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source: palm/trunk/SOURCE/boundary_conds.f90 @ 2282

Last change on this file since 2282 was 2233, checked in by suehring, 8 years ago
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[1682]	1	!> @file boundary_conds.f90
[2000]	2	!------------------------------------------------------------------------------!
[1036]	3	! This file is part of PALM.
	4	!
[2000]	5	! PALM is free software: you can redistribute it and/or modify it under the
	6	! terms of the GNU General Public License as published by the Free Software
	7	! Foundation, either version 3 of the License, or (at your option) any later
	8	! version.
[1036]	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	!
[2101]	17	! Copyright 1997-2017 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[484]	20	! Current revisions:
[1]	21	! -----------------
[1933]	22	!
[2233]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: boundary_conds.f90 2233 2017-05-30 18:08:54Z schwenkel $
	27	!
[2233]	28	! 2232 2017-05-30 17:47:52Z suehring
	29	! Set boundary conditions on topography top using flag method.
	30	!
[2119]	31	! 2118 2017-01-17 16:38:49Z raasch
	32	! OpenACC directives removed
	33	!
[2001]	34	! 2000 2016-08-20 18:09:15Z knoop
	35	! Forced header and separation lines into 80 columns
	36	!
[1993]	37	! 1992 2016-08-12 15:14:59Z suehring
	38	! Adjustments for top boundary condition for passive scalar
	39	!
[1961]	40	! 1960 2016-07-12 16:34:24Z suehring
	41	! Treat humidity and passive scalar separately
	42	!
[1933]	43	! 1823 2016-04-07 08:57:52Z hoffmann
	44	! Initial version of purely vertical nesting introduced.
	45	!
[1823]	46	! 1822 2016-04-07 07:49:42Z hoffmann
	47	! icloud_scheme removed. microphyisics_seifert added.
	48	!
[1765]	49	! 1764 2016-02-28 12:45:19Z raasch
	50	! index bug for u_p at left outflow removed
	51	!
[1763]	52	! 1762 2016-02-25 12:31:13Z hellstea
	53	! Introduction of nested domain feature
	54	!
[1744]	55	! 1742 2016-01-13 09:50:06Z raasch
	56	! bugfix for outflow Neumann boundary conditions at bottom and top
	57	!
[1718]	58	! 1717 2015-11-11 15:09:47Z raasch
	59	! Bugfix: index error in outflow conditions for left boundary
	60	!
[1683]	61	! 1682 2015-10-07 23:56:08Z knoop
	62	! Code annotations made doxygen readable
	63	!
[1717]	64	! 1410 2014-05-23 12:16:18Z suehring
[1463]	65	! Bugfix: set dirichlet boundary condition for passive_scalar at model domain
	66	! top
	67	!
[1410]	68	! 1399 2014-05-07 11:16:25Z heinze
	69	! Bugfix: set inflow boundary conditions also if no humidity or passive_scalar
	70	! is used.
	71	!
[1399]	72	! 1398 2014-05-07 11:15:00Z heinze
	73	! Dirichlet-condition at the top for u and v changed to u_init and v_init also
	74	! for large_scale_forcing
	75	!
[1381]	76	! 1380 2014-04-28 12:40:45Z heinze
	77	! Adjust Dirichlet-condition at the top for pt in case of nudging
	78	!
[1362]	79	! 1361 2014-04-16 15:17:48Z hoffmann
	80	! Bottom and top boundary conditions of rain water content (qr) and
	81	! rain drop concentration (nr) changed to Dirichlet
	82	!
[1354]	83	! 1353 2014-04-08 15:21:23Z heinze
	84	! REAL constants provided with KIND-attribute
	85	!
[1321]	86	! 1320 2014-03-20 08:40:49Z raasch
[1320]	87	! ONLY-attribute added to USE-statements,
	88	! kind-parameters added to all INTEGER and REAL declaration statements,
	89	! kinds are defined in new module kinds,
	90	! revision history before 2012 removed,
	91	! comment fields (!:) to be used for variable explanations added to
	92	! all variable declaration statements
[1160]	93	!
[1258]	94	! 1257 2013-11-08 15:18:40Z raasch
	95	! loop independent clauses added
	96	!
[1242]	97	! 1241 2013-10-30 11:36:58Z heinze
	98	! Adjust ug and vg at each timestep in case of large_scale_forcing
	99	!
[1160]	100	! 1159 2013-05-21 11:58:22Z fricke
[1159]	101	! Bugfix: Neumann boundary conditions for the velocity components at the
	102	! outflow are in fact radiation boundary conditions using the maximum phase
	103	! velocity that ensures numerical stability (CFL-condition).
	104	! Hence, logical operator use_cmax is now used instead of bc_lr_dirneu/_neudir.
	105	! Bugfix: In case of use_cmax at the outflow, u, v, w are replaced by
	106	! u_p, v_p, w_p
[1116]	107	!
	108	! 1115 2013-03-26 18:16:16Z hoffmann
	109	! boundary conditions of two-moment cloud scheme are restricted to Neumann-
	110	! boundary-conditions
	111	!
[1114]	112	! 1113 2013-03-10 02:48:14Z raasch
	113	! GPU-porting
	114	! dummy argument "range" removed
	115	! Bugfix: wrong index in loops of radiation boundary condition
[1113]	116	!
[1054]	117	! 1053 2012-11-13 17:11:03Z hoffmann
	118	! boundary conditions for the two new prognostic equations (nr, qr) of the
	119	! two-moment cloud scheme
	120	!
[1037]	121	! 1036 2012-10-22 13:43:42Z raasch
	122	! code put under GPL (PALM 3.9)
	123	!
[997]	124	! 996 2012-09-07 10:41:47Z raasch
	125	! little reformatting
	126	!
[979]	127	! 978 2012-08-09 08:28:32Z fricke
	128	! Neumann boudnary conditions are added at the inflow boundary for the SGS-TKE.
	129	! Outflow boundary conditions for the velocity components can be set to Neumann
	130	! conditions or to radiation conditions with a horizontal averaged phase
	131	! velocity.
	132	!
[876]	133	! 875 2012-04-02 15:35:15Z gryschka
	134	! Bugfix in case of dirichlet inflow bc at the right or north boundary
	135	!
[1]	136	! Revision 1.1 1997/09/12 06:21:34 raasch
	137	! Initial revision
	138	!
	139	!
	140	! Description:
	141	! ------------
[1682]	142	!> Boundary conditions for the prognostic quantities.
	143	!> One additional bottom boundary condition is applied for the TKE (=(u)*2)
	144	!> in prandtl_fluxes. The cyclic lateral boundary conditions are implicitly
	145	!> handled in routine exchange_horiz. Pressure boundary conditions are
	146	!> explicitly set in routines pres, poisfft, poismg and sor.
[1]	147	!------------------------------------------------------------------------------!
