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source: palm/trunk/SOURCE/pres.f90 @ 1927

Last change on this file since 1927 was 1919, checked in by raasch, 8 years ago
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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	!
[1818]	16	! Copyright 1997-2016 Leibniz Universitaet Hannover
[1036]	17	!--------------------------------------------------------------------------------!
	18	!
[484]	19	! Current revisions:
[1212]	20	! ------------------
[1919]	21	!
	22	!
	23	! Former revisions:
	24	! -----------------
	25	! $Id: pres.f90 1919 2016-05-27 14:51:23Z hellstea $
	26	!
	27	! 1918 2016-05-27 14:35:57Z raasch
[1918]	28	! sum of divergence is also calculated when pres is called before the initial
	29	! first time step,
	30	! stearing is modified by using intermediate_timestep_count = 0 in order to
	31	! determine if pres is called before the first initial timestep,
	32	! bugfix: in case of Neumann conditions for pressure both at bottom and top,
	33	! mean vertical velocity is also removed for the first time step
	34	! bugfix for calculating divergences
[1321]	35	!
[1909]	36	! 1908 2016-05-25 17:22:32Z suehring
	37	! New divergence for output into RUN_CONTROL file is calculated only at last
	38	! Runge-Kutta step
	39	!
[1846]	40	! 1845 2016-04-08 08:29:13Z raasch
	41	! nzb_2d replace by nzb_u\|v_inner
	42	!
[1800]	43	! 1799 2016-04-05 08:35:55Z gronemeier
	44	! Bugfix: excluded third dimension from horizontal volume flow calculation
	45	!
[1763]	46	! 1762 2016-02-25 12:31:13Z hellstea
	47	! Introduction of nested domain feature
	48	!
[1683]	49	! 1682 2015-10-07 23:56:08Z knoop
	50	! Code annotations made doxygen readable
	51	!
[1576]	52	! 1575 2015-03-27 09:56:27Z raasch
	53	! poismg_fast + respective module added, adjustments for psolver-queries
	54	!
[1343]	55	! 1342 2014-03-26 17:04:47Z kanani
	56	! REAL constants defined as wp-kind
	57	!
[1321]	58	! 1320 2014-03-20 08:40:49Z raasch
[1320]	59	! ONLY-attribute added to USE-statements,
	60	! kind-parameters added to all INTEGER and REAL declaration statements,
	61	! kinds are defined in new module kinds,
	62	! old module precision_kind is removed,
	63	! revision history before 2012 removed,
	64	! comment fields (!:) to be used for variable explanations added to
	65	! all variable declaration statements
[708]	66	!
[1319]	67	! 1318 2014-03-17 13:35:16Z raasch
	68	! module interfaces removed
	69	!
[1307]	70	! 1306 2014-03-13 14:30:59Z raasch
	71	! second argument removed from routine poisfft
	72	!
[1258]	73	! 1257 2013-11-08 15:18:40Z raasch
	74	! openacc loop and loop vector clauses removed, independent clauses added,
	75	! end parallel replaced by end parallel loop
	76	!
[1222]	77	! 1221 2013-09-10 08:59:13Z raasch
	78	! openACC porting of reduction operations, loops for calculating d are
	79	! using the rflags_s_inner multiply flag instead of the nzb_s_inner loop index
	80	!
[1213]	81	! 1212 2013-08-15 08:46:27Z raasch
	82	! call of poisfft_hybrid removed
	83	!
[1118]	84	! 1117 2013-03-27 11:15:36Z suehring
	85	! Bugfix in OpenMP parallelization.
	86	!
[1114]	87	! 1113 2013-03-10 02:48:14Z raasch
	88	! GPU-porting of several loops, some loops rearranged
	89	!
[1112]	90	! 1111 2013-03-08 23:54:10Z
	91	! openACC statements added,
	92	! ibc_p_b = 2 removed
	93	!
[1093]	94	! 1092 2013-02-02 11:24:22Z raasch
	95	! unused variables removed
	96	!
[1037]	97	! 1036 2012-10-22 13:43:42Z raasch
	98	! code put under GPL (PALM 3.9)
	99	!
