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source: palm/trunk/SOURCE/pres.f90 @ 1762

Last change on this file since 1762 was 1762, checked in by hellstea, 8 years ago
Introduction of nested domain system
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[1682]	1	!> @file pres.f90
[1036]	2	!--------------------------------------------------------------------------------!
	3	! This file is part of PALM.
	4	!
	5	! PALM is free software: you can redistribute it and/or modify it under the terms
	6	! of the GNU General Public License as published by the Free Software Foundation,
	7	! either version 3 of the License, or (at your option) any later version.
	8	!
	9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	10	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	11	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	12	!
	13	! You should have received a copy of the GNU General Public License along with
	14	! PALM. If not, see <http://www.gnu.org/licenses/>.
	15	!
[1310]	16	! Copyright 1997-2014 Leibniz Universitaet Hannover
[1036]	17	!--------------------------------------------------------------------------------!
	18	!
[484]	19	! Current revisions:
[1212]	20	! ------------------
[1762]	21	! Introduction of nested domain feature
[1683]	22	!
[1321]	23	! Former revisions:
	24	! -----------------
	25	! $Id: pres.f90 1762 2016-02-25 12:31:13Z hellstea $
	26	!
[1683]	27	! 1682 2015-10-07 23:56:08Z knoop
	28	! Code annotations made doxygen readable
	29	!
[1576]	30	! 1575 2015-03-27 09:56:27Z raasch
	31	! poismg_fast + respective module added, adjustments for psolver-queries
	32	!
[1343]	33	! 1342 2014-03-26 17:04:47Z kanani
	34	! REAL constants defined as wp-kind
	35	!
[1321]	36	! 1320 2014-03-20 08:40:49Z raasch
[1320]	37	! ONLY-attribute added to USE-statements,
	38	! kind-parameters added to all INTEGER and REAL declaration statements,
	39	! kinds are defined in new module kinds,
	40	! old module precision_kind is removed,
	41	! revision history before 2012 removed,
	42	! comment fields (!:) to be used for variable explanations added to
	43	! all variable declaration statements
[708]	44	!
[1319]	45	! 1318 2014-03-17 13:35:16Z raasch
	46	! module interfaces removed
	47	!
[1307]	48	! 1306 2014-03-13 14:30:59Z raasch
	49	! second argument removed from routine poisfft
	50	!
[1258]	51	! 1257 2013-11-08 15:18:40Z raasch
	52	! openacc loop and loop vector clauses removed, independent clauses added,
	53	! end parallel replaced by end parallel loop
	54	!
[1222]	55	! 1221 2013-09-10 08:59:13Z raasch
	56	! openACC porting of reduction operations, loops for calculating d are
	57	! using the rflags_s_inner multiply flag instead of the nzb_s_inner loop index
	58	!
[1213]	59	! 1212 2013-08-15 08:46:27Z raasch
	60	! call of poisfft_hybrid removed
	61	!
[1118]	62	! 1117 2013-03-27 11:15:36Z suehring
	63	! Bugfix in OpenMP parallelization.
	64	!
[1114]	65	! 1113 2013-03-10 02:48:14Z raasch
	66	! GPU-porting of several loops, some loops rearranged
	67	!
[1112]	68	! 1111 2013-03-08 23:54:10Z
	69	! openACC statements added,
	70	! ibc_p_b = 2 removed
	71	!
[1093]	72	! 1092 2013-02-02 11:24:22Z raasch
	73	! unused variables removed
	74	!
[1037]	75	! 1036 2012-10-22 13:43:42Z raasch
	76	! code put under GPL (PALM 3.9)
	77	!
[1004]	78	! 1003 2012-09-14 14:35:53Z raasch
	79	! adjustment of array tend for cases with unequal subdomain sizes removed
	80	!
[1]	81	! Revision 1.1 1997/07/24 11:24:44 raasch
	82	! Initial revision
	83	!
	84	!
