acc end kernels
	171	ENDIF
	172	!$acc kernels present( w_p )
[1353]	173	w_p(nzt:nzt+1,:,:) = 0.0_wp ! nzt is not a prognostic level (but cf. pres)
[1113]	174	!$acc end kernels
	175
	176	!
	177	!-- Temperature at bottom boundary.
	178	!-- In case of coupled runs (ibc_pt_b = 2) the temperature is given by
	179	!-- the sea surface temperature of the coupled ocean model.
	180	IF ( ibc_pt_b == 0 ) THEN
	181	!$acc kernels present( nzb_s_inner, pt, pt_p )
[1257]	182	!$acc loop independent
[667]	183	DO i = nxlg, nxrg
[1257]	184	!$acc loop independent
[667]	185	DO j = nysg, nyng
[1113]	186	pt_p(nzb_s_inner(j,i),j,i) = pt(nzb_s_inner(j,i),j,i)
[1]	187	ENDDO
	188	ENDDO
[1113]	189	!$acc end kernels
	190	ELSEIF ( ibc_pt_b == 1 ) THEN
	191	!$acc kernels present( nzb_s_inner, pt_p )
[1257]	192	!$acc loop independent
[1113]	193	DO i = nxlg, nxrg
[1257]	194	!$acc loop independent
[1113]	195	DO j = nysg, nyng
	196	pt_p(nzb_s_inner(j,i),j,i) = pt_p(nzb_s_inner(j,i)+1,j,i)
	197	ENDDO
	198	ENDDO
	199	!$acc end kernels
	200	ENDIF
[1]	201
	202	!
[1113]	203	!-- Temperature at top boundary
	204	IF ( ibc_pt_t == 0 ) THEN
	205	!$acc kernels present( pt, pt_p )
	206	pt_p(nzt+1,:,:) = pt(nzt+1,:,:)
[1380]	207	!
	208	!-- In case of nudging adjust top boundary to pt which is
	209	!-- read in from NUDGING-DATA
	210	IF ( nudging ) THEN
	211	pt_p(nzt+1,:,:) = pt_init(nzt+1)
	212	ENDIF
[1113]	213	!$acc end kernels
	214	ELSEIF ( ibc_pt_t == 1 ) THEN
	215	!$acc kernels present( pt_p )
	216	pt_p(nzt+1,:,:) = pt_p(nzt,:,:)
	217	!$acc end kernels
	218	ELSEIF ( ibc_pt_t == 2 ) THEN
	219	!$acc kernels present( dzu, pt_p )
	220	pt_p(nzt+1,:,:) = pt_p(nzt,:,:) + bc_pt_t_val * dzu(nzt+1)
	221	!$acc end kernels
	222	ENDIF
[1]	223
	224	!
[1113]	225	!-- Boundary conditions for TKE
	226	!-- Generally Neumann conditions with de/dz=0 are assumed
	227	IF ( .NOT. constant_diffusion ) THEN
	228	!$acc kernels present( e_p, nzb_s_inner )
[1257]	229	!$acc loop independent
[1113]	230	DO i = nxlg, nxrg
[1257]	231	!$acc loop independent
[1113]	232	DO j = nysg, nyng
	233	e_p(nzb_s_inner(j,i),j,i) = e_p(nzb_s_inner(j,i)+1,j,i)
[73]	234	ENDDO
[1113]	235	ENDDO
	236	e_p(nzt+1,:,:) = e_p(nzt,:,:)
	237	!$acc end kernels
	238	ENDIF
	239
	240	!
	241	!-- Boundary conditions for salinity
	242	IF ( ocean ) THEN
	243	!
	244	!-- Bottom boundary: Neumann condition because salinity flux is always
	245	!-- given
	246	DO i = nxlg, nxrg
	247	DO j = nysg, nyng
	248	sa_p(nzb_s_inner(j,i),j,i) = sa_p(nzb_s_inner(j,i)+1,j,i)
[1]	249	ENDDO
[1113]	250	ENDDO
[1]	251
	252	!
[1113]	253	!-- Top boundary: Dirichlet or Neumann
	254	IF ( ibc_sa_t == 0 ) THEN
	255	sa_p(nzt+1,:,:) = sa(nzt+1,:,:)
	256	ELSEIF ( ibc_sa_t == 1 ) THEN
	257	sa_p(nzt+1,:,:) = sa_p(nzt,:,:)
[1]	258	ENDIF
	259
[1113]	260	ENDIF
	261
[1]	262	!
[1113]	263	!-- Boundary conditions for total water content or scalar,
	264	!-- bottom and top boundary (see also temperature)
	265	IF ( humidity .OR. passive_scalar ) THEN
	266	!