[1004]	100	! 1003 2012-09-14 14:35:53Z raasch
	101	! adjustment of array tend for cases with unequal subdomain sizes removed
	102	!
[1]	103	! Revision 1.1 1997/07/24 11:24:44 raasch
	104	! Initial revision
	105	!
	106	!
	107	! Description:
	108	! ------------
[1682]	109	!> Compute the divergence of the provisional velocity field. Solve the Poisson
	110	!> equation for the perturbation pressure. Compute the final velocities using
	111	!> this perturbation pressure. Compute the remaining divergence.
[1]	112	!------------------------------------------------------------------------------!
[1682]	113	SUBROUTINE pres
	114
[1]	115
[1320]	116	USE arrays_3d, &
	117	ONLY: d, ddzu, ddzu_pres, ddzw, dzw, p, p_loc, tend, u, v, w
	118
	119	USE control_parameters, &
	120	ONLY: bc_lr_cyc, bc_ns_cyc, conserve_volume_flow, dt_3d, &
	121	gathered_size, ibc_p_b, ibc_p_t, intermediate_timestep_count, &
[1908]	122	intermediate_timestep_count_max, mg_switch_to_pe0_level, &
	123	nest_domain, nest_bound_l, nest_bound_n, nest_bound_r, &
	124	nest_bound_s, on_device, outflow_l, outflow_n, outflow_r, &
[1918]	125	outflow_s, psolver, subdomain_size, topography, volume_flow, &
	126	volume_flow_area, volume_flow_initial
[1320]	127
	128	USE cpulog, &
	129	ONLY: cpu_log, log_point, log_point_s
	130
	131	USE grid_variables, &
	132	ONLY: ddx, ddy
	133
	134	USE indices, &
	135	ONLY: nbgp, ngp_2dh_outer, nx, nxl, nxlg, nxl_mg, nxr, nxrg, nxr_mg, &
	136	ny, nys, nysg, nys_mg, nyn, nyng, nyn_mg, nzb, nzb_s_inner, &
[1845]	137	nzb_u_inner, nzb_v_inner, nzb_w_inner, nzt, nzt_mg, &
[1320]	138	rflags_s_inner
	139
	140	USE kinds
	141
[1]	142	USE pegrid
	143
[1320]	144	USE poisfft_mod, &
	145	ONLY: poisfft
	146
[1575]	147	USE poismg_mod
	148
[1320]	149	USE statistics, &
	150	ONLY: statistic_regions, sums_divnew_l, sums_divold_l, weight_pres, &
	151	weight_substep
	152
[1]	153	IMPLICIT NONE
	154
[1682]	155	INTEGER(iwp) :: i !<
	156	INTEGER(iwp) :: j !<
	157	INTEGER(iwp) :: k !<
[1]	158
[1682]	159	REAL(wp) :: ddt_3d !<
[1918]	160	REAL(wp) :: d_weight_pres !<
[1682]	161	REAL(wp) :: localsum !<
	162	REAL(wp) :: threadsum !<
[1918]	163	REAL(wp) :: weight_pres_l !<
[1]	164
[1762]	165	REAL(wp), DIMENSION(1:3) :: volume_flow_l !<
	166	REAL(wp), DIMENSION(1:3) :: volume_flow_offset !<
[1682]	167	REAL(wp), DIMENSION(1:nzt) :: w_l !<
	168	REAL(wp), DIMENSION(1:nzt) :: w_l_l !<
[1]	169
	170
	171	CALL cpu_log( log_point(8), 'pres', 'start' )
	172
[85]	173
[1918]	174	!
	175	!-- Calculate quantities to be used locally
[1342]	176	ddt_3d = 1.0_wp / dt_3d
[1918]	177	IF ( intermediate_timestep_count == 0 ) THEN
	178	!
	179	!-- If pres is called before initial time step
	180	weight_pres_l = 1.0_wp
	181	d_weight_pres = 1.0_wp
	182	ELSE
	183	weight_pres_l = weight_pres(intermediate_timestep_count)
	184	d_weight_pres = 1.0_wp / weight_pres(intermediate_timestep_count)
	185	ENDIF
[85]	186
[1]	187	!
[707]	188	!-- Multigrid method expects array d to have one ghost layer.