	85	! Description:
	86	! ------------
[1682]	87	!> Compute the divergence of the provisional velocity field. Solve the Poisson
	88	!> equation for the perturbation pressure. Compute the final velocities using
	89	!> this perturbation pressure. Compute the remaining divergence.
[1]	90	!------------------------------------------------------------------------------!
[1682]	91	SUBROUTINE pres
	92
[1]	93
[1320]	94	USE arrays_3d, &
	95	ONLY: d, ddzu, ddzu_pres, ddzw, dzw, p, p_loc, tend, u, v, w
	96
	97	USE control_parameters, &
	98	ONLY: bc_lr_cyc, bc_ns_cyc, conserve_volume_flow, dt_3d, &
	99	gathered_size, ibc_p_b, ibc_p_t, intermediate_timestep_count, &
[1762]	100	mg_switch_to_pe0_level, nest_domain, nest_bound_l, &
	101	nest_bound_n, nest_bound_r, nest_bound_s, on_device, outflow_l, &
	102	outflow_n, outflow_r, outflow_s, psolver, simulated_time, &
	103	subdomain_size, topography, volume_flow, volume_flow_area, &
	104	volume_flow_initial
[1320]	105
	106	USE cpulog, &
	107	ONLY: cpu_log, log_point, log_point_s
	108
	109	USE grid_variables, &
	110	ONLY: ddx, ddy
	111
	112	USE indices, &
	113	ONLY: nbgp, ngp_2dh_outer, nx, nxl, nxlg, nxl_mg, nxr, nxrg, nxr_mg, &
	114	ny, nys, nysg, nys_mg, nyn, nyng, nyn_mg, nzb, nzb_s_inner, &
	115	nzb_u_inner, nzb_v_inner, nzb_w_inner, nzb_2d, nzt, nzt_mg, &
	116	rflags_s_inner
	117
	118	USE kinds
	119
[1]	120	USE pegrid
	121
[1320]	122	USE poisfft_mod, &
	123	ONLY: poisfft
	124
[1575]	125	USE poismg_mod
	126
[1320]	127	USE statistics, &
	128	ONLY: statistic_regions, sums_divnew_l, sums_divold_l, weight_pres, &
	129	weight_substep
	130
[1]	131	IMPLICIT NONE
	132
[1682]	133	INTEGER(iwp) :: i !<
	134	INTEGER(iwp) :: j !<
	135	INTEGER(iwp) :: k !<
[1]	136
[1682]	137	REAL(wp) :: ddt_3d !<
	138	REAL(wp) :: localsum !<
	139	REAL(wp) :: threadsum !<
	140	REAL(wp) :: d_weight_pres !<
[1]	141
[1762]	142	REAL(wp), DIMENSION(1:3) :: volume_flow_l !<
	143	REAL(wp), DIMENSION(1:3) :: volume_flow_offset !<
[1682]	144	REAL(wp), DIMENSION(1:nzt) :: w_l !<
	145	REAL(wp), DIMENSION(1:nzt) :: w_l_l !<
[1]	146
	147
	148	CALL cpu_log( log_point(8), 'pres', 'start' )
	149
[85]	150
[1342]	151	ddt_3d = 1.0_wp / dt_3d
	152	d_weight_pres = 1.0_wp / weight_pres(intermediate_timestep_count)
[85]	153
[1]	154	!
[707]	155	!-- Multigrid method expects array d to have one ghost layer.
	156	!--
[1575]	157	IF ( psolver(1:9) == 'multigrid' ) THEN
[667]	158
[1]	159	DEALLOCATE( d )
[667]	160	ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
[707]	161
	162	!
	163	!-- Since p is later used to hold the weighted average of the substeps, it
	164	!-- cannot be used in the iterative solver. Therefore, its initial value is
	165	!-- stored on p_loc, which is then iteratively advanced in every substep.