	267	!-- Surface conditions for constant_humidity_flux
	268	IF ( ibc_q_b == 0 ) THEN
[667]	269	DO i = nxlg, nxrg
	270	DO j = nysg, nyng
[1113]	271	q_p(nzb_s_inner(j,i),j,i) = q(nzb_s_inner(j,i),j,i)
[1]	272	ENDDO
	273	ENDDO
[1113]	274	ELSE
[667]	275	DO i = nxlg, nxrg
	276	DO j = nysg, nyng
[1113]	277	q_p(nzb_s_inner(j,i),j,i) = q_p(nzb_s_inner(j,i)+1,j,i)
[95]	278	ENDDO
	279	ENDDO
[1113]	280	ENDIF
[95]	281	!
[1113]	282	!-- Top boundary
	283	q_p(nzt+1,:,:) = q_p(nzt,:,:) + bc_q_t_val * dzu(nzt+1)
[95]	284
[1361]	285	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. precipitation ) THEN
[1113]	286	!
[1361]	287	!-- Surface conditions rain water (Dirichlet)
[1115]	288	DO i = nxlg, nxrg
	289	DO j = nysg, nyng
[1361]	290	qr_p(nzb_s_inner(j,i),j,i) = 0.0_wp
	291	nr_p(nzb_s_inner(j,i),j,i) = 0.0_wp
[73]	292	ENDDO
[1115]	293	ENDDO
[1]	294	!
[1361]	295	!-- Top boundary condition for rain water (Dirichlet)
	296	qr_p(nzt+1,:,:) = 0.0_wp
	297	nr_p(nzt+1,:,:) = 0.0_wp
[1115]	298
[1]	299	ENDIF
	300	!
[875]	301	!-- In case of inflow at the south boundary the boundary for v is at nys
	302	!-- and in case of inflow at the left boundary the boundary for u is at nxl.
	303	!-- Since in prognostic_equations (cache optimized version) these levels are
	304	!-- handled as a prognostic level, boundary values have to be restored here.
[978]	305	!-- For the SGS-TKE, Neumann boundary conditions are used at the inflow.
[1]	306	IF ( inflow_s ) THEN
[73]	307	v_p(:,nys,:) = v_p(:,nys-1,:)
[978]	308	IF ( .NOT. constant_diffusion ) e_p(:,nys-1,:) = e_p(:,nys,:)
	309	ELSEIF ( inflow_n ) THEN
	310	IF ( .NOT. constant_diffusion ) e_p(:,nyn+1,:) = e_p(:,nyn,:)
[1]	311	ELSEIF ( inflow_l ) THEN
[73]	312	u_p(:,:,nxl) = u_p(:,:,nxl-1)
[978]	313	IF ( .NOT. constant_diffusion ) e_p(:,:,nxl-1) = e_p(:,:,nxl)
	314	ELSEIF ( inflow_r ) THEN
	315	IF ( .NOT. constant_diffusion ) e_p(:,:,nxr+1) = e_p(:,:,nxr)
[1]	316	ENDIF
	317
	318	!
	319	!-- Lateral boundary conditions for scalar quantities at the outflow
	320	IF ( outflow_s ) THEN
[73]	321	pt_p(:,nys-1,:) = pt_p(:,nys,:)
	322	IF ( .NOT. constant_diffusion ) e_p(:,nys-1,:) = e_p(:,nys,:)
[1115]	323	IF ( humidity .OR. passive_scalar ) THEN
[1053]	324	q_p(:,nys-1,:) = q_p(:,nys,:)
[1320]	325	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
[1115]	326	precipitation) THEN
[1053]	327	qr_p(:,nys-1,:) = qr_p(:,nys,:)
	328	nr_p(:,nys-1,:) = nr_p(:,nys,:)
	329	ENDIF
	330	ENDIF
[1]	331	ELSEIF ( outflow_n ) THEN
[73]	332	pt_p(:,nyn+1,:) = pt_p(:,nyn,:)
	333	IF ( .NOT. constant_diffusion ) e_p(:,nyn+1,:) = e_p(:,nyn,:)
[1115]	334	IF ( humidity .OR. passive_scalar ) THEN
[1053]	335	q_p(:,nyn+1,:) = q_p(:,nyn,:)
[1320]	336	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
[1115]	337	precipitation ) THEN
[1053]	338	qr_p(:,nyn+1,:) = qr_p(:,nyn,:)
	339	nr_p(:,nyn+1,:) = nr_p(:,nyn,:)
	340	ENDIF
	341	ENDIF
[1]	342	ELSEIF ( outflow_l ) THEN
[73]	343	pt_p(:,:,nxl-1) = pt_p(:,:,nxl)
	344	IF ( .NOT. constant_diffusion ) e_p(:,:,nxl-1) = e_p(:,:,nxl)
[1115]	345	IF ( humidity .OR. passive_scalar ) THEN
[1053]	346	q_p(:,:,nxl-1) = q_p(:,:,nxl)
[1320]	347	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
[1115]	348	precipitation ) THEN
[1053]	349	qr_p(:,:,nxl-1) = qr_p(:,:,nxl)
	350	nr_p(:,:,nxl-1) = nr_p(:,:,nxl)
	351	ENDIF
	352	ENDIF
[1]	353	ELSEIF ( outflow_r ) THEN
[73]	354	pt_p(:,:,nxr+1) = pt_p(:,:,nxr)
	355	IF ( .NOT. constant_diffusion ) e_p(:,:,nxr+1) = e_p(:,:,nxr)
[1053]	356	IF ( humidity .OR. passive_scalar ) THEN
	357	q_p(:,:,nxr+1) = q_p(:,:,nxr)
[1115]	358	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. precipitation ) THEN
[1053]	359	qr_p(:,:,nxr+1) = qr_p(:,:,nxr)
	360	nr_p(:,:,nxr+1) = nr_p(:,:,nxr)
	361	ENDIF
	362	ENDIF
[1]	363	ENDIF
	364
	365	ENDIF
	366
	367	!