	189	!--
[1575]	190	IF ( psolver(1:9) == 'multigrid' ) THEN
[667]	191
[1]	192	DEALLOCATE( d )
[667]	193	ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
[707]	194
	195	!
	196	!-- Since p is later used to hold the weighted average of the substeps, it
	197	!-- cannot be used in the iterative solver. Therefore, its initial value is
	198	!-- stored on p_loc, which is then iteratively advanced in every substep.
[1762]	199	IF ( intermediate_timestep_count <= 1 ) THEN
[707]	200	DO i = nxl-1, nxr+1
	201	DO j = nys-1, nyn+1
	202	DO k = nzb, nzt+1
	203	p_loc(k,j,i) = p(k,j,i)
	204	ENDDO
	205	ENDDO
	206	ENDDO
[667]	207	ENDIF
	208
[1918]	209	ELSEIF ( psolver == 'sor' .AND. intermediate_timestep_count <= 1 ) THEN
[707]	210
	211	!
	212	!-- Since p is later used to hold the weighted average of the substeps, it
	213	!-- cannot be used in the iterative solver. Therefore, its initial value is
	214	!-- stored on p_loc, which is then iteratively advanced in every substep.
	215	p_loc = p
	216
[1]	217	ENDIF
	218
	219	!
[75]	220	!-- Conserve the volume flow at the outflow in case of non-cyclic lateral
	221	!-- boundary conditions
[106]	222	!-- WARNING: so far, this conservation does not work at the left/south
	223	!-- boundary if the topography at the inflow differs from that at the
	224	!-- outflow! For this case, volume_flow_area needs adjustment!
	225	!
	226	!-- Left/right
[709]	227	IF ( conserve_volume_flow .AND. ( outflow_l .OR. outflow_r ) ) THEN
[680]	228
[1342]	229	volume_flow(1) = 0.0_wp
	230	volume_flow_l(1) = 0.0_wp
[106]	231
	232	IF ( outflow_l ) THEN
	233	i = 0
	234	ELSEIF ( outflow_r ) THEN
	235	i = nx+1
	236	ENDIF
	237
	238	DO j = nys, nyn
	239	!
	240	!-- Sum up the volume flow through the south/north boundary
[1845]	241	DO k = nzb_u_inner(j,i)+1, nzt
[667]	242	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k)
[106]	243	ENDDO
	244	ENDDO
	245
	246	#if defined( __parallel )
[680]	247	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
[106]	248	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, &
	249	MPI_SUM, comm1dy, ierr )
	250	#else
	251	volume_flow = volume_flow_l
	252	#endif
[709]	253	volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) &
[106]	254	/ volume_flow_area(1)
	255
[667]	256	DO j = nysg, nyng
[1845]	257	DO k = nzb_u_inner(j,i)+1, nzt
[106]	258	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
	259	ENDDO
	260	ENDDO
	261
	262	ENDIF
	263
	264	!
	265	!-- South/north
[709]	266	IF ( conserve_volume_flow .AND. ( outflow_n .OR. outflow_s ) ) THEN
[106]	267
[1342]	268	volume_flow(2) = 0.0_wp
	269	volume_flow_l(2) = 0.0_wp
[75]	270
[106]	271	IF ( outflow_s ) THEN
	272	j = 0
	273	ELSEIF ( outflow_n ) THEN
[75]	274	j = ny+1
[106]	275	ENDIF
	276
	277	DO i = nxl, nxr
[75]	278	!
[106]	279	!-- Sum up the volume flow through the south/north boundary
[1845]	280	DO k = nzb_v_inner(j,i)+1, nzt
[667]	281	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k)
[75]	282	ENDDO
[106]	283	ENDDO
	284
[75]	285	#if defined( __parallel )
[680]	286	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
[75]	287	CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, &
	288	MPI_SUM, comm1dx, ierr )
	289	#else
	290	volume_flow = volume_flow_l
	291	#endif
	292	volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) ) &
[106]	293	/ volume_flow_area(2)
[75]	294
[667]	295	DO i = nxlg, nxrg
[709]	296	DO k = nzb_v_inner(j,i)+1, nzt
[106]	297	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
[75]	298	ENDDO
[106]	299	ENDDO
[75]	300
	301	ENDIF
	302
[76]	303	!