[1762]	166	IF ( intermediate_timestep_count <= 1 ) THEN
[707]	167	DO i = nxl-1, nxr+1
	168	DO j = nys-1, nyn+1
	169	DO k = nzb, nzt+1
	170	p_loc(k,j,i) = p(k,j,i)
	171	ENDDO
	172	ENDDO
	173	ENDDO
[667]	174	ENDIF
	175
[707]	176	ELSEIF ( psolver == 'sor' .AND. intermediate_timestep_count == 1 ) THEN
	177
	178	!
	179	!-- Since p is later used to hold the weighted average of the substeps, it
	180	!-- cannot be used in the iterative solver. Therefore, its initial value is
	181	!-- stored on p_loc, which is then iteratively advanced in every substep.
	182	p_loc = p
	183
[1]	184	ENDIF
	185
	186	!
[75]	187	!-- Conserve the volume flow at the outflow in case of non-cyclic lateral
	188	!-- boundary conditions
[106]	189	!-- WARNING: so far, this conservation does not work at the left/south
	190	!-- boundary if the topography at the inflow differs from that at the
	191	!-- outflow! For this case, volume_flow_area needs adjustment!
	192	!
	193	!-- Left/right
[709]	194	IF ( conserve_volume_flow .AND. ( outflow_l .OR. outflow_r ) ) THEN
[680]	195
[1342]	196	volume_flow(1) = 0.0_wp
	197	volume_flow_l(1) = 0.0_wp
[106]	198
	199	IF ( outflow_l ) THEN
	200	i = 0
	201	ELSEIF ( outflow_r ) THEN
	202	i = nx+1
	203	ENDIF
	204
	205	DO j = nys, nyn
	206	!
	207	!-- Sum up the volume flow through the south/north boundary
[709]	208	DO k = nzb_2d(j,i)+1, nzt
[667]	209	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k)
[106]	210	ENDDO
	211	ENDDO
	212
	213	#if defined( __parallel )
[680]	214	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
[106]	215	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, &
	216	MPI_SUM, comm1dy, ierr )
	217	#else
	218	volume_flow = volume_flow_l
	219	#endif
[709]	220	volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) &
[106]	221	/ volume_flow_area(1)
	222
[667]	223	DO j = nysg, nyng
[709]	224	DO k = nzb_2d(j,i)+1, nzt
[106]	225	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
	226	ENDDO
	227	ENDDO
	228
	229	ENDIF
	230
	231	!
	232	!-- South/north
[709]	233	IF ( conserve_volume_flow .AND. ( outflow_n .OR. outflow_s ) ) THEN
[106]	234
[1342]	235	volume_flow(2) = 0.0_wp
	236	volume_flow_l(2) = 0.0_wp
[75]	237
[106]	238	IF ( outflow_s ) THEN
	239	j = 0
	240	ELSEIF ( outflow_n ) THEN
[75]	241	j = ny+1
[106]	242	ENDIF
	243
	244	DO i = nxl, nxr
[75]	245	!
[106]	246	!-- Sum up the volume flow through the south/north boundary
[709]	247	DO k = nzb_2d(j,i)+1, nzt
[667]	248	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k)
[75]	249	ENDDO
[106]	250	ENDDO
	251
[75]	252	#if defined( __parallel )
[680]	253	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
[75]	254	CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, &
	255	MPI_SUM, comm1dx, ierr )
	256	#else
	257	volume_flow = volume_flow_l
	258	#endif
	259	volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) ) &
[106]	260	/ volume_flow_area(2)
[75]	261
[667]	262	DO i = nxlg, nxrg
[709]	263	DO k = nzb_v_inner(j,i)+1, nzt
[106]	264	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
[75]	265	ENDDO
[106]	266	ENDDO
[75]	267
	268	ENDIF
	269
[76]	270	!