[1682]	148	SUBROUTINE boundary_conds
	149
[1]	150
[1320]	151	USE arrays_3d, &
	152	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, &
[1960]	153	dzu, e_p, nr_p, pt, pt_p, q, q_p, qr_p, s, s_p, sa, sa_p, &
[1320]	154	u, ug, u_init, u_m_l, u_m_n, u_m_r, u_m_s, u_p, &
	155	v, vg, v_init, v_m_l, v_m_n, v_m_r, v_m_s, v_p, &
[1960]	156	w, w_p, w_m_l, w_m_n, w_m_r, w_m_s, pt_init
[1320]	157
	158	USE control_parameters, &
[1960]	159	ONLY: bc_pt_t_val, bc_q_t_val, bc_s_t_val, constant_diffusion, &
[1320]	160	cloud_physics, dt_3d, humidity, &
[1960]	161	ibc_pt_b, ibc_pt_t, ibc_q_b, ibc_q_t, ibc_s_b, ibc_s_t, &
	162	ibc_sa_t, ibc_uv_b, ibc_uv_t, inflow_l, inflow_n, inflow_r, &
	163	inflow_s, intermediate_timestep_count, large_scale_forcing, &
[1822]	164	microphysics_seifert, nest_domain, nest_bound_l, nest_bound_s, &
	165	nudging, ocean, outflow_l, outflow_n, outflow_r, outflow_s, &
	166	passive_scalar, tsc, use_cmax
[1320]	167
	168	USE grid_variables, &
	169	ONLY: ddx, ddy, dx, dy
	170
	171	USE indices, &
	172	ONLY: nx, nxl, nxlg, nxr, nxrg, ny, nyn, nyng, nys, nysg, &
[2232]	173	nzb, nzt, wall_flags_0
[1320]	174
	175	USE kinds
	176
[1]	177	USE pegrid
	178
[1933]	179	USE pmc_interface, &
	180	ONLY : nesting_mode
[1320]	181
[2232]	182	USE surface_mod, &
	183	ONLY : bc_h
[1933]	184
[1]	185	IMPLICIT NONE
	186
[2232]	187	INTEGER(iwp) :: i !< grid index x direction
	188	INTEGER(iwp) :: j !< grid index y direction
	189	INTEGER(iwp) :: k !< grid index z direction
	190	INTEGER(iwp) :: kb !< variable to set respective boundary value, depends on facing.
	191	INTEGER(iwp) :: l !< running index boundary type, for up- and downward-facing walls
	192	INTEGER(iwp) :: m !< running index surface elements
[1]	193
[1682]	194	REAL(wp) :: c_max !<
	195	REAL(wp) :: denom !<
[1]	196
[73]	197
[1]	198	!
[1113]	199	!-- Bottom boundary
	200	IF ( ibc_uv_b == 1 ) THEN
	201	u_p(nzb,:,:) = u_p(nzb+1,:,:)
	202	v_p(nzb,:,:) = v_p(nzb+1,:,:)
	203	ENDIF
[2232]	204	!
	205	!-- Set zero vertical velocity at topography top (l=0), or bottom (l=1) in case
	206	!-- of downward-facing surfaces.
	207	DO l = 0, 1
	208	!
	209	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	210	!-- for downward-facing surfaces at topography bottom (k+1).
	211	kb = MERGE( -1, 1, l == 0 )
	212	!$OMP PARALLEL DO PRIVATE( i, j, k )
	213	DO m = 1, bc_h(l)%ns
	214	i = bc_h(l)%i(m)
	215	j = bc_h(l)%j(m)
	216	k = bc_h(l)%k(m)
	217	w_p(k+kb,j,i) = 0.0_wp
[1113]	218	ENDDO
	219	ENDDO
	220
	221	!
[1762]	222	!-- Top boundary. A nested domain ( ibc_uv_t = 3 ) does not require settings.
[1113]	223	IF ( ibc_uv_t == 0 ) THEN
	224	u_p(nzt+1,:,:) = u_init(nzt+1)
	225	v_p(nzt+1,:,:) = v_init(nzt+1)
[1762]	226	ELSEIF ( ibc_uv_t == 1 ) THEN
[1113]	227	u_p(nzt+1,:,:) = u_p(nzt,:,:)
	228	v_p(nzt+1,:,:) = v_p(nzt,:,:)
	229	ENDIF
	230
[1762]	231	IF ( .NOT. nest_domain ) THEN
	232	w_p(nzt:nzt+1,:,:) = 0.0_wp ! nzt is not a prognostic level (but cf. pres)
	233	ENDIF
	234
[1113]	235	!
[2232]	236	!-- Temperature at bottom and top boundary.
[1113]	237	!-- In case of coupled runs (ibc_pt_b = 2) the temperature is given by
	238	!-- the sea surface temperature of the coupled ocean model.
[2232]	239	!-- Dirichlet
[1113]	240	IF ( ibc_pt_b == 0 ) THEN
[2232]	241	DO l = 0, 1
	242	!
	243	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	244	!-- for downward-facing surfaces at topography bottom (k+1).
	245	kb = MERGE( -1, 1, l == 0 )
	246	!$OMP PARALLEL DO PRIVATE( i, j, k )
	247	DO m = 1, bc_h(l)%ns
	248	i = bc_h(l)%i(m)
	249	j = bc_h(l)%j(m)
	250	k = bc_h(l)%k(m)
	251	pt_p(k+kb,j,i) = pt(k+kb,j,i)
[1]	252	ENDDO
	253	ENDDO
[2232]	254	!
	255	!-- Neumann, zero-gradient
[1113]	256	ELSEIF ( ibc_pt_b == 1 ) THEN
[2232]	257	DO l = 0, 1
	258	!
	259	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	260	!-- for downward-facing surfaces at topography bottom (k+1).
	261	kb = MERGE( -1, 1, l == 0 )
	262	!$OMP PARALLEL DO PRIVATE( i, j, k )
	263	DO m = 1, bc_h(l)%ns
	264	i = bc_h(l)%i(m)
	265	j = bc_h(l)%j(m)
	266	k = bc_h(l)%k(m)
	267	pt_p(k+kb,j,i) = pt_p(k,j,i)
[1113]	268	ENDDO
	269	ENDDO
	270	ENDIF
[1]	271
	272	!
[1113]	273	!-- Temperature at top boundary
	274	IF ( ibc_pt_t == 0 ) THEN
	275	pt_p(nzt+1,:,:) = pt(nzt+1,:,:)
[1380]	276	!
	277	!-- In case of nudging adjust top boundary to pt which is
	278	!-- read in from NUDGING-DATA
	279	IF ( nudging ) THEN
	280	pt_p(nzt+1,:,:) = pt_init(nzt+1)
	281	ENDIF
[1113]	282	ELSEIF ( ibc_pt_t == 1 ) THEN
	283	pt_p(nzt+1,:,:) = pt_p(nzt,:,:)
	284	ELSEIF ( ibc_pt_t == 2 ) THEN
[1992]	285	pt_p(nzt+1,:,:) = pt_p(nzt,:,:) + bc_pt_t_val * dzu(nzt+1)
[1113]	286	ENDIF
[1]	287
	288	!