[1762]	304	!-- Remove mean vertical velocity in case that Neumann conditions are
[1918]	305	!-- used both at bottom and top boundary, and if not a nested domain.
	306	!-- This cannot be done before the first initial time step because ngp_2dh_outer
	307	!-- is not yet known then.
	308	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 .AND. .NOT. nest_domain .AND. &
	309	intermediate_timestep_count /= 0 ) &
	310	THEN
	311	w_l = 0.0_wp; w_l_l = 0.0_wp
	312	DO i = nxl, nxr
	313	DO j = nys, nyn
	314	DO k = nzb_w_inner(j,i)+1, nzt
	315	w_l_l(k) = w_l_l(k) + w(k,j,i)
[76]	316	ENDDO
	317	ENDDO
[1918]	318	ENDDO
[76]	319	#if defined( __parallel )
[1918]	320	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
	321	CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, &
	322	comm2d, ierr )
[76]	323	#else
[1918]	324	w_l = w_l_l
[76]	325	#endif
[1918]	326	DO k = 1, nzt
	327	w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
	328	ENDDO
	329	DO i = nxlg, nxrg
	330	DO j = nysg, nyng
	331	DO k = nzb_w_inner(j,i)+1, nzt
	332	w(k,j,i) = w(k,j,i) - w_l(k)
[76]	333	ENDDO
	334	ENDDO
[1918]	335	ENDDO
[76]	336	ENDIF
[75]	337
	338	!
[1]	339	!-- Compute the divergence of the provisional velocity field.
	340	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
	341
[1575]	342	IF ( psolver(1:9) == 'multigrid' ) THEN
[1]	343	!$OMP PARALLEL DO SCHEDULE( STATIC )
	344	DO i = nxl-1, nxr+1
	345	DO j = nys-1, nyn+1
	346	DO k = nzb, nzt+1
[1342]	347	d(k,j,i) = 0.0_wp
[1]	348	ENDDO
	349	ENDDO
	350	ENDDO
	351	ELSE
	352	!$OMP PARALLEL DO SCHEDULE( STATIC )
[1111]	353	!$acc kernels present( d )
[1003]	354	DO i = nxl, nxr
	355	DO j = nys, nyn
	356	DO k = nzb+1, nzt
[1342]	357	d(k,j,i) = 0.0_wp
[1]	358	ENDDO
	359	ENDDO
	360	ENDDO
[1111]	361	!$acc end kernels
[1]	362	ENDIF
	363
[1342]	364	localsum = 0.0_wp
	365	threadsum = 0.0_wp
[1]	366
	367	#if defined( __ibm )
	368	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
	369	!$OMP DO SCHEDULE( STATIC )
	370	DO i = nxl, nxr
	371	DO j = nys, nyn
	372	DO k = nzb_s_inner(j,i)+1, nzt
[85]	373	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
	374	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
[673]	375	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
	376	* d_weight_pres
[1]	377	ENDDO
	378	!
	379	!-- Compute possible PE-sum of divergences for flow_statistics
	380	DO k = nzb_s_inner(j,i)+1, nzt
	381	threadsum = threadsum + ABS( d(k,j,i) )
	382	ENDDO
	383
	384	ENDDO
	385	ENDDO
	386
[1918]	387	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	388	intermediate_timestep_count == 0 ) THEN
	389	localsum = localsum + threadsum * dt_3d * weight_pres_l
[1908]	390	ENDIF
[1]	391	!$OMP END PARALLEL
	392	#else
	393
[1111]	394	!$OMP PARALLEL PRIVATE (i,j,k)
	395	!$OMP DO SCHEDULE( STATIC )
[1221]	396	!$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
	397	!$acc loop collapse( 3 )
[1111]	398	DO i = nxl, nxr
	399	DO j = nys, nyn
	400	DO k = 1, nzt
[1221]	401	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
	402	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
	403	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
	404	* d_weight_pres * rflags_s_inner(k,j,i)
[1]	405	ENDDO
	406	ENDDO
[1111]	407	ENDDO
	408	!$acc end kernels
	409	!$OMP END PARALLEL
[1]	410
	411	!