[1762]	271	!-- Remove mean vertical velocity in case that Neumann conditions are
	272	!-- used both at bottom and top boundary, and if not a nested domain
	273	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 .AND. .NOT. nest_domain) THEN
[1342]	274	IF ( simulated_time > 0.0_wp ) THEN ! otherwise nzb_w_inner not yet known
	275	w_l = 0.0_wp; w_l_l = 0.0_wp
[76]	276	DO i = nxl, nxr
	277	DO j = nys, nyn
	278	DO k = nzb_w_inner(j,i)+1, nzt
	279	w_l_l(k) = w_l_l(k) + w(k,j,i)
	280	ENDDO
	281	ENDDO
	282	ENDDO
	283	#if defined( __parallel )
[622]	284	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[709]	285	CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, &
	286	comm2d, ierr )
[76]	287	#else
	288	w_l = w_l_l
	289	#endif
	290	DO k = 1, nzt
	291	w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
	292	ENDDO
[667]	293	DO i = nxlg, nxrg
	294	DO j = nysg, nyng
[76]	295	DO k = nzb_w_inner(j,i)+1, nzt
	296	w(k,j,i) = w(k,j,i) - w_l(k)
	297	ENDDO
	298	ENDDO
	299	ENDDO
	300	ENDIF
	301	ENDIF
[75]	302
	303	!
[1]	304	!-- Compute the divergence of the provisional velocity field.
	305	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
	306
[1575]	307	IF ( psolver(1:9) == 'multigrid' ) THEN
[1]	308	!$OMP PARALLEL DO SCHEDULE( STATIC )
	309	DO i = nxl-1, nxr+1
	310	DO j = nys-1, nyn+1
	311	DO k = nzb, nzt+1
[1342]	312	d(k,j,i) = 0.0_wp
[1]	313	ENDDO
	314	ENDDO
	315	ENDDO
	316	ELSE
	317	!$OMP PARALLEL DO SCHEDULE( STATIC )
[1111]	318	!$acc kernels present( d )
[1003]	319	DO i = nxl, nxr
	320	DO j = nys, nyn
	321	DO k = nzb+1, nzt
[1342]	322	d(k,j,i) = 0.0_wp
[1]	323	ENDDO
	324	ENDDO
	325	ENDDO
[1111]	326	!$acc end kernels
[1]	327	ENDIF
	328
[1342]	329	localsum = 0.0_wp
	330	threadsum = 0.0_wp
[1]	331
	332	#if defined( __ibm )
	333	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
	334	!$OMP DO SCHEDULE( STATIC )
	335	DO i = nxl, nxr
	336	DO j = nys, nyn
	337	DO k = nzb_s_inner(j,i)+1, nzt
[85]	338	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
	339	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
[673]	340	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
	341	* d_weight_pres
[1]	342	ENDDO
	343	!
	344	!-- Compute possible PE-sum of divergences for flow_statistics
	345	DO k = nzb_s_inner(j,i)+1, nzt
	346	threadsum = threadsum + ABS( d(k,j,i) )
	347	ENDDO
	348
	349	ENDDO
	350	ENDDO
	351
[707]	352	localsum = localsum + threadsum * dt_3d * &
	353	weight_pres(intermediate_timestep_count)
[693]	354
[1]	355	!$OMP END PARALLEL
	356	#else
	357
[1111]	358	!$OMP PARALLEL PRIVATE (i,j,k)
	359	!$OMP DO SCHEDULE( STATIC )
[1221]	360	!$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
	361	!$acc loop collapse( 3 )
[1111]	362	DO i = nxl, nxr
	363	DO j = nys, nyn
	364	DO k = 1, nzt
[1221]	365	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
	366	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
	367	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
	368	* d_weight_pres * rflags_s_inner(k,j,i)
[1]	369	ENDDO
	370	ENDDO
[1111]	371	ENDDO
	372	!$acc end kernels
	373	!$OMP END PARALLEL
[1]	374
	375	!