[1159]	368	!-- Radiation boundary conditions for the velocities at the respective outflow.
	369	!-- The phase velocity is either assumed to the maximum phase velocity that
	370	!-- ensures numerical stability (CFL-condition) or calculated after
	371	!-- Orlanski(1976) and averaged along the outflow boundary.
[106]	372	IF ( outflow_s ) THEN
[75]	373
[1159]	374	IF ( use_cmax ) THEN
	375	u_p(:,-1,:) = u(:,0,:)
	376	v_p(:,0,:) = v(:,1,:)
	377	w_p(:,-1,:) = w(:,0,:)
	378	ELSEIF ( .NOT. use_cmax ) THEN
[75]	379
[978]	380	c_max = dy / dt_3d
[75]	381
[1353]	382	c_u_m_l = 0.0_wp
	383	c_v_m_l = 0.0_wp
	384	c_w_m_l = 0.0_wp
[978]	385
[1353]	386	c_u_m = 0.0_wp
	387	c_v_m = 0.0_wp
	388	c_w_m = 0.0_wp
[978]	389
[75]	390	!
[996]	391	!-- Calculate the phase speeds for u, v, and w, first local and then
	392	!-- average along the outflow boundary.
	393	DO k = nzb+1, nzt+1
	394	DO i = nxl, nxr
[75]	395
[106]	396	denom = u_m_s(k,0,i) - u_m_s(k,1,i)
	397
[1353]	398	IF ( denom /= 0.0_wp ) THEN
[996]	399	c_u(k,i) = -c_max * ( u(k,0,i) - u_m_s(k,0,i) ) / ( denom * tsc(2) )
[1353]	400	IF ( c_u(k,i) < 0.0_wp ) THEN
	401	c_u(k,i) = 0.0_wp
[106]	402	ELSEIF ( c_u(k,i) > c_max ) THEN
	403	c_u(k,i) = c_max
	404	ENDIF
	405	ELSE
	406	c_u(k,i) = c_max
[75]	407	ENDIF
	408
[106]	409	denom = v_m_s(k,1,i) - v_m_s(k,2,i)
	410
[1353]	411	IF ( denom /= 0.0_wp ) THEN
[996]	412	c_v(k,i) = -c_max * ( v(k,1,i) - v_m_s(k,1,i) ) / ( denom * tsc(2) )
[1353]	413	IF ( c_v(k,i) < 0.0_wp ) THEN
	414	c_v(k,i) = 0.0_wp
[106]	415	ELSEIF ( c_v(k,i) > c_max ) THEN
	416	c_v(k,i) = c_max
	417	ENDIF
	418	ELSE
	419	c_v(k,i) = c_max
[75]	420	ENDIF
	421
[106]	422	denom = w_m_s(k,0,i) - w_m_s(k,1,i)
[75]	423
[1353]	424	IF ( denom /= 0.0_wp ) THEN
[996]	425	c_w(k,i) = -c_max * ( w(k,0,i) - w_m_s(k,0,i) ) / ( denom * tsc(2) )
[1353]	426	IF ( c_w(k,i) < 0.0_wp ) THEN
	427	c_w(k,i) = 0.0_wp
[106]	428	ELSEIF ( c_w(k,i) > c_max ) THEN
	429	c_w(k,i) = c_max
	430	ENDIF
	431	ELSE
	432	c_w(k,i) = c_max
[75]	433	ENDIF
[106]	434
[978]	435	c_u_m_l(k) = c_u_m_l(k) + c_u(k,i)
	436	c_v_m_l(k) = c_v_m_l(k) + c_v(k,i)
	437	c_w_m_l(k) = c_w_m_l(k) + c_w(k,i)
[106]	438
[978]	439	ENDDO
	440	ENDDO
[75]	441
[978]	442	#if defined( __parallel )
	443	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
	444	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
	445	MPI_SUM, comm1dx, ierr )
	446	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
	447	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_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_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
	451	MPI_SUM, comm1dx, ierr )
	452	#else
	453	c_u_m = c_u_m_l
	454	c_v_m = c_v_m_l
	455	c_w_m = c_w_m_l
	456	#endif
	457
	458	c_u_m = c_u_m / (nx+1)
	459	c_v_m = c_v_m / (nx+1)
	460	c_w_m = c_w_m / (nx+1)
	461
[75]	462	!