[1113]	289	!-- Boundary conditions for TKE
	290	!-- Generally Neumann conditions with de/dz=0 are assumed
	291	IF ( .NOT. constant_diffusion ) THEN
[2232]	292
	293	DO l = 0, 1
	294	!
	295	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	296	!-- for downward-facing surfaces at topography bottom (k+1).
	297	kb = MERGE( -1, 1, l == 0 )
	298	!$OMP PARALLEL DO PRIVATE( i, j, k )
	299	DO m = 1, bc_h(l)%ns
	300	i = bc_h(l)%i(m)
	301	j = bc_h(l)%j(m)
	302	k = bc_h(l)%k(m)
	303	e_p(k+kb,j,i) = e_p(k,j,i)
[73]	304	ENDDO
[1113]	305	ENDDO
[2232]	306
[1762]	307	IF ( .NOT. nest_domain ) THEN
	308	e_p(nzt+1,:,:) = e_p(nzt,:,:)
	309	ENDIF
[1113]	310	ENDIF
	311
	312	!
	313	!-- Boundary conditions for salinity
	314	IF ( ocean ) THEN
	315	!
	316	!-- Bottom boundary: Neumann condition because salinity flux is always
[2232]	317	!-- given.
	318	DO l = 0, 1
	319	!
	320	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	321	!-- for downward-facing surfaces at topography bottom (k+1).
	322	kb = MERGE( -1, 1, l == 0 )
	323	!$OMP PARALLEL DO PRIVATE( i, j, k )
	324	DO m = 1, bc_h(l)%ns
	325	i = bc_h(l)%i(m)
	326	j = bc_h(l)%j(m)
	327	k = bc_h(l)%k(m)
	328	sa_p(k+kb,j,i) = sa_p(k,j,i)
[1]	329	ENDDO
[1113]	330	ENDDO
[1]	331	!
[1113]	332	!-- Top boundary: Dirichlet or Neumann
	333	IF ( ibc_sa_t == 0 ) THEN
	334	sa_p(nzt+1,:,:) = sa(nzt+1,:,:)
	335	ELSEIF ( ibc_sa_t == 1 ) THEN
	336	sa_p(nzt+1,:,:) = sa_p(nzt,:,:)
[1]	337	ENDIF
	338
[1113]	339	ENDIF
	340
[1]	341	!
[1960]	342	!-- Boundary conditions for total water content,
[1113]	343	!-- bottom and top boundary (see also temperature)
[1960]	344	IF ( humidity ) THEN
[1113]	345	!
	346	!-- Surface conditions for constant_humidity_flux
[2232]	347	!-- Run loop over all non-natural and natural walls. Note, in wall-datatype
	348	!-- the k coordinate belongs to the atmospheric grid point, therefore, set
	349	!-- q_p at k-1
[1113]	350	IF ( ibc_q_b == 0 ) THEN
[2232]	351
	352	DO l = 0, 1
	353	!
	354	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	355	!-- for downward-facing surfaces at topography bottom (k+1).
	356	kb = MERGE( -1, 1, l == 0 )
	357	!$OMP PARALLEL DO PRIVATE( i, j, k )
	358	DO m = 1, bc_h(l)%ns
	359	i = bc_h(l)%i(m)
	360	j = bc_h(l)%j(m)
	361	k = bc_h(l)%k(m)
	362	q_p(k+kb,j,i) = q(k+kb,j,i)
[1]	363	ENDDO
	364	ENDDO
[2232]	365
[1113]	366	ELSE
[2232]	367	!$OMP PARALLEL DO PRIVATE( i, j, k )
	368	DO m = 1, bc_h(0)%ns
	369	i = bc_h(0)%i(m)
	370	j = bc_h(0)%j(m)
	371	k = bc_h(0)%k(m)
	372	q_p(k-1,j,i) = q_p(k,j,i)
	373	ENDDO
	374
	375	DO l = 0, 1
	376	!
	377	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	378	!-- for downward-facing surfaces at topography bottom (k+1).
	379	kb = MERGE( -1, 1, l == 0 )
	380	!$OMP PARALLEL DO PRIVATE( i, j, k )
	381	DO m = 1, bc_h(l)%ns
	382	i = bc_h(l)%i(m)
	383	j = bc_h(l)%j(m)
	384	k = bc_h(l)%k(m)
	385	q_p(k+kb,j,i) = q_p(k,j,i)
[95]	386	ENDDO
	387	ENDDO
[1113]	388	ENDIF
[95]	389	!
[1113]	390	!-- Top boundary
[1462]	391	IF ( ibc_q_t == 0 ) THEN
	392	q_p(nzt+1,:,:) = q(nzt+1,:,:)
	393	ELSEIF ( ibc_q_t == 1 ) THEN
[1992]	394	q_p(nzt+1,:,:) = q_p(nzt,:,:) + bc_q_t_val * dzu(nzt+1)
[1462]	395	ENDIF
[95]	396
[1822]	397	IF ( cloud_physics .AND. microphysics_seifert ) THEN
[1113]	398	!
[1361]	399	!-- Surface conditions rain water (Dirichlet)
[2232]	400	!-- Run loop over all non-natural and natural walls. Note, in wall-datatype
	401	!-- the k coordinate belongs to the atmospheric grid point, therefore, set
	402	!-- qr_p and nr_p at k-1
	403	!$OMP PARALLEL DO PRIVATE( i, j, k )
	404	DO m = 1, bc_h(0)%ns
	405	i = bc_h(0)%i(m)
	406	j = bc_h(0)%j(m)
	407	k = bc_h(0)%k(m)
	408	qr_p(k-1,j,i) = 0.0_wp
	409	nr_p(k-1,j,i) = 0.0_wp
[1115]	410	ENDDO
[1]	411	!
[1361]	412	!-- Top boundary condition for rain water (Dirichlet)
	413	qr_p(nzt+1,:,:) = 0.0_wp
	414	nr_p(nzt+1,:,:) = 0.0_wp
[1115]	415
[1]	416	ENDIF
[1409]	417	ENDIF
[1]	418	!
[1960]	419	!-- Boundary conditions for scalar,
	420	!-- bottom and top boundary (see also temperature)
	421	IF ( passive_scalar ) THEN
	422	!
	423	!-- Surface conditions for constant_humidity_flux
[2232]	424	!-- Run loop over all non-natural and natural walls. Note, in wall-datatype
	425	!-- the k coordinate belongs to the atmospheric grid point, therefore, set
	426	!-- s_p at k-1
[1960]	427	IF ( ibc_s_b == 0 ) THEN
[2232]	428
	429	DO l = 0, 1
	430	!
	431	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	432	!-- for downward-facing surfaces at topography bottom (k+1).