[1908]	412	!-- Compute possible PE-sum of divergences for flow_statistics. Carry out
	413	!-- computation only at last Runge-Kutta substep.
[1918]	414	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	415	intermediate_timestep_count == 0 ) THEN
[1908]	416	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
	417	!$OMP DO SCHEDULE( STATIC )
	418	!$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
	419	DO i = nxl, nxr
	420	DO j = nys, nyn
	421	DO k = nzb+1, nzt
	422	threadsum = threadsum + ABS( d(k,j,i) )
	423	ENDDO
[1]	424	ENDDO
	425	ENDDO
[1908]	426	!$acc end parallel loop
[1918]	427	localsum = localsum + threadsum * dt_3d * weight_pres_l
[1908]	428	!$OMP END PARALLEL
	429	ENDIF
[1]	430	#endif
	431
	432	!
	433	!-- For completeness, set the divergence sum of all statistic regions to those
	434	!-- of the total domain
[1918]	435	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	436	intermediate_timestep_count == 0 ) THEN
[1908]	437	sums_divold_l(0:statistic_regions) = localsum
[1918]	438	ENDIF
[1]	439
	440	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
	441
	442	!
	443	!-- Compute the pressure perturbation solving the Poisson equation
[1575]	444	IF ( psolver == 'poisfft' ) THEN
[1]	445
	446	!
	447	!-- Solve Poisson equation via FFT and solution of tridiagonal matrices
[1575]	448	CALL poisfft( d )
[1212]	449
[1]	450	!
	451	!-- Store computed perturbation pressure and set boundary condition in
	452	!-- z-direction
	453	!$OMP PARALLEL DO
[1113]	454	!$acc kernels present( d, tend )
[1]	455	DO i = nxl, nxr
	456	DO j = nys, nyn
	457	DO k = nzb+1, nzt
	458	tend(k,j,i) = d(k,j,i)
	459	ENDDO
	460	ENDDO
	461	ENDDO
[1113]	462	!$acc end kernels
[1]	463
	464	!
	465	!-- Bottom boundary:
	466	!-- This condition is only required for internal output. The pressure
	467	!-- gradient (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
	468	IF ( ibc_p_b == 1 ) THEN
	469	!
	470	!-- Neumann (dp/dz = 0)
	471	!$OMP PARALLEL DO
[1113]	472	!$acc kernels present( nzb_s_inner, tend )
[667]	473	DO i = nxlg, nxrg
	474	DO j = nysg, nyng
[1]	475	tend(nzb_s_inner(j,i),j,i) = tend(nzb_s_inner(j,i)+1,j,i)
	476	ENDDO
	477	ENDDO
[1113]	478	!$acc end kernels
[1]	479
	480	ELSE
	481	!
	482	!-- Dirichlet
	483	!$OMP PARALLEL DO
[1113]	484	!$acc kernels present( tend )
[667]	485	DO i = nxlg, nxrg
	486	DO j = nysg, nyng
[1342]	487	tend(nzb_s_inner(j,i),j,i) = 0.0_wp
[1]	488	ENDDO
	489	ENDDO
[1113]	490	!$acc end kernels
[1]	491
	492	ENDIF
	493
	494	!
	495	!-- Top boundary
	496	IF ( ibc_p_t == 1 ) THEN
	497	!
	498	!-- Neumann
	499	!$OMP PARALLEL DO
[1113]	500	!$acc kernels present( tend )
[667]	501	DO i = nxlg, nxrg
	502	DO j = nysg, nyng
[1]	503	tend(nzt+1,j,i) = tend(nzt,j,i)
	504	ENDDO
	505	ENDDO
[1113]	506	!$acc end kernels
[1]	507
	508	ELSE
	509	!
	510	!-- Dirichlet
	511	!$OMP PARALLEL DO
[1113]	512	!$acc kernels present( tend )
[667]	513	DO i = nxlg, nxrg
	514	DO j = nysg, nyng
[1342]	515	tend(nzt+1,j,i) = 0.0_wp
[1]	516	ENDDO
	517	ENDDO
[1113]	518	!$acc end kernels
[1]	519
	520	ENDIF
	521
	522	!