[978]	463	!-- Save old timelevels for the next timestep
	464	IF ( intermediate_timestep_count == 1 ) THEN
	465	u_m_s(:,:,:) = u(:,0:1,:)
	466	v_m_s(:,:,:) = v(:,1:2,:)
	467	w_m_s(:,:,:) = w(:,0:1,:)
	468	ENDIF
	469
	470	!
	471	!-- Calculate the new velocities
[996]	472	DO k = nzb+1, nzt+1
	473	DO i = nxlg, nxrg
[978]	474	u_p(k,-1,i) = u(k,-1,i) - dt_3d * tsc(2) * c_u_m(k) * &
[75]	475	( u(k,-1,i) - u(k,0,i) ) * ddy
	476
[978]	477	v_p(k,0,i) = v(k,0,i) - dt_3d * tsc(2) * c_v_m(k) * &
[106]	478	( v(k,0,i) - v(k,1,i) ) * ddy
[75]	479
[978]	480	w_p(k,-1,i) = w(k,-1,i) - dt_3d * tsc(2) * c_w_m(k) * &
[75]	481	( w(k,-1,i) - w(k,0,i) ) * ddy
[978]	482	ENDDO
[75]	483	ENDDO
	484
	485	!
[978]	486	!-- Bottom boundary at the outflow
	487	IF ( ibc_uv_b == 0 ) THEN
[1353]	488	u_p(nzb,-1,:) = 0.0_wp
	489	v_p(nzb,0,:) = 0.0_wp
[978]	490	ELSE
	491	u_p(nzb,-1,:) = u_p(nzb+1,-1,:)
	492	v_p(nzb,0,:) = v_p(nzb+1,0,:)
	493	ENDIF
[1353]	494	w_p(nzb,-1,:) = 0.0_wp
[73]	495
[75]	496	!
[978]	497	!-- Top boundary at the outflow
	498	IF ( ibc_uv_t == 0 ) THEN
	499	u_p(nzt+1,-1,:) = u_init(nzt+1)
	500	v_p(nzt+1,0,:) = v_init(nzt+1)
	501	ELSE
	502	u_p(nzt+1,-1,:) = u(nzt,-1,:)
	503	v_p(nzt+1,0,:) = v(nzt,0,:)
	504	ENDIF
[1353]	505	w_p(nzt:nzt+1,-1,:) = 0.0_wp
[978]	506
[75]	507	ENDIF
[73]	508
[75]	509	ENDIF
[73]	510
[106]	511	IF ( outflow_n ) THEN
[73]	512
[1159]	513	IF ( use_cmax ) THEN
	514	u_p(:,ny+1,:) = u(:,ny,:)
	515	v_p(:,ny+1,:) = v(:,ny,:)
	516	w_p(:,ny+1,:) = w(:,ny,:)
	517	ELSEIF ( .NOT. use_cmax ) THEN
[75]	518
[978]	519	c_max = dy / dt_3d
[75]	520
[1353]	521	c_u_m_l = 0.0_wp
	522	c_v_m_l = 0.0_wp
	523	c_w_m_l = 0.0_wp
[978]	524
[1353]	525	c_u_m = 0.0_wp
	526	c_v_m = 0.0_wp
	527	c_w_m = 0.0_wp
[978]	528
[1]	529	!
[996]	530	!-- Calculate the phase speeds for u, v, and w, first local and then
	531	!-- average along the outflow boundary.