	433	kb = MERGE( -1, 1, l == 0 )
	434	!$OMP PARALLEL DO PRIVATE( i, j, k )
	435	DO m = 1, bc_h(l)%ns
	436	i = bc_h(l)%i(m)
	437	j = bc_h(l)%j(m)
	438	k = bc_h(l)%k(m)
	439	s_p(k+kb,j,i) = s(k+kb,j,i)
[1960]	440	ENDDO
	441	ENDDO
[2232]	442
[1960]	443	ELSE
[2232]	444	!$OMP PARALLEL DO PRIVATE( i, j, k )
	445	DO m = 1, bc_h(0)%ns
	446	i = bc_h(0)%i(m)
	447	j = bc_h(0)%j(m)
	448	k = bc_h(0)%k(m)
	449	s_p(k-1,j,i) = s_p(k,j,i)
	450	ENDDO
	451
	452	DO l = 0, 1
	453	!
	454	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	455	!-- for downward-facing surfaces at topography bottom (k+1).
	456	kb = MERGE( -1, 1, l == 0 )
	457	!$OMP PARALLEL DO PRIVATE( i, j, k )
	458	DO m = 1, bc_h(l)%ns
	459	i = bc_h(l)%i(m)
	460	j = bc_h(l)%j(m)
	461	k = bc_h(l)%k(m)
	462	s_p(k+kb,j,i) = s_p(k,j,i)
[1960]	463	ENDDO
	464	ENDDO
	465	ENDIF
	466	!
[1992]	467	!-- Top boundary condition
	468	IF ( ibc_s_t == 0 ) THEN
[1960]	469	s_p(nzt+1,:,:) = s(nzt+1,:,:)
[1992]	470	ELSEIF ( ibc_s_t == 1 ) THEN
	471	s_p(nzt+1,:,:) = s_p(nzt,:,:)
	472	ELSEIF ( ibc_s_t == 2 ) THEN
	473	s_p(nzt+1,:,:) = s_p(nzt,:,:) + bc_s_t_val * dzu(nzt+1)
[1960]	474	ENDIF
	475
	476	ENDIF
	477	!
[1762]	478	!-- In case of inflow or nest boundary at the south boundary the boundary for v
	479	!-- is at nys and in case of inflow or nest boundary at the left boundary the
	480	!-- boundary for u is at nxl. Since in prognostic_equations (cache optimized
	481	!-- version) these levels are handled as a prognostic level, boundary values
	482	!-- have to be restored here.
[1409]	483	!-- For the SGS-TKE, Neumann boundary conditions are used at the inflow.
	484	IF ( inflow_s ) THEN
	485	v_p(:,nys,:) = v_p(:,nys-1,:)
	486	IF ( .NOT. constant_diffusion ) e_p(:,nys-1,:) = e_p(:,nys,:)
	487	ELSEIF ( inflow_n ) THEN
	488	IF ( .NOT. constant_diffusion ) e_p(:,nyn+1,:) = e_p(:,nyn,:)
	489	ELSEIF ( inflow_l ) THEN
	490	u_p(:,:,nxl) = u_p(:,:,nxl-1)
	491	IF ( .NOT. constant_diffusion ) e_p(:,:,nxl-1) = e_p(:,:,nxl)
	492	ELSEIF ( inflow_r ) THEN
	493	IF ( .NOT. constant_diffusion ) e_p(:,:,nxr+1) = e_p(:,:,nxr)
	494	ENDIF
[1]	495
	496	!
[1762]	497	!-- The same restoration for u at i=nxl and v at j=nys as above must be made
[1933]	498	!-- in case of nest boundaries. This must not be done in case of vertical nesting
	499	!-- mode as in that case the lateral boundaries are actually cyclic.
	500	IF ( nesting_mode /= 'vertical' ) THEN
	501	IF ( nest_bound_s ) THEN
	502	v_p(:,nys,:) = v_p(:,nys-1,:)
	503	ENDIF
	504	IF ( nest_bound_l ) THEN
	505	u_p(:,:,nxl) = u_p(:,:,nxl-1)
	506	ENDIF
[1762]	507	ENDIF
	508
	509	!
[1409]	510	!-- Lateral boundary conditions for scalar quantities at the outflow
	511	IF ( outflow_s ) THEN
	512	pt_p(:,nys-1,:) = pt_p(:,nys,:)
[2232]	513	IF ( .NOT. constant_diffusion ) e_p(:,nys-1,:) = e_p(:,nys,:)
[1960]	514	IF ( humidity ) THEN
[1409]	515	q_p(:,nys-1,:) = q_p(:,nys,:)
[1822]	516	IF ( cloud_physics .AND. microphysics_seifert ) THEN
[1409]	517	qr_p(:,nys-1,:) = qr_p(:,nys,:)
	518	nr_p(:,nys-1,:) = nr_p(:,nys,:)
[1053]	519	ENDIF
[1409]	520	ENDIF
[1960]	521	IF ( passive_scalar ) s_p(:,nys-1,:) = s_p(:,nys,:)
[1409]	522	ELSEIF ( outflow_n ) THEN
	523	pt_p(:,nyn+1,:) = pt_p(:,nyn,:)
	524	IF ( .NOT. constant_diffusion ) e_p(:,nyn+1,:) = e_p(:,nyn,:)
[1960]	525	IF ( humidity ) THEN
[1409]	526	q_p(:,nyn+1,:) = q_p(:,nyn,:)
[1822]	527	IF ( cloud_physics .AND. microphysics_seifert ) THEN
[1409]	528	qr_p(:,nyn+1,:) = qr_p(:,nyn,:)
	529	nr_p(:,nyn+1,:) = nr_p(:,nyn,:)
[1053]	530	ENDIF
[1409]	531	ENDIF
[1960]	532	IF ( passive_scalar ) s_p(:,nyn+1,:) = s_p(:,nyn,:)
[1409]	533	ELSEIF ( outflow_l ) THEN
	534	pt_p(:,:,nxl-1) = pt_p(:,:,nxl)
	535	IF ( .NOT. constant_diffusion ) e_p(:,:,nxl-1) = e_p(:,:,nxl)
[1960]	536	IF ( humidity ) THEN
[1409]	537	q_p(:,:,nxl-1) = q_p(:,:,nxl)
[1822]	538	IF ( cloud_physics .AND. microphysics_seifert ) THEN
[1409]	539	qr_p(:,:,nxl-1) = qr_p(:,:,nxl)
	540	nr_p(:,:,nxl-1) = nr_p(:,:,nxl)
[1053]	541	ENDIF
[1409]	542	ENDIF
[1960]	543	IF ( passive_scalar ) s_p(:,:,nxl-1) = s_p(:,:,nxl)
[1409]	544	ELSEIF ( outflow_r ) THEN
	545	pt_p(:,:,nxr+1) = pt_p(:,:,nxr)
	546	IF ( .NOT. constant_diffusion ) e_p(:,:,nxr+1) = e_p(:,:,nxr)
[1960]	547	IF ( humidity ) THEN
[1409]	548	q_p(:,:,nxr+1) = q_p(:,:,nxr)
[1822]	549	IF ( cloud_physics .AND. microphysics_seifert ) THEN
[1409]	550	qr_p(:,:,nxr+1) = qr_p(:,:,nxr)
	551	nr_p(:,:,nxr+1) = nr_p(:,:,nxr)
[1053]	552	ENDIF
[1]	553	ENDIF
[1960]	554	IF ( passive_scalar ) s_p(:,:,nxr+1) = s_p(:,:,nxr)
[1]	555	ENDIF
	556
	557	!