	376	!-- Compute possible PE-sum of divergences for flow_statistics
	377	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
	378	!$OMP DO SCHEDULE( STATIC )
[1221]	379	!$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
[1]	380	DO i = nxl, nxr
	381	DO j = nys, nyn
	382	DO k = nzb+1, nzt
	383	threadsum = threadsum + ABS( d(k,j,i) )
	384	ENDDO
	385	ENDDO
	386	ENDDO
[1257]	387	!$acc end parallel loop
[707]	388	localsum = localsum + threadsum * dt_3d * &
	389	weight_pres(intermediate_timestep_count)
[1]	390	!$OMP END PARALLEL
	391	#endif
	392
	393	!
	394	!-- For completeness, set the divergence sum of all statistic regions to those
	395	!-- of the total domain
	396	sums_divold_l(0:statistic_regions) = localsum
	397
	398	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
	399
	400	!
	401	!-- Compute the pressure perturbation solving the Poisson equation
[1575]	402	IF ( psolver == 'poisfft' ) THEN
[1]	403
	404	!
	405	!-- Solve Poisson equation via FFT and solution of tridiagonal matrices
[1575]	406	CALL poisfft( d )
[1212]	407
[1]	408	!
	409	!-- Store computed perturbation pressure and set boundary condition in
	410	!-- z-direction
	411	!$OMP PARALLEL DO
[1113]	412	!$acc kernels present( d, tend )
[1]	413	DO i = nxl, nxr
	414	DO j = nys, nyn
	415	DO k = nzb+1, nzt
	416	tend(k,j,i) = d(k,j,i)
	417	ENDDO
	418	ENDDO
	419	ENDDO
[1113]	420	!$acc end kernels
[1]	421
	422	!
	423	!-- Bottom boundary:
	424	!-- This condition is only required for internal output. The pressure
	425	!-- gradient (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
	426	IF ( ibc_p_b == 1 ) THEN
	427	!
	428	!-- Neumann (dp/dz = 0)
	429	!$OMP PARALLEL DO
[1113]	430	!$acc kernels present( nzb_s_inner, tend )
[667]	431	DO i = nxlg, nxrg
	432	DO j = nysg, nyng
[1]	433	tend(nzb_s_inner(j,i),j,i) = tend(nzb_s_inner(j,i)+1,j,i)
	434	ENDDO
	435	ENDDO
[1113]	436	!$acc end kernels
[1]	437
	438	ELSE
	439	!
	440	!-- Dirichlet
	441	!$OMP PARALLEL DO
[1113]	442	!$acc kernels present( tend )
[667]	443	DO i = nxlg, nxrg
	444	DO j = nysg, nyng
[1342]	445	tend(nzb_s_inner(j,i),j,i) = 0.0_wp
[1]	446	ENDDO
	447	ENDDO
[1113]	448	!$acc end kernels
[1]	449
	450	ENDIF
	451
	452	!
	453	!-- Top boundary
	454	IF ( ibc_p_t == 1 ) THEN
	455	!
	456	!-- Neumann
	457	!$OMP PARALLEL DO
[1113]	458	!$acc kernels present( tend )
[667]	459	DO i = nxlg, nxrg
	460	DO j = nysg, nyng
[1]	461	tend(nzt+1,j,i) = tend(nzt,j,i)
	462	ENDDO
	463	ENDDO
[1113]	464	!$acc end kernels
[1]	465
	466	ELSE
	467	!
	468	!-- Dirichlet
	469	!$OMP PARALLEL DO
[1113]	470	!$acc kernels present( tend )
[667]	471	DO i = nxlg, nxrg
	472	DO j = nysg, nyng
[1342]	473	tend(nzt+1,j,i) = 0.0_wp
[1]	474	ENDDO
	475	ENDDO
[1113]	476	!$acc end kernels
[1]	477
	478	ENDIF
	479
	480	!
	481	!-- Exchange boundaries for p
[1113]	482	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
	483	on_device = .TRUE. ! to be removed after complete porting
	484	ELSE ! of ghost point exchange
	485	!$acc update host( tend )
	486	ENDIF
[667]	487	CALL exchange_horiz( tend, nbgp )
[1113]	488	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
	489	on_device = .FALSE. ! to be removed after complete porting
	490	ELSE ! of ghost point exchange
	491	!$acc update device( tend )
	492	ENDIF
[1]	493
	494	ELSEIF ( psolver == 'sor' ) THEN
	495
	496	!
