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source: palm/trunk/SOURCE/diffusion_u.f90 @ 2026

Last change on this file since 2026 was 2001, checked in by knoop, 8 years ago
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[1873]	1	!> @file diffusion_u.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	!
[1818]	17	! Copyright 1997-2016 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[484]	20	! Current revisions:
[1]	21	! -----------------
[1341]	22	!
[2001]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: diffusion_u.f90 2001 2016-08-20 18:41:22Z suehring $
	27	!
[2001]	28	! 2000 2016-08-20 18:09:15Z knoop
	29	! Forced header and separation lines into 80 columns
	30	!
[1874]	31	! 1873 2016-04-18 14:50:06Z maronga
	32	! Module renamed (removed _mod)
	33	!
	34	!
[1851]	35	! 1850 2016-04-08 13:29:27Z maronga
	36	! Module renamed
	37	!
	38	!
[1741]	39	! 1740 2016-01-13 08:19:40Z raasch
	40	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
	41	!
[1692]	42	! 1691 2015-10-26 16:17:44Z maronga
	43	! Formatting corrections.
	44	!
[1683]	45	! 1682 2015-10-07 23:56:08Z knoop
	46	! Code annotations made doxygen readable
	47	!
[1341]	48	! 1340 2014-03-25 19:45:13Z kanani
	49	! REAL constants defined as wp-kind
	50	!
[1321]	51	! 1320 2014-03-20 08:40:49Z raasch
[1320]	52	! ONLY-attribute added to USE-statements,
	53	! kind-parameters added to all INTEGER and REAL declaration statements,
	54	! kinds are defined in new module kinds,
	55	! revision history before 2012 removed,
	56	! comment fields (!:) to be used for variable explanations added to
	57	! all variable declaration statements
[1321]	58	!
[1258]	59	! 1257 2013-11-08 15:18:40Z raasch
	60	! openacc loop and loop vector clauses removed, declare create moved after
	61	! the FORTRAN declaration statement
	62	!
[1132]	63	! 1128 2013-04-12 06:19:32Z raasch
	64	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	65	! j_north
	66	!
[1037]	67	! 1036 2012-10-22 13:43:42Z raasch
	68	! code put under GPL (PALM 3.9)
	69	!
[1017]	70	! 1015 2012-09-27 09:23:24Z raasch
	71	! accelerator version (*_acc) added
	72	!
[1002]	73	! 1001 2012-09-13 14:08:46Z raasch
	74	! arrays comunicated by module instead of parameter list
	75	!
[979]	76	! 978 2012-08-09 08:28:32Z fricke
	77	! outflow damping layer removed
	78	! kmym_x/_y and kmyp_x/_y change to kmym and kmyp
	79	!
[1]	80	! Revision 1.1 1997/09/12 06:23:51 raasch
	81	! Initial revision
	82	!
	83	!
	84	! Description:
	85	! ------------
[1682]	86	!> Diffusion term of the u-component
	87	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
	88	!> and slows down the speed on NEC about 5-10%
[1]	89	!------------------------------------------------------------------------------!
[1682]	90	MODULE diffusion_u_mod
	91
[1]	92
[56]	93	USE wall_fluxes_mod
	94
[1]	95	PRIVATE
[1015]	96	PUBLIC diffusion_u, diffusion_u_acc
[1]	97
	98	INTERFACE diffusion_u
	99	MODULE PROCEDURE diffusion_u
	100	MODULE PROCEDURE diffusion_u_ij
	101	END INTERFACE diffusion_u
	102
[1015]	103	INTERFACE diffusion_u_acc
	104	MODULE PROCEDURE diffusion_u_acc
	105	END INTERFACE diffusion_u_acc
	106
[1]	107	CONTAINS
	108
	109
	110	!------------------------------------------------------------------------------!
[1682]	111	! Description:
	112	! ------------
	113	!> Call for all grid points
[1]	114	!------------------------------------------------------------------------------!
[1001]	115	SUBROUTINE diffusion_u
[1]	116
[1320]	117	USE arrays_3d, &
	118	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w
	119
	120	USE control_parameters, &
	121	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	122	use_top_fluxes
	123
	124	USE grid_variables, &
	125	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	126
	127	USE indices, &
	128	ONLY: nxl, nxlu, nxr, nyn, nys, nzb, nzb_diff_u, nzb_u_inner, &
	129	nzb_u_outer, nzt, nzt_diff
	130
	131	USE kinds
[1]	132
	133	IMPLICIT NONE
	134
[1682]	135	INTEGER(iwp) :: i !<
	136	INTEGER(iwp) :: j !<
	137	INTEGER(iwp) :: k !<
	138	REAL(wp) :: kmym !<
	139	REAL(wp) :: kmyp !<
	140	REAL(wp) :: kmzm !<
	141	REAL(wp) :: kmzp !<
[1001]	142
[1682]	143	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs !<
[1]	144
[56]	145	!
	146	!-- First calculate horizontal momentum flux u'v' at vertical walls,
	147	!-- if neccessary
	148	IF ( topography /= 'flat' ) THEN
[1320]	149	CALL wall_fluxes( usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, nzb_u_inner, &
[56]	150	nzb_u_outer, wall_u )
	151	ENDIF
	152
[106]	153	DO i = nxlu, nxr
[1001]	154	DO j = nys, nyn
[1]	155	!
	156	!-- Compute horizontal diffusion
	157	DO k = nzb_u_outer(j,i)+1, nzt
	158	!
	159	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	160	kmyp = 0.25_wp * &
[978]	161	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	162	kmym = 0.25_wp * &
[978]	163	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	164
[1320]	165	tend(k,j,i) = tend(k,j,i) &
[1340]	166	& + 2.0_wp * ( &
[1320]	167	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	168	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	169	& ) * ddx2 &
[1320]	170	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	171	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	172	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	173	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	174	& ) * ddy
	175	ENDDO
	176
	177	!
	178	!-- Wall functions at the north and south walls, respectively
[1340]	179	IF ( wall_u(j,i) /= 0.0_wp ) THEN
[51]	180
[1]	181	DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i)
[1340]	182	kmyp = 0.25_wp * &
[978]	183	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	184	kmym = 0.25_wp * &
[978]	185	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	186
	187	tend(k,j,i) = tend(k,j,i) &
[1340]	188	+ 2.0_wp * ( &
[1]	189	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	190	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	191	) * ddx2 &
[1]	192	+ ( fyp(j