[1159]	558	!-- Radiation boundary conditions for the velocities at the respective outflow.
	559	!-- The phase velocity is either assumed to the maximum phase velocity that
	560	!-- ensures numerical stability (CFL-condition) or calculated after
	561	!-- Orlanski(1976) and averaged along the outflow boundary.
[106]	562	IF ( outflow_s ) THEN
[75]	563
[1159]	564	IF ( use_cmax ) THEN
	565	u_p(:,-1,:) = u(:,0,:)
	566	v_p(:,0,:) = v(:,1,:)
	567	w_p(:,-1,:) = w(:,0,:)
	568	ELSEIF ( .NOT. use_cmax ) THEN
[75]	569
[978]	570	c_max = dy / dt_3d
[75]	571
[1353]	572	c_u_m_l = 0.0_wp
	573	c_v_m_l = 0.0_wp
	574	c_w_m_l = 0.0_wp
[978]	575
[1353]	576	c_u_m = 0.0_wp
	577	c_v_m = 0.0_wp
	578	c_w_m = 0.0_wp
[978]	579
[75]	580	!
[996]	581	!-- Calculate the phase speeds for u, v, and w, first local and then
	582	!-- average along the outflow boundary.
	583	DO k = nzb+1, nzt+1
	584	DO i = nxl, nxr
[75]	585
[106]	586	denom = u_m_s(k,0,i) - u_m_s(k,1,i)
	587
[1353]	588	IF ( denom /= 0.0_wp ) THEN
[996]	589	c_u(k,i) = -c_max * ( u(k,0,i) - u_m_s(k,0,i) ) / ( denom * tsc(2) )
[1353]	590	IF ( c_u(k,i) < 0.0_wp ) THEN
	591	c_u(k,i) = 0.0_wp
[106]	592	ELSEIF ( c_u(k,i) > c_max ) THEN
	593	c_u(k,i) = c_max
	594	ENDIF
	595	ELSE
	596	c_u(k,i) = c_max
[75]	597	ENDIF
	598
[106]	599	denom = v_m_s(k,1,i) - v_m_s(k,2,i)
	600
[1353]	601	IF ( denom /= 0.0_wp ) THEN
[996]	602	c_v(k,i) = -c_max * ( v(k,1,i) - v_m_s(k,1,i) ) / ( denom * tsc(2) )
[1353]	603	IF ( c_v(k,i) < 0.0_wp ) THEN
	604	c_v(k,i) = 0.0_wp
[106]	605	ELSEIF ( c_v(k,i) > c_max ) THEN
	606	c_v(k,i) = c_max
	607	ENDIF
	608	ELSE
	609	c_v(k,i) = c_max
[75]	610	ENDIF
	611
[106]	612	denom = w_m_s(k,0,i) - w_m_s(k,1,i)
[75]	613
[1353]	614	IF ( denom /= 0.0_wp ) THEN
[996]	615	c_w(k,i) = -c_max * ( w(k,0,i) - w_m_s(k,0,i) ) / ( denom * tsc(2) )
[1353]	616	IF ( c_w(k,i) < 0.0_wp ) THEN
	617	c_w(k,i) = 0.0_wp
[106]	618	ELSEIF ( c_w(k,i) > c_max ) THEN
	619	c_w(k,i) = c_max
	620	ENDIF
	621	ELSE
	622	c_w(k,i) = c_max
[75]	623	ENDIF
[106]	624
[978]	625	c_u_m_l(k) = c_u_m_l(k) + c_u(k,i)
	626	c_v_m_l(k) = c_v_m_l(k) + c_v(k,i)
	627	c_w_m_l(k) = c_w_m_l(k) + c_w(k,i)
[106]	628
[978]	629	ENDDO
	630	ENDDO
[75]	631
[978]	632	#if defined( __parallel )
	633	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
	634	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
	635	MPI_SUM, comm1dx, ierr )
	636	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
	637	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
	638	MPI_SUM, comm1dx, ierr )
	639	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
	640	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
	641	MPI_SUM, comm1dx, ierr )
	642	#else
	643	c_u_m = c_u_m_l
	644	c_v_m = c_v_m_l
	645	c_w_m = c_w_m_l
	646	#endif
	647
	648	c_u_m = c_u_m / (nx+1)
	649	c_v_m = c_v_m / (nx+1)
	650	c_w_m = c_w_m / (nx+1)
	651
[75]	652	!
[978]	653	!-- Save old timelevels for the next timestep
	654	IF ( intermediate_timestep_count == 1 ) THEN
	655	u_m_s(:,:,:) = u(:,0:1,:)
	656	v_m_s(:,:,:) = v(:,1:2,:)
	657	w_m_s(:,:,:) = w(:,0:1,:)
	658	ENDIF
	659
	660	!
	661	!-- Calculate the new velocities
[996]	662	DO k = nzb+1, nzt+1
	663	DO i = nxlg, nxrg
[978]	664	u_p(k,-1,i) = u(k,-1,i) - dt_3d * tsc(2) * c_u_m(k) * &
[75]	665	( u(k,-1,i) - u(k,0,i) ) * ddy
	666
[978]	667	v_p(k,0,i) = v(k,0,i) - dt_3d * tsc(2) * c_v_m(k) * &
[106]	668	( v(k,0,i) - v(k,1,i) ) * ddy
[75]	669
[978]	670	w_p(k,-1,i) = w(k,-1,i) - dt_3d * tsc(2) * c_w_m(k) * &
[75]	671	( w(k,-1,i) - w(k,0,i) ) * ddy
[978]	672	ENDDO
[75]	673	ENDDO
	674
	675	!
[978]	676	!-- Bottom boundary at the outflow
	677	IF ( ibc_uv_b == 0 ) THEN
[1353]	678	u_p(nzb,-1,:) = 0.0_wp
	679	v_p(nzb,0,:) = 0.0_wp
[978]	680	ELSE
	681	u_p(nzb,-1,:) = u_p(nzb+1,-1,:)
	682	v_p(nzb,0,:) = v_p(nzb+1,0,:)
	683	ENDIF
[1353]	684	w_p(nzb,-1,:) = 0.0_wp
[73]	685
[75]	686	!