	497	!-- Solve Poisson equation for perturbation pressure using SOR-Red/Black
	498	!-- scheme
[707]	499	CALL sor( d, ddzu_pres, ddzw, p_loc )
	500	tend = p_loc
[1]	501
[1575]	502	ELSEIF ( psolver(1:9) == 'multigrid' ) THEN
[1]	503
	504	!
	505	!-- Solve Poisson equation for perturbation pressure using Multigrid scheme,
[667]	506	!-- array tend is used to store the residuals, logical exchange_mg is used
	507	!-- to discern data exchange in multigrid ( 1 ghostpoint ) and normal grid
	508	!-- ( nbgp ghost points ).
[778]	509
	510	!-- If the number of grid points of the gathered grid, which is collected
	511	!-- on PE0, is larger than the number of grid points of an PE, than array
	512	!-- tend will be enlarged.
	513	IF ( gathered_size > subdomain_size ) THEN
	514	DEALLOCATE( tend )
	515	ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
	516	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
	517	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg( &
	518	mg_switch_to_pe0_level)+1) )
	519	ENDIF
	520
[1575]	521	IF ( psolver == 'multigrid' ) THEN
	522	CALL poismg( tend )
	523	ELSE
	524	CALL poismg_fast( tend )
	525	ENDIF
[707]	526
[778]	527	IF ( gathered_size > subdomain_size ) THEN
	528	DEALLOCATE( tend )
	529	ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
	530	ENDIF
	531
[1]	532	!
	533	!-- Restore perturbation pressure on tend because this array is used
	534	!-- further below to correct the velocity fields
[707]	535	DO i = nxl-1, nxr+1
	536	DO j = nys-1, nyn+1
	537	DO k = nzb, nzt+1
	538	tend(k,j,i) = p_loc(k,j,i)
	539	ENDDO
	540	ENDDO
	541	ENDDO
[667]	542
[1]	543	ENDIF
	544
	545	!
[707]	546	!-- Store perturbation pressure on array p, used for pressure data output.
	547	!-- Ghost layers are added in the output routines (except sor-method: see below)
	548	IF ( intermediate_timestep_count == 1 ) THEN
	549	!$OMP PARALLEL PRIVATE (i,j,k)
	550	!$OMP DO
[1113]	551	!$acc kernels present( p, tend, weight_substep )
[1257]	552	!$acc loop independent
[707]	553	DO i = nxl-1, nxr+1
[1257]	554	!$acc loop independent
[707]	555	DO j = nys-1, nyn+1
[1257]	556	!$acc loop independent
[707]	557	DO k = nzb, nzt+1
	558	p(k,j,i) = tend(k,j,i) * &
	559	weight_substep(intermediate_timestep_count)
[673]	560	ENDDO
[1]	561	ENDDO
[707]	562	ENDDO
[1113]	563	!$acc end kernels
[707]	564	!$OMP END PARALLEL
	565
[1762]	566	ELSEIF ( intermediate_timestep_count > 1 ) THEN
[707]	567	!$OMP PARALLEL PRIVATE (i,j,k)
	568	!$OMP DO
[1113]	569	!$acc kernels present( p, tend, weight_substep )
[1257]	570	!$acc loop independent
[707]	571	DO i = nxl-1, nxr+1
[1257]	572	!$acc loop independent
[707]	573	DO j = nys-1, nyn+1
[1257]	574	!$acc loop independent
[707]	575	DO k = nzb, nzt+1
	576	p(k,j,i) = p(k,j,i) + tend(k,j,i) * &
	577	weight_substep(intermediate_timestep_count)
[673]	578	ENDDO
	579	ENDDO
[707]	580	ENDDO
[1113]	581	!$acc end kernels
[707]	582	!$OMP END PARALLEL
	583
	584	ENDIF
[673]	585
[707]	586	!