	532	DO k = nzb+1, nzt+1
	533	DO i = nxl, nxr
[73]	534
[106]	535	denom = u_m_n(k,ny,i) - u_m_n(k,ny-1,i)
	536
[1353]	537	IF ( denom /= 0.0_wp ) THEN
[996]	538	c_u(k,i) = -c_max * ( u(k,ny,i) - u_m_n(k,ny,i) ) / ( denom * tsc(2) )
[1353]	539	IF ( c_u(k,i) < 0.0_wp ) THEN
	540	c_u(k,i) = 0.0_wp
[106]	541	ELSEIF ( c_u(k,i) > c_max ) THEN
	542	c_u(k,i) = c_max
	543	ENDIF
	544	ELSE
	545	c_u(k,i) = c_max
[73]	546	ENDIF
	547
[106]	548	denom = v_m_n(k,ny,i) - v_m_n(k,ny-1,i)
[73]	549
[1353]	550	IF ( denom /= 0.0_wp ) THEN
[996]	551	c_v(k,i) = -c_max * ( v(k,ny,i) - v_m_n(k,ny,i) ) / ( denom * tsc(2) )
[1353]	552	IF ( c_v(k,i) < 0.0_wp ) THEN
	553	c_v(k,i) = 0.0_wp
[106]	554	ELSEIF ( c_v(k,i) > c_max ) THEN
	555	c_v(k,i) = c_max
	556	ENDIF
	557	ELSE
	558	c_v(k,i) = c_max
[73]	559	ENDIF
	560
[106]	561	denom = w_m_n(k,ny,i) - w_m_n(k,ny-1,i)
[73]	562
[1353]	563	IF ( denom /= 0.0_wp ) THEN
[996]	564	c_w(k,i) = -c_max * ( w(k,ny,i) - w_m_n(k,ny,i) ) / ( denom * tsc(2) )
[1353]	565	IF ( c_w(k,i) < 0.0_wp ) THEN
	566	c_w(k,i) = 0.0_wp
[106]	567	ELSEIF ( c_w(k,i) > c_max ) THEN
	568	c_w(k,i) = c_max
	569	ENDIF
	570	ELSE
	571	c_w(k,i) = c_max
[73]	572	ENDIF
[106]	573
[978]	574	c_u_m_l(k) = c_u_m_l(k) + c_u(k,i)
	575	c_v_m_l(k) = c_v_m_l(k) + c_v(k,i)
	576	c_w_m_l(k) = c_w_m_l(k) + c_w(k,i)
[106]	577
[978]	578	ENDDO
	579	ENDDO
[73]	580
[978]	581	#if defined( __parallel )
	582	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
	583	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
	584	MPI_SUM, comm1dx, ierr )
	585	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
	586	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_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_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
	590	MPI_SUM, comm1dx, ierr )
	591	#else
	592	c_u_m = c_u_m_l
	593	c_v_m = c_v_m_l
	594	c_w_m = c_w_m_l
	595	#endif
	596
	597	c_u_m = c_u_m / (nx+1)
	598	c_v_m = c_v_m / (nx+1)
	599	c_w_m = c_w_m / (nx+1)
	600
[73]	601	!
[978]	602	!-- Save old timelevels for the next timestep
	603	IF ( intermediate_timestep_count == 1 ) THEN
	604	u_m_n(:,:,:) = u(:,ny-1:ny,:)
	605	v_m_n(:,:,:) = v(:,ny-1:ny,:)
	606	w_m_n(:,:,:) = w(:,ny-1:ny,:)
	607	ENDIF
[73]	608
[978]	609	!
	610	!-- Calculate the new velocities
[996]	611	DO k = nzb+1, nzt+1
	612	DO i = nxlg, nxrg
[978]	613	u_p(k,ny+1,i) = u(k,ny+1,i) - dt_3d * tsc(2) * c_u_m(k) * &
	614	( u(k,ny+1,i) - u(k,ny,i) ) * ddy
[73]	615
[978]	616	v_p(k,ny+1,i) = v(k,ny+1,i) - dt_3d * tsc(2) * c_v_m(k) * &
	617	( v(k,ny+1,i) - v(k,ny,i) ) * ddy
[73]	618
[978]	619	w_p(k,ny+1,i) = w(k,ny+1,i) - dt_3d * tsc(2) * c_w_m(k) * &
	620	( w(k,ny+1,i) - w(k,ny,i) ) * ddy
	621	ENDDO
[1]	622	ENDDO
	623
	624	!
[978]	625	!-- Bottom boundary at the outflow
	626	IF ( ibc_uv_b == 0 ) THEN
[1353]	627	u_p(nzb,ny+1,:) = 0.0_wp
	628	v_p(nzb,ny+1,:) = 0.0_wp
[978]	629	ELSE
	630	u_p(nzb,ny+1,:) = u_p(nzb+1,ny+1,:)
	631	v_p(nzb,ny+1,:) = v_p(nzb+1,ny+1,:)
	632	ENDIF
[1353]	633	w_p(nzb,ny+1,:) = 0.0_wp
[73]	634
	635	!