	523	!-- Exchange boundaries for p
[1113]	524	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
	525	on_device = .TRUE. ! to be removed after complete porting
	526	ELSE ! of ghost point exchange
	527	!$acc update host( tend )
	528	ENDIF
[667]	529	CALL exchange_horiz( tend, nbgp )
[1113]	530	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
	531	on_device = .FALSE. ! to be removed after complete porting
	532	ELSE ! of ghost point exchange
	533	!$acc update device( tend )
	534	ENDIF
[1]	535
	536	ELSEIF ( psolver == 'sor' ) THEN
	537
	538	!
	539	!-- Solve Poisson equation for perturbation pressure using SOR-Red/Black
	540	!-- scheme
[707]	541	CALL sor( d, ddzu_pres, ddzw, p_loc )
	542	tend = p_loc
[1]	543
[1575]	544	ELSEIF ( psolver(1:9) == 'multigrid' ) THEN
[1]	545
	546	!
	547	!-- Solve Poisson equation for perturbation pressure using Multigrid scheme,
[667]	548	!-- array tend is used to store the residuals, logical exchange_mg is used
	549	!-- to discern data exchange in multigrid ( 1 ghostpoint ) and normal grid
	550	!-- ( nbgp ghost points ).
[778]	551
	552	!-- If the number of grid points of the gathered grid, which is collected
	553	!-- on PE0, is larger than the number of grid points of an PE, than array
	554	!-- tend will be enlarged.
	555	IF ( gathered_size > subdomain_size ) THEN
	556	DEALLOCATE( tend )
	557	ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
	558	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
	559	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg( &
	560	mg_switch_to_pe0_level)+1) )
	561	ENDIF
	562
[1575]	563	IF ( psolver == 'multigrid' ) THEN
	564	CALL poismg( tend )
	565	ELSE
	566	CALL poismg_fast( tend )
	567	ENDIF
[707]	568
[778]	569	IF ( gathered_size > subdomain_size ) THEN
	570	DEALLOCATE( tend )
	571	ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
	572	ENDIF
	573
[1]	574	!
	575	!-- Restore perturbation pressure on tend because this array is used
	576	!-- further below to correct the velocity fields
[707]	577	DO i = nxl-1, nxr+1
	578	DO j = nys-1, nyn+1
	579	DO k = nzb, nzt+1
	580	tend(k,j,i) = p_loc(k,j,i)
	581	ENDDO
	582	ENDDO
	583	ENDDO
[667]	584
[1]	585	ENDIF
	586
	587	!
[707]	588	!-- Store perturbation pressure on array p, used for pressure data output.
	589	!-- Ghost layers are added in the output routines (except sor-method: see below)
[1918]	590	IF ( intermediate_timestep_count <= 1 ) THEN
[707]	591	!$OMP PARALLEL PRIVATE (i,j,k)
	592	!$OMP DO
[1113]	593	!$acc kernels present( p, tend, weight_substep )
[1257]	594	!$acc loop independent
[707]	595	DO i = nxl-1, nxr+1
[1257]	596	!$acc loop independent
[707]	597	DO j = nys-1, nyn+1
[1257]	598	!$acc loop independent
[707]	599	DO k = nzb, nzt+1
	600	p(k,j,i) = tend(k,j,i) * &
	601	weight_substep(intermediate_timestep_count)
[673]	602	ENDDO
[1]	603	ENDDO
[707]	604	ENDDO
[1113]	605	!$acc end kernels
[707]	606	!$OMP END PARALLEL
	607
[1762]	608	ELSEIF ( intermediate_timestep_count > 1 ) THEN
[707]	609	!$OMP PARALLEL PRIVATE (i,j,k)
	610	!$OMP DO
[1113]	611	!$acc kernels present( p, tend, weight_substep )
[1257]	612	!$acc loop independent
[707]	613	DO i = nxl-1, nxr+1
[1257]	614	!$acc loop independent
[707]	615	DO j = nys-1, nyn+1
[1257]	616	!$acc loop independent
[707]	617	DO k = nzb, nzt+1
	618	p(k,j,i) = p(k,j,i) + tend(k,j,i) * &
	619	weight_substep(intermediate_timestep_count)
[673]	620	ENDDO
	621	ENDDO
[707]	622	ENDDO
[1113]	623	!$acc end kernels
[707]	624	!$OMP END PARALLEL
	625
	626	ENDIF
[673]	627
[707]	628	!