	587	!-- SOR-method needs ghost layers for the next timestep
	588	IF ( psolver == 'sor' ) CALL exchange_horiz( p, nbgp )
[682]	589
[1]	590	!
	591	!-- Correction of the provisional velocities with the current perturbation
	592	!-- pressure just computed
[709]	593	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .OR. bc_ns_cyc ) ) THEN
[1342]	594	volume_flow_l(1) = 0.0_wp
	595	volume_flow_l(2) = 0.0_wp
[1]	596	ENDIF
[707]	597
[1]	598	!$OMP PARALLEL PRIVATE (i,j,k)
	599	!$OMP DO
[1113]	600	!$acc kernels present( ddzu, nzb_u_inner, nzb_v_inner, nzb_w_inner, tend, u, v, w, weight_pres )
[1257]	601	!$acc loop independent
[673]	602	DO i = nxl, nxr
[1257]	603	!$acc loop independent
[1]	604	DO j = nys, nyn
[1257]	605	!$acc loop independent
[1113]	606	DO k = 1, nzt
	607	IF ( k > nzb_w_inner(j,i) ) THEN
	608	w(k,j,i) = w(k,j,i) - dt_3d * &
	609	( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) * &
	610	weight_pres(intermediate_timestep_count)
	611	ENDIF
[1]	612	ENDDO
[1257]	613	!$acc loop independent
[1113]	614	DO k = 1, nzt
	615	IF ( k > nzb_u_inner(j,i) ) THEN
	616	u(k,j,i) = u(k,j,i) - dt_3d * &
	617	( tend(k,j,i) - tend(k,j,i-1) ) * ddx * &
	618	weight_pres(intermediate_timestep_count)
	619	ENDIF
[1]	620	ENDDO
[1257]	621	!$acc loop independent
[1113]	622	DO k = 1, nzt
	623	IF ( k > nzb_v_inner(j,i) ) THEN
	624	v(k,j,i) = v(k,j,i) - dt_3d * &
	625	( tend(k,j,i) - tend(k,j-1,i) ) * ddy * &
	626	weight_pres(intermediate_timestep_count)
	627	ENDIF
[673]	628	ENDDO
[1]	629
	630	ENDDO
	631	ENDDO
[1113]	632	!$acc end kernels
[1]	633	!$OMP END PARALLEL
[1113]	634
	635	!
	636	!-- Sum up the volume flow through the right and north boundary
	637	IF ( conserve_volume_flow .AND. bc_lr_cyc .AND. bc_ns_cyc .AND. &
	638	nxr == nx ) THEN
	639
	640	!$OMP PARALLEL PRIVATE (j,k)
	641	!$OMP DO
	642	DO j = nys, nyn
	643	!$OMP CRITICAL
	644	DO k = nzb_2d(j,nx) + 1, nzt
	645	volume_flow_l(1) = volume_flow_l(1) + u(k,j,nx) * dzw(k)
	646	ENDDO
	647	!$OMP END CRITICAL
	648	ENDDO
	649	!$OMP END PARALLEL
	650
	651	ENDIF
	652
	653	IF ( conserve_volume_flow .AND. bc_ns_cyc .AND. bc_lr_cyc .AND. &
	654	nyn == ny ) THEN
	655
	656	!$OMP PARALLEL PRIVATE (i,k)
	657	!$OMP DO
	658	DO i = nxl, nxr
	659	!$OMP CRITICAL
	660	DO k = nzb_2d(ny,i) + 1, nzt
	661	volume_flow_l(2) = volume_flow_l(2) + v(k,ny,i) * dzw(k)
	662	ENDDO
	663	!$OMP END CRITICAL
	664	ENDDO
	665	!$OMP END PARALLEL
	666
	667	ENDIF
[673]	668
[1]	669	!