[978]	636	!-- Top boundary at the outflow
	637	IF ( ibc_uv_t == 0 ) THEN
	638	u_p(nzt+1,ny+1,:) = u_init(nzt+1)
	639	v_p(nzt+1,ny+1,:) = v_init(nzt+1)
	640	ELSE
	641	u_p(nzt+1,ny+1,:) = u_p(nzt,nyn+1,:)
	642	v_p(nzt+1,ny+1,:) = v_p(nzt,nyn+1,:)
	643	ENDIF
[1353]	644	w_p(nzt:nzt+1,ny+1,:) = 0.0_wp
[978]	645
[1]	646	ENDIF
	647
[75]	648	ENDIF
	649
[106]	650	IF ( outflow_l ) THEN
[75]	651
[1159]	652	IF ( use_cmax ) THEN
	653	u_p(:,:,-1) = u(:,:,0)
	654	v_p(:,:,0) = v(:,:,1)
	655	w_p(:,:,-1) = w(:,:,0)
	656	ELSEIF ( .NOT. use_cmax ) THEN
[75]	657
[978]	658	c_max = dx / dt_3d
[75]	659
[1353]	660	c_u_m_l = 0.0_wp
	661	c_v_m_l = 0.0_wp
	662	c_w_m_l = 0.0_wp
[978]	663
[1353]	664	c_u_m = 0.0_wp
	665	c_v_m = 0.0_wp
	666	c_w_m = 0.0_wp
[978]	667
[1]	668	!
[996]	669	!-- Calculate the phase speeds for u, v, and w, first local and then
	670	!-- average along the outflow boundary.
	671	DO k = nzb+1, nzt+1
	672	DO j = nys, nyn
[75]	673
[106]	674	denom = u_m_l(k,j,1) - u_m_l(k,j,2)
	675
[1353]	676	IF ( denom /= 0.0_wp ) THEN
[996]	677	c_u(k,j) = -c_max * ( u(k,j,1) - u_m_l(k,j,1) ) / ( denom * tsc(2) )
[1353]	678	IF ( c_u(k,j) < 0.0_wp ) THEN
	679	c_u(k,j) = 0.0_wp
[107]	680	ELSEIF ( c_u(k,j) > c_max ) THEN
	681	c_u(k,j) = c_max
[106]	682	ENDIF
	683	ELSE
[107]	684	c_u(k,j) = c_max
[75]	685	ENDIF
	686
[106]	687	denom = v_m_l(k,j,0) - v_m_l(k,j,1)
[75]	688
[1353]	689	IF ( denom /= 0.0_wp ) THEN
[996]	690	c_v(k,j) = -c_max * ( v(k,j,0) - v_m_l(k,j,0) ) / ( denom * tsc(2) )
[1353]	691	IF ( c_v(k,j) < 0.0_wp ) THEN
	692	c_v(k,j) = 0.0_wp
[106]	693	ELSEIF ( c_v(k,j) > c_max ) THEN
	694	c_v(k,j) = c_max
	695	ENDIF
	696	ELSE
	697	c_v(k,j) = c_max
[75]	698	ENDIF
	699
[106]	700	denom = w_m_l(k,j,0) - w_m_l(k,j,1)
[75]	701
[1353]	702	IF ( denom /= 0.0_wp ) THEN
[996]	703	c_w(k,j) = -c_max * ( w(k,j,0) - w_m_l(k,j,0) ) / ( denom * tsc(2) )
[1353]	704	IF ( c_w(k,j) < 0.0_wp ) THEN
	705	c_w(k,j) = 0.0_wp
[106]	706	ELSEIF ( c_w(k,j) > c_max ) THEN
	707	c_w(k,j) = c_max
	708	ENDIF
	709	ELSE
	710	c_w(k,j) = c_max
[75]	711	ENDIF
[106]	712
[978]	713	c_u_m_l(k) = c_u_m_l(k) + c_u(k,j)
	714	c_v_m_l(k) = c_v_m_l(k) + c_v(k,j)
	715	c_w_m_l(k) = c_w_m_l(k) + c_w(k,j)
[106]	716
[978]	717	ENDDO
	718	ENDDO
[75]	719
[978]	720	#if defined( __parallel )
	721	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
	722	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
	723	MPI_SUM, comm1dy, ierr )
	724	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
	725	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_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_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
	729	MPI_SUM, comm1dy, ierr )
	730	#else
	731	c_u_m = c_u_m_l
	732	c_v_m = c_v_m_l
	733	c_w_m = c_w_m_l
	734	#endif
	735
	736	c_u_m = c_u_m / (ny+1)
	737	c_v_m = c_v_m / (ny+1)
	738	c_w_m = c_w_m / (ny+1)
	739
[73]	740	!