[978]	687	!-- Top boundary at the outflow
	688	IF ( ibc_uv_t == 0 ) THEN
	689	u_p(nzt+1,-1,:) = u_init(nzt+1)
	690	v_p(nzt+1,0,:) = v_init(nzt+1)
	691	ELSE
[1742]	692	u_p(nzt+1,-1,:) = u_p(nzt,-1,:)
	693	v_p(nzt+1,0,:) = v_p(nzt,0,:)
[978]	694	ENDIF
[1353]	695	w_p(nzt:nzt+1,-1,:) = 0.0_wp
[978]	696
[75]	697	ENDIF
[73]	698
[75]	699	ENDIF
[73]	700
[106]	701	IF ( outflow_n ) THEN
[73]	702
[1159]	703	IF ( use_cmax ) THEN
	704	u_p(:,ny+1,:) = u(:,ny,:)
	705	v_p(:,ny+1,:) = v(:,ny,:)
	706	w_p(:,ny+1,:) = w(:,ny,:)
	707	ELSEIF ( .NOT. use_cmax ) THEN
[75]	708
[978]	709	c_max = dy / dt_3d
[75]	710
[1353]	711	c_u_m_l = 0.0_wp
	712	c_v_m_l = 0.0_wp
	713	c_w_m_l = 0.0_wp
[978]	714
[1353]	715	c_u_m = 0.0_wp
	716	c_v_m = 0.0_wp
	717	c_w_m = 0.0_wp
[978]	718
[1]	719	!
[996]	720	!-- Calculate the phase speeds for u, v, and w, first local and then
	721	!-- average along the outflow boundary.
	722	DO k = nzb+1, nzt+1
	723	DO i = nxl, nxr
[73]	724
[106]	725	denom = u_m_n(k,ny,i) - u_m_n(k,ny-1,i)
	726
[1353]	727	IF ( denom /= 0.0_wp ) THEN
[996]	728	c_u(k,i) = -c_max * ( u(k,ny,i) - u_m_n(k,ny,i) ) / ( denom * tsc(2) )
[1353]	729	IF ( c_u(k,i) < 0.0_wp ) THEN
	730	c_u(k,i) = 0.0_wp
[106]	731	ELSEIF ( c_u(k,i) > c_max ) THEN
	732	c_u(k,i) = c_max
	733	ENDIF
	734	ELSE
	735	c_u(k,i) = c_max
[73]	736	ENDIF
	737
[106]	738	denom = v_m_n(k,ny,i) - v_m_n(k,ny-1,i)
[73]	739
[1353]	740	IF ( denom /= 0.0_wp ) THEN
[996]	741	c_v(k,i) = -c_max * ( v(k,ny,i) - v_m_n(k,ny,i) ) / ( denom * tsc(2) )
[1353]	742	IF ( c_v(k,i) < 0.0_wp ) THEN
	743	c_v(k,i) = 0.0_wp
[106]	744	ELSEIF ( c_v(k,i) > c_max ) THEN
	745	c_v(k,i) = c_max
	746	ENDIF
	747	ELSE
	748	c_v(k,i) = c_max
[73]	749	ENDIF
	750
[106]	751	denom = w_m_n(k,ny,i) - w_m_n(k,ny-1,i)
[73]	752
[1353]	753	IF ( denom /= 0.0_wp ) THEN
[996]	754	c_w(k,i) = -c_max * ( w(k,ny,i) - w_m_n(k,ny,i) ) / ( denom * tsc(2) )
[1353]	755	IF ( c_w(k,i) < 0.0_wp ) THEN
	756	c_w(k,i) = 0.0_wp
[106]	757	ELSEIF ( c_w(k,i) > c_max ) THEN
	758	c_w(k,i) = c_max
	759	ENDIF
	760	ELSE
	761	c_w(k,i) = c_max
[73]	762	ENDIF
[106]	763
[978]	764	c_u_m_l(k) = c_u_m_l(k) + c_u(k,i)
	765	c_v_m_l(k) = c_v_m_l(k) + c_v(k,i)
	766	c_w_m_l(k) = c_w_m_l(k) + c_w(k,i)
[106]	767
[978]	768	ENDDO
	769	ENDDO
[73]	770
[978]	771	#if defined( __parallel )
	772	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
	773	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
	774	MPI_SUM, comm1dx, ierr )
	775	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
	776	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
	777	MPI_SUM, comm1dx, ierr )
	778	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
	779	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
	780	MPI_SUM, comm1dx, ierr )
	781	#else
	782	c_u_m = c_u_m_l
	783	c_v_m = c_v_m_l
	784	c_w_m = c_w_m_l
	785	#endif
	786
	787	c_u_m = c_u_m / (nx+1)
	788	c_v_m = c_v_m / (nx+1)
	789	c_w_m = c_w_m / (nx+1)
	790
[73]	791	!
[978]	792	!-- Save old timelevels for the next timestep
	793	IF ( intermediate_timestep_count == 1 ) THEN
	794	u_m_n(:,:,:) = u(:,ny-1:ny,:)
	795	v_m_n(:,:,:) = v(:,ny-1:ny,:)
	796	w_m_n(:,:,:) = w(:,ny-1:ny,:)
	797	ENDIF
[73]	798
[978]	799	!
	800	!-- Calculate the new velocities
[996]	801	DO k = nzb+1, nzt+1
	802	DO i = nxlg, nxrg
[978]	803	u_p(k,ny+1,i) = u(k,ny+1,i) - dt_3d * tsc(2) * c_u_m(k) * &
	804	( u(k,ny+1,i) - u(k,ny,i) ) * ddy
[73]	805
[978]	806	v_p(k,ny+1,i) = v(k,ny+1,i) - dt_3d * tsc(2) * c_v_m(k) * &
	807	( v(k,ny+1,i) - v(k,ny,i) ) * ddy
[73]	808
[978]	809	w_p(k,ny+1,i) = w(k,ny+1,i) - dt_3d * tsc(2) * c_w_m(k) * &
	810	( w(k,ny+1,i) - w(k,ny,i) ) * ddy
	811	ENDDO
[1]	812	ENDDO
	813
	814	!
[978]	815	!-- Bottom boundary at the outflow
	816	IF ( ibc_uv_b == 0 ) THEN
[1353]	817	u_p(nzb,ny+1,:) = 0.0_wp
	818	v_p(nzb,ny+1,:) = 0.0_wp
[978]	819	ELSE
	820	u_p(nzb,ny+1,:) = u_p(nzb+1,ny+1,:)
	821	v_p(nzb,ny+1,:) = v_p(nzb+1,ny+1,:)
	822	ENDIF
[1353]	823	w_p(nzb,ny+1,:) = 0.0_wp
[73]	824
	825	!