	670	!-- Conserve the volume flow
[707]	671	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .AND. bc_ns_cyc ) ) THEN
[1]	672
	673	#if defined( __parallel )
[622]	674	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[1]	675	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, &
	676	MPI_SUM, comm2d, ierr )
	677	#else
	678	volume_flow = volume_flow_l
	679	#endif
	680
	681	volume_flow_offset = ( volume_flow_initial - volume_flow ) / &
	682	volume_flow_area
	683
	684	!$OMP PARALLEL PRIVATE (i,j,k)
	685	!$OMP DO
	686	DO i = nxl, nxr
	687	DO j = nys, nyn
[667]	688	DO k = nzb_u_inner(j,i) + 1, nzt
	689	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
[719]	690	ENDDO
	691	DO k = nzb_v_inner(j,i) + 1, nzt
[667]	692	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
	693	ENDDO
[1]	694	ENDDO
	695	ENDDO
[667]	696
[1]	697	!$OMP END PARALLEL
	698
	699	ENDIF
	700
	701	!
	702	!-- Exchange of boundaries for the velocities
[1113]	703	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
	704	on_device = .TRUE. ! to be removed after complete porting
	705	ELSE ! of ghost point exchange
	706	!$acc update host( u, v, w )
	707	ENDIF
[667]	708	CALL exchange_horiz( u, nbgp )
	709	CALL exchange_horiz( v, nbgp )
	710	CALL exchange_horiz( w, nbgp )
[1113]	711	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
	712	on_device = .FALSE. ! to be removed after complete porting
	713	ELSE ! of ghost point exchange
	714	!$acc update device( u, v, w )
	715	ENDIF
[1]	716
	717	!
	718	!-- Compute the divergence of the corrected velocity field,
	719	!-- a possible PE-sum is computed in flow_statistics
	720	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
[1342]	721	sums_divnew_l = 0.0_wp
[1]	722
	723	!
	724	!-- d must be reset to zero because it can contain nonzero values below the
	725	!-- topography
[1342]	726	IF ( topography /= 'flat' ) d = 0.0_wp
[1]	727
[1342]	728	localsum = 0.0_wp
	729	threadsum = 0.0_wp
[1]	730
	731	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
	732	!$OMP DO SCHEDULE( STATIC )
	733	#if defined( __ibm )
	734	DO i = nxl, nxr
	735	DO j = nys, nyn
	736	DO k = nzb_s_inner(j,i)+1, nzt
	737	d(k,j,i) = ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
	738	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
	739	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k)
	740	ENDDO
	741	DO k = nzb+1, nzt
	742	threadsum = threadsum + ABS( d(k,j,i) )
	743	ENDDO
	744	ENDDO
	745	ENDDO
	746	#else
[1221]	747	!$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
	748	!$acc loop collapse( 3 )
[1]	749	DO i = nxl, nxr
	750	DO j = nys, nyn
[1113]	751	DO k = 1, nzt
[1221]	752	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
	753	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
	754	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) &
	755	) * rflags_s_inner(k,j,i)
[1113]	756	ENDDO
	757	ENDDO
	758	ENDDO
	759	!$acc end kernels
	760	!
	761	!-- Compute possible PE-sum of divergences for flow_statistics
[1221]	762	!$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
[1113]	763	DO i = nxl, nxr
	764	DO j = nys, nyn
[1221]	765	DO k = nzb+1, nzt
[1]	766	threadsum = threadsum + ABS( d(k,j,i) )
	767	ENDDO
	768	ENDDO
	769	ENDDO
[1257]	770	!$acc end parallel loop
[1]	771	#endif
[667]	772
[1]	773	localsum = localsum + threadsum
	774	!$OMP END PARALLEL
	775
	776	!
	777	!-- For completeness, set the divergence sum of all statistic regions to those
	778	!-- of the total domain
	779	sums_divnew_l(0:statistic_regions) = localsum
	780
	781	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
	782
	783	CALL cpu_log( log_point(8), 'pres', 'stop' )
	784
	785
	786	END SUBROUTINE pres

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