[978]	741	!-- Save old timelevels for the next timestep
	742	IF ( intermediate_timestep_count == 1 ) THEN
	743	u_m_l(:,:,:) = u(:,:,1:2)
	744	v_m_l(:,:,:) = v(:,:,0:1)
	745	w_m_l(:,:,:) = w(:,:,0:1)
	746	ENDIF
	747
	748	!
	749	!-- Calculate the new velocities
[996]	750	DO k = nzb+1, nzt+1
[1113]	751	DO j = nysg, nyng
[978]	752	u_p(k,j,0) = u(k,j,0) - dt_3d * tsc(2) * c_u_m(k) * &
[106]	753	( u(k,j,0) - u(k,j,1) ) * ddx
[75]	754
[978]	755	v_p(k,j,-1) = v(k,j,-1) - dt_3d * tsc(2) * c_v_m(k) * &
[75]	756	( v(k,j,-1) - v(k,j,0) ) * ddx
	757
[978]	758	w_p(k,j,-1) = w(k,j,-1) - dt_3d * tsc(2) * c_w_m(k) * &
[75]	759	( w(k,j,-1) - w(k,j,0) ) * ddx
[978]	760	ENDDO
[75]	761	ENDDO
	762
	763	!
[978]	764	!-- Bottom boundary at the outflow
	765	IF ( ibc_uv_b == 0 ) THEN
[1353]	766	u_p(nzb,:,0) = 0.0_wp
	767	v_p(nzb,:,-1) = 0.0_wp
[978]	768	ELSE
	769	u_p(nzb,:,0) = u_p(nzb+1,:,0)
	770	v_p(nzb,:,-1) = v_p(nzb+1,:,-1)
	771	ENDIF
[1353]	772	w_p(nzb,:,-1) = 0.0_wp
[1]	773
[75]	774	!
[978]	775	!-- Top boundary at the outflow
	776	IF ( ibc_uv_t == 0 ) THEN
	777	u_p(nzt+1,:,-1) = u_init(nzt+1)
	778	v_p(nzt+1,:,-1) = v_init(nzt+1)
	779	ELSE
	780	u_p(nzt+1,:,-1) = u_p(nzt,:,-1)
	781	v_p(nzt+1,:,-1) = v_p(nzt,:,-1)
	782	ENDIF
[1353]	783	w_p(nzt:nzt+1,:,-1) = 0.0_wp
[978]	784
[75]	785	ENDIF
[73]	786
[75]	787	ENDIF
[73]	788
[106]	789	IF ( outflow_r ) THEN
[73]	790
[1159]	791	IF ( use_cmax ) THEN
	792	u_p(:,:,nx+1) = u(:,:,nx)
	793	v_p(:,:,nx+1) = v(:,:,nx)
	794	w_p(:,:,nx+1) = w(:,:,nx)
	795	ELSEIF ( .NOT. use_cmax ) THEN
[75]	796
[978]	797	c_max = dx / dt_3d
[75]	798
[1353]	799	c_u_m_l = 0.0_wp
	800	c_v_m_l = 0.0_wp
	801	c_w_m_l = 0.0_wp
[978]	802
[1353]	803	c_u_m = 0.0_wp
	804	c_v_m = 0.0_wp
	805	c_w_m = 0.0_wp
[978]	806
[1]	807	!
[996]	808	!-- Calculate the phase speeds for u, v, and w, first local and then
	809	!-- average along the outflow boundary.