[978]	826	!-- Top boundary at the outflow
	827	IF ( ibc_uv_t == 0 ) THEN
	828	u_p(nzt+1,ny+1,:) = u_init(nzt+1)
	829	v_p(nzt+1,ny+1,:) = v_init(nzt+1)
	830	ELSE
	831	u_p(nzt+1,ny+1,:) = u_p(nzt,nyn+1,:)
	832	v_p(nzt+1,ny+1,:) = v_p(nzt,nyn+1,:)
	833	ENDIF
[1353]	834	w_p(nzt:nzt+1,ny+1,:) = 0.0_wp
[978]	835
[1]	836	ENDIF
	837
[75]	838	ENDIF
	839
[106]	840	IF ( outflow_l ) THEN
[75]	841
[1159]	842	IF ( use_cmax ) THEN
[1717]	843	u_p(:,:,0) = u(:,:,1)
	844	v_p(:,:,-1) = v(:,:,0)
[1159]	845	w_p(:,:,-1) = w(:,:,0)
	846	ELSEIF ( .NOT. use_cmax ) THEN
[75]	847
[978]	848	c_max = dx / dt_3d
[75]	849
[1353]	850	c_u_m_l = 0.0_wp
	851	c_v_m_l = 0.0_wp
	852	c_w_m_l = 0.0_wp
[978]	853
[1353]	854	c_u_m = 0.0_wp
	855	c_v_m = 0.0_wp
	856	c_w_m = 0.0_wp
[978]	857
[1]	858	!
[996]	859	!-- Calculate the phase speeds for u, v, and w, first local and then
	860	!-- average along the outflow boundary.
	861	DO k = nzb+1, nzt+1
	862	DO j = nys, nyn
[75]	863
[106]	864	denom = u_m_l(k,j,1) - u_m_l(k,j,2)
	865
[1353]	866	IF ( denom /= 0.0_wp ) THEN
[996]	867	c_u(k,j) = -c_max * ( u(k,j,1) - u_m_l(k,j,1) ) / ( denom * tsc(2) )
[1353]	868	IF ( c_u(k,j) < 0.0_wp ) THEN
	869	c_u(k,j) = 0.0_wp
[107]	870	ELSEIF ( c_u(k,j) > c_max ) THEN
	871	c_u(k,j) = c_max
[106]	872	ENDIF
	873	ELSE
[107]	874	c_u(k,j) = c_max
[75]	875	ENDIF
	876
[106]	877	denom = v_m_l(k,j,0) - v_m_l(k,j,1)
[75]	878
[1353]	879	IF ( denom /= 0.0_wp ) THEN
[996]	880	c_v(k,j) = -c_max * ( v(k,j,0) - v_m_l(k,j,0) ) / ( denom * tsc(2) )
[1353]	881	IF ( c_v(k,j) < 0.0_wp ) THEN
	882	c_v(k,j) = 0.0_wp
[106]	883	ELSEIF ( c_v(k,j) > c_max ) THEN
	884	c_v(k,j) = c_max
	885	ENDIF
	886	ELSE
	887	c_v(k,j) = c_max
[75]	888	ENDIF
	889
[106]	890	denom = w_m_l(k,j,0) - w_m_l(k,j,1)
[75]	891
[1353]	892	IF ( denom /= 0.0_wp ) THEN
[996]	893	c_w(k,j) = -c_max * ( w(k,j,0) - w_m_l(k,j,0) ) / ( denom * tsc(2) )
[1353]	894	IF ( c_w(k,j) < 0.0_wp ) THEN
	895	c_w(k,j) = 0.0_wp
[106]	896	ELSEIF ( c_w(k,j) > c_max ) THEN
	897	c_w(k,j) = c_max
	898	ENDIF
	899	ELSE
	900	c_w(k,j) = c_max
[75]	901	ENDIF
[106]	902
[978]	903	c_u_m_l(k) = c_u_m_l(k) + c_u(k,j)
	904	c_v_m_l(k) = c_v_m_l(k) + c_v(k,j)
	905	c_w_m_l(k) = c_w_m_l(k) + c_w(k,j)
[106]	906
[978]	907	ENDDO
	908	ENDDO
[75]	909
[978]	910	#if defined( __parallel )
	911	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
	912	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
	913	MPI_SUM, comm1dy, ierr )
	914	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
	915	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
	916	MPI_SUM, comm1dy, ierr )
	917	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
	918	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
	919	MPI_SUM, comm1dy, ierr )
	920	#else
	921	c_u_m = c_u_m_l
	922	c_v_m = c_v_m_l
	923	c_w_m = c_w_m_l
	924	#endif
	925
	926	c_u_m = c_u_m / (ny+1)
	927	c_v_m = c_v_m / (ny+1)
	928	c_w_m = c_w_m / (ny+1)
	929
[73]	930	!
[978]	931	!-- Save old timelevels for the next timestep
	932	IF ( intermediate_timestep_count == 1 ) THEN
	933	u_m_l(:,:,:) = u(:,:,1:2)
	934	v_m_l(:,:,:) = v(:,:,0:1)
	935	w_m_l(:,:,:) = w(:,:,0:1)
	936	ENDIF
	937
	938	!
	939	!-- Calculate the new velocities
[996]	940	DO k = nzb+1, nzt+1
[1113]	941	DO j = nysg, nyng
[978]	942	u_p(k,j,0) = u(k,j,0) - dt_3d * tsc(2) * c_u_m(k) * &
[106]	943	( u(k,j,0) - u(k,j,1) ) * ddx
[75]	944
[978]	945	v_p(k,j,-1) = v(k,j,-1) - dt_3d * tsc(2) * c_v_m(k) * &
[75]	946	( v(k,j,-1) - v(k,j,0) ) * ddx
	947
[978]	948	w_p(k,j,-1) = w(k,j,-1) - dt_3d * tsc(2) * c_w_m(k) * &
[75]	949	( w(k,j,-1) - w(k,j,0) ) * ddx
[978]	950	ENDDO
[75]	951	ENDDO
	952
	953	!
[978]	954	!-- Bottom boundary at the outflow
	955	IF ( ibc_uv_b == 0 ) THEN
[1353]	956	u_p(nzb,:,0) = 0.0_wp
	957	v_p(nzb,:,-1) = 0.0_wp
[978]	958	ELSE
	959	u_p(nzb,:,0) = u_p(nzb+1,:,0)
	960	v_p(nzb,:,-1) = v_p(nzb+1,:,-1)
	961	ENDIF
[1353]	962	w_p(nzb,:,-1) = 0.0_wp
[1]	963
[75]	964	!
[978]	965	!-- Top boundary at the outflow
	966	IF ( ibc_uv_t == 0 ) THEN
[1764]	967	u_p(nzt+1,:,0) = u_init(nzt+1)
[978]	968	v_p(nzt+1,:,-1) = v_init(nzt+1)
	969	ELSE
[1764]	970	u_p(nzt+1,:,0) = u_p(nzt,:,0)
[978]	971	v_p(nzt+1,:,-1) = v_p(nzt,:,-1)
	972	ENDIF
[1353]	973	w_p(nzt:nzt+1,:,-1) = 0.0_wp
[978]	974
[75]	975	ENDIF
[73]	976
[75]	977	ENDIF
[73]	978
[106]	979	IF ( outflow_r ) THEN
[73]	980
[1159]	981	IF ( use_cmax ) THEN
	982	u_p(:,:,nx+1) = u(:,:,nx)
	983	v_p(:,:,nx+1) = v(:,:,nx)
	984	w_p(:,:,nx+1) = w(:,:,nx)
	985	ELSEIF ( .NOT. use_cmax ) THEN
[75]	986
[978]	987	c_max = dx / dt_3d
[75]	988
[1353]	989	c_u_m_l = 0.0_wp
	990	c_v_m_l = 0.0_wp
	991	c_w_m_l = 0.0_wp
[978]	992
[1353]	993	c_u_m = 0.0_wp
	994	c_v_m = 0.0_wp
	995	c_w_m = 0.0_wp
[978]	996
[1]	997	!