	629	!-- SOR-method needs ghost layers for the next timestep
	630	IF ( psolver == 'sor' ) CALL exchange_horiz( p, nbgp )
[682]	631
[1]	632	!
	633	!-- Correction of the provisional velocities with the current perturbation
	634	!-- pressure just computed
[709]	635	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .OR. bc_ns_cyc ) ) THEN
[1342]	636	volume_flow_l(1) = 0.0_wp
	637	volume_flow_l(2) = 0.0_wp
[1]	638	ENDIF
[707]	639
[1]	640	!$OMP PARALLEL PRIVATE (i,j,k)
	641	!$OMP DO
[1918]	642	!$acc kernels present( ddzu, nzb_u_inner, nzb_v_inner, nzb_w_inner, tend, u, v, w )
[1257]	643	!$acc loop independent
[673]	644	DO i = nxl, nxr
[1257]	645	!$acc loop independent
[1]	646	DO j = nys, nyn
[1257]	647	!$acc loop independent
[1113]	648	DO k = 1, nzt
	649	IF ( k > nzb_w_inner(j,i) ) THEN
	650	w(k,j,i) = w(k,j,i) - dt_3d * &
	651	( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) * &
[1918]	652	weight_pres_l
[1113]	653	ENDIF
[1]	654	ENDDO
[1257]	655	!$acc loop independent
[1113]	656	DO k = 1, nzt
	657	IF ( k > nzb_u_inner(j,i) ) THEN
	658	u(k,j,i) = u(k,j,i) - dt_3d * &
	659	( tend(k,j,i) - tend(k,j,i-1) ) * ddx * &
[1918]	660	weight_pres_l
[1113]	661	ENDIF
[1]	662	ENDDO
[1257]	663	!$acc loop independent
[1113]	664	DO k = 1, nzt
	665	IF ( k > nzb_v_inner(j,i) ) THEN
	666	v(k,j,i) = v(k,j,i) - dt_3d * &
	667	( tend(k,j,i) - tend(k,j-1,i) ) * ddy * &
[1918]	668	weight_pres_l
[1113]	669	ENDIF
[673]	670	ENDDO
[1]	671
	672	ENDDO
	673	ENDDO
[1113]	674	!$acc end kernels
[1]	675	!$OMP END PARALLEL
[1113]	676
	677	!
	678	!-- Sum up the volume flow through the right and north boundary
	679	IF ( conserve_volume_flow .AND. bc_lr_cyc .AND. bc_ns_cyc .AND. &
	680	nxr == nx ) THEN
	681
	682	!$OMP PARALLEL PRIVATE (j,k)
	683	!$OMP DO
	684	DO j = nys, nyn
	685	!$OMP CRITICAL
[1845]	686	DO k = nzb_u_inner(j,nx) + 1, nzt
[1113]	687	volume_flow_l(1) = volume_flow_l(1) + u(k,j,nx) * dzw(k)
	688	ENDDO
	689	!$OMP END CRITICAL
	690	ENDDO
	691	!$OMP END PARALLEL
	692
	693	ENDIF
	694
	695	IF ( conserve_volume_flow .AND. bc_ns_cyc .AND. bc_lr_cyc .AND. &
	696	nyn == ny ) THEN
	697
	698	!$OMP PARALLEL PRIVATE (i,k)
	699	!$OMP DO
	700	DO i = nxl, nxr
	701	!$OMP CRITICAL
[1845]	702	DO k = nzb_v_inner(ny,i) + 1, nzt
[1113]	703	volume_flow_l(2) = volume_flow_l(2) + v(k,ny,i) * dzw(k)
	704	ENDDO
	705	!$OMP END CRITICAL
	706	ENDDO
	707	!$OMP END PARALLEL
	708
	709	ENDIF
[673]	710
[1]	711	!