	810	DO k = nzb+1, nzt+1
	811	DO j = nys, nyn
[73]	812
[106]	813	denom = u_m_r(k,j,nx) - u_m_r(k,j,nx-1)
	814
[1353]	815	IF ( denom /= 0.0_wp ) THEN
[996]	816	c_u(k,j) = -c_max * ( u(k,j,nx) - u_m_r(k,j,nx) ) / ( denom * tsc(2) )
[1353]	817	IF ( c_u(k,j) < 0.0_wp ) THEN
	818	c_u(k,j) = 0.0_wp
[106]	819	ELSEIF ( c_u(k,j) > c_max ) THEN
	820	c_u(k,j) = c_max
	821	ENDIF
	822	ELSE
	823	c_u(k,j) = c_max
[73]	824	ENDIF
	825
[106]	826	denom = v_m_r(k,j,nx) - v_m_r(k,j,nx-1)
[73]	827
[1353]	828	IF ( denom /= 0.0_wp ) THEN
[996]	829	c_v(k,j) = -c_max * ( v(k,j,nx) - v_m_r(k,j,nx) ) / ( denom * tsc(2) )
[1353]	830	IF ( c_v(k,j) < 0.0_wp ) THEN
	831	c_v(k,j) = 0.0_wp
[106]	832	ELSEIF ( c_v(k,j) > c_max ) THEN
	833	c_v(k,j) = c_max
	834	ENDIF
	835	ELSE
	836	c_v(k,j) = c_max
[73]	837	ENDIF
	838
[106]	839	denom = w_m_r(k,j,nx) - w_m_r(k,j,nx-1)
[73]	840
[1353]	841	IF ( denom /= 0.0_wp ) THEN
[996]	842	c_w(k,j) = -c_max * ( w(k,j,nx) - w_m_r(k,j,nx) ) / ( denom * tsc(2) )
[1353]	843	IF ( c_w(k,j) < 0.0_wp ) THEN
	844	c_w(k,j) = 0.0_wp
[106]	845	ELSEIF ( c_w(k,j) > c_max ) THEN
	846	c_w(k,j) = c_max
	847	ENDIF
	848	ELSE
	849	c_w(k,j) = c_max
[73]	850	ENDIF
[106]	851
[978]	852	c_u_m_l(k) = c_u_m_l(k) + c_u(k,j)
	853	c_v_m_l(k) = c_v_m_l(k) + c_v(k,j)
	854	c_w_m_l(k) = c_w_m_l(k) + c_w(k,j)
[106]	855
[978]	856	ENDDO
	857	ENDDO
[73]	858
[978]	859	#if defined( __parallel )
	860	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
	861	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
	862	MPI_SUM, comm1dy, ierr )
	863	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
	864	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_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_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
	868	MPI_SUM, comm1dy, ierr )
	869	#else
	870	c_u_m = c_u_m_l
	871	c_v_m = c_v_m_l
	872	c_w_m = c_w_m_l
	873	#endif
	874
	875	c_u_m = c_u_m / (ny+1)
	876	c_v_m = c_v_m / (ny+1)
	877	c_w_m = c_w_m / (ny+1)
	878
[73]	879	!
[978]	880	!-- Save old timelevels for the next timestep
	881	IF ( intermediate_timestep_count == 1 ) THEN
	882	u_m_r(:,:,:) = u(:,:,nx-1:nx)
	883	v_m_r(:,:,:) = v(:,:,nx-1:nx)
	884	w_m_r(:,:,:) = w(:,:,nx-1:nx)
	885	ENDIF
[73]	886
[978]	887	!
	888	!-- Calculate the new velocities
[996]	889	DO k = nzb+1, nzt+1
[1113]	890	DO j = nysg, nyng
[978]	891	u_p(k,j,nx+1) = u(k,j,nx+1) - dt_3d * tsc(2) * c_u_m(k) * &
	892	( u(k,j,nx+1) - u(k,j,nx) ) * ddx
[73]	893
[978]	894	v_p(k,j,nx+1) = v(k,j,nx+1) - dt_3d * tsc(2) * c_v_m(k) * &
	895	( v(k,j,nx+1) - v(k,j,nx) ) * ddx
[73]	896
[978]	897	w_p(k,j,nx+1) = w(k,j,nx+1) - dt_3d * tsc(2) * c_w_m(k) * &
	898	( w(k,j,nx+1) - w(k,j,nx) ) * ddx
	899	ENDDO
[73]	900	ENDDO
	901
	902	!
[978]	903	!-- Bottom boundary at the outflow
	904	IF ( ibc_uv_b == 0 ) THEN
[1353]	905	u_p(nzb,:,nx+1) = 0.0_wp
	906	v_p(nzb,:,nx+1) = 0.0_wp
[978]	907	ELSE
	908	u_p(nzb,:,nx+1) = u_p(nzb+1,:,nx+1)
	909	v_p(nzb,:,nx+1) = v_p(nzb+1,:,nx+1)
	910	ENDIF
[1353]	911	w_p(nzb,:,nx+1) = 0.0_wp
[73]	912
	913	!
[978]	914	!-- Top boundary at the outflow
	915	IF ( ibc_uv_t == 0 ) THEN
	916	u_p(nzt+1,:,nx+1) = u_init(nzt+1)
	917	v_p(nzt+1,:,nx+1) = v_init(nzt+1)
	918	ELSE
	919	u_p(nzt+1,:,nx+1) = u_p(nzt,:,nx+1)
	920	v_p(nzt+1,:,nx+1) = v_p(nzt,:,nx+1)
	921	ENDIF
[1353]	922	w(nzt:nzt+1,:,nx+1) = 0.0_wp
[978]	923
[1]	924	ENDIF
	925
	926	ENDIF
	927
	928	END SUBROUTINE boundary_conds

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