[996]	998	!-- Calculate the phase speeds for u, v, and w, first local and then
	999	!-- average along the outflow boundary.
	1000	DO k = nzb+1, nzt+1
	1001	DO j = nys, nyn
[73]	1002
[106]	1003	denom = u_m_r(k,j,nx) - u_m_r(k,j,nx-1)
	1004
[1353]	1005	IF ( denom /= 0.0_wp ) THEN
[996]	1006	c_u(k,j) = -c_max * ( u(k,j,nx) - u_m_r(k,j,nx) ) / ( denom * tsc(2) )
[1353]	1007	IF ( c_u(k,j) < 0.0_wp ) THEN
	1008	c_u(k,j) = 0.0_wp
[106]	1009	ELSEIF ( c_u(k,j) > c_max ) THEN
	1010	c_u(k,j) = c_max
	1011	ENDIF
	1012	ELSE
	1013	c_u(k,j) = c_max
[73]	1014	ENDIF
	1015
[106]	1016	denom = v_m_r(k,j,nx) - v_m_r(k,j,nx-1)
[73]	1017
[1353]	1018	IF ( denom /= 0.0_wp ) THEN
[996]	1019	c_v(k,j) = -c_max * ( v(k,j,nx) - v_m_r(k,j,nx) ) / ( denom * tsc(2) )
[1353]	1020	IF ( c_v(k,j) < 0.0_wp ) THEN
	1021	c_v(k,j) = 0.0_wp
[106]	1022	ELSEIF ( c_v(k,j) > c_max ) THEN
	1023	c_v(k,j) = c_max
	1024	ENDIF
	1025	ELSE
	1026	c_v(k,j) = c_max
[73]	1027	ENDIF
	1028
[106]	1029	denom = w_m_r(k,j,nx) - w_m_r(k,j,nx-1)
[73]	1030
[1353]	1031	IF ( denom /= 0.0_wp ) THEN
[996]	1032	c_w(k,j) = -c_max * ( w(k,j,nx) - w_m_r(k,j,nx) ) / ( denom * tsc(2) )
[1353]	1033	IF ( c_w(k,j) < 0.0_wp ) THEN
	1034	c_w(k,j) = 0.0_wp
[106]	1035	ELSEIF ( c_w(k,j) > c_max ) THEN
	1036	c_w(k,j) = c_max
	1037	ENDIF
	1038	ELSE
	1039	c_w(k,j) = c_max
[73]	1040	ENDIF
[106]	1041
[978]	1042	c_u_m_l(k) = c_u_m_l(k) + c_u(k,j)
	1043	c_v_m_l(k) = c_v_m_l(k) + c_v(k,j)
	1044	c_w_m_l(k) = c_w_m_l(k) + c_w(k,j)
[106]	1045
[978]	1046	ENDDO
	1047	ENDDO
[73]	1048
[978]	1049	#if defined( __parallel )
	1050	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
	1051	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
	1052	MPI_SUM, comm1dy, ierr )
	1053	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
	1054	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
	1055	MPI_SUM, comm1dy, ierr )
	1056	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
	1057	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
	1058	MPI_SUM, comm1dy, ierr )
	1059	#else
	1060	c_u_m = c_u_m_l
	1061	c_v_m = c_v_m_l
	1062	c_w_m = c_w_m_l
	1063	#endif
	1064
	1065	c_u_m = c_u_m / (ny+1)
	1066	c_v_m = c_v_m / (ny+1)
	1067	c_w_m = c_w_m / (ny+1)
	1068
[73]	1069	!
[978]	1070	!-- Save old timelevels for the next timestep
	1071	IF ( intermediate_timestep_count == 1 ) THEN
	1072	u_m_r(:,:,:) = u(:,:,nx-1:nx)
	1073	v_m_r(:,:,:) = v(:,:,nx-1:nx)
	1074	w_m_r(:,:,:) = w(:,:,nx-1:nx)
	1075	ENDIF
[73]	1076
[978]	1077	!
	1078	!-- Calculate the new velocities
[996]	1079	DO k = nzb+1, nzt+1
[1113]	1080	DO j = nysg, nyng
[978]	1081	u_p(k,j,nx+1) = u(k,j,nx+1) - dt_3d * tsc(2) * c_u_m(k) * &
	1082	( u(k,j,nx+1) - u(k,j,nx) ) * ddx
[73]	1083
[978]	1084	v_p(k,j,nx+1) = v(k,j,nx+1) - dt_3d * tsc(2) * c_v_m(k) * &
	1085	( v(k,j,nx+1) - v(k,j,nx) ) * ddx
[73]	1086
[978]	1087	w_p(k,j,nx+1) = w(k,j,nx+1) - dt_3d * tsc(2) * c_w_m(k) * &
	1088	( w(k,j,nx+1) - w(k,j,nx) ) * ddx
	1089	ENDDO
[73]	1090	ENDDO
	1091
	1092	!
[978]	1093	!-- Bottom boundary at the outflow
	1094	IF ( ibc_uv_b == 0 ) THEN
[1353]	1095	u_p(nzb,:,nx+1) = 0.0_wp
	1096	v_p(nzb,:,nx+1) = 0.0_wp
[978]	1097	ELSE
	1098	u_p(nzb,:,nx+1) = u_p(nzb+1,:,nx+1)
	1099	v_p(nzb,:,nx+1) = v_p(nzb+1,:,nx+1)
	1100	ENDIF
[1353]	1101	w_p(nzb,:,nx+1) = 0.0_wp
[73]	1102
	1103	!
[978]	1104	!-- Top boundary at the outflow
	1105	IF ( ibc_uv_t == 0 ) THEN
	1106	u_p(nzt+1,:,nx+1) = u_init(nzt+1)
	1107	v_p(nzt+1,:,nx+1) = v_init(nzt+1)
	1108	ELSE
	1109	u_p(nzt+1,:,nx+1) = u_p(nzt,:,nx+1)
	1110	v_p(nzt+1,:,nx+1) = v_p(nzt,:,nx+1)
	1111	ENDIF
[1742]	1112	w_p(nzt:nzt+1,:,nx+1) = 0.0_wp
[978]	1113
[1]	1114	ENDIF
	1115
	1116	ENDIF
	1117
	1118	END SUBROUTINE boundary_conds

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