	712	!-- Conserve the volume flow
[707]	713	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .AND. bc_ns_cyc ) ) THEN
[1]	714
	715	#if defined( __parallel )
[622]	716	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[1]	717	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, &
	718	MPI_SUM, comm2d, ierr )
	719	#else
	720	volume_flow = volume_flow_l
	721	#endif
	722
[1799]	723	volume_flow_offset(1:2) = ( volume_flow_initial(1:2) - volume_flow(1:2) ) / &
	724	volume_flow_area(1:2)
[1]	725
	726	!$OMP PARALLEL PRIVATE (i,j,k)
	727	!$OMP DO
	728	DO i = nxl, nxr
	729	DO j = nys, nyn
[667]	730	DO k = nzb_u_inner(j,i) + 1, nzt
	731	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
[719]	732	ENDDO
[1845]	733	DO k = nzb_v_inner(j,i) + 1, nzt
[667]	734	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
	735	ENDDO
[1]	736	ENDDO
	737	ENDDO
[667]	738
[1]	739	!$OMP END PARALLEL
	740
	741	ENDIF
	742
	743	!
	744	!-- Exchange of boundaries for the velocities
[1113]	745	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
	746	on_device = .TRUE. ! to be removed after complete porting
	747	ELSE ! of ghost point exchange
	748	!$acc update host( u, v, w )
	749	ENDIF
[667]	750	CALL exchange_horiz( u, nbgp )
	751	CALL exchange_horiz( v, nbgp )
	752	CALL exchange_horiz( w, nbgp )
[1113]	753	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
	754	on_device = .FALSE. ! to be removed after complete porting
	755	ELSE ! of ghost point exchange
	756	!$acc update device( u, v, w )
	757	ENDIF
[1]	758
	759	!
	760	!-- Compute the divergence of the corrected velocity field,
[1908]	761	!-- A possible PE-sum is computed in flow_statistics. Carry out computation
	762	!-- only at last Runge-Kutta step.
[1918]	763	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	764	intermediate_timestep_count == 0 ) THEN
[1908]	765	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
	766	sums_divnew_l = 0.0_wp
[1]	767
	768	!
[1908]	769	!-- d must be reset to zero because it can contain nonzero values below the
	770	!-- topography
	771	IF ( topography /= 'flat' ) d = 0.0_wp
[1]	772
[1908]	773	localsum = 0.0_wp
	774	threadsum = 0.0_wp
[1]	775
[1908]	776	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
	777	!$OMP DO SCHEDULE( STATIC )
[1]	778	#if defined( __ibm )
[1908]	779	DO i = nxl, nxr
	780	DO j = nys, nyn
	781	DO k = nzb_s_inner(j,i)+1, nzt
	782	d(k,j,i) = ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
	783	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
	784	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k)
	785	ENDDO
	786	DO k = nzb+1, nzt
	787	threadsum = threadsum + ABS( d(k,j,i) )
	788	ENDDO
[1]	789	ENDDO
	790	ENDDO
	791	#else
[1908]	792	!$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
	793	!$acc loop collapse( 3 )
	794	DO i = nxl, nxr
	795	DO j = nys, nyn
	796	DO k = 1, nzt
	797	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
	798	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
	799	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) &
	800	) * rflags_s_inner(k,j,i)
	801	ENDDO
[1113]	802	ENDDO
	803	ENDDO
[1908]	804	!$acc end kernels
[1113]	805	!
[1908]	806	!-- Compute possible PE-sum of divergences for flow_statistics
	807	!$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
	808	DO i = nxl, nxr
	809	DO j = nys, nyn
	810	DO k = nzb+1, nzt
	811	threadsum = threadsum + ABS( d(k,j,i) )
	812	ENDDO
[1]	813	ENDDO
	814	ENDDO
[1908]	815	!$acc end parallel loop
[1]	816	#endif
[667]	817
[1908]	818	localsum = localsum + threadsum
	819	!$OMP END PARALLEL
[1]	820
	821	!
[1908]	822	!-- For completeness, set the divergence sum of all statistic regions to those
	823	!-- of the total domain
	824	sums_divnew_l(0:statistic_regions) = localsum
[1]	825
[1908]	826	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
[1]	827
[1908]	828	ENDIF
	829
[1]	830	CALL cpu_log( log_point(8), 'pres', 'stop' )
	831
	832
	833	END SUBROUTINE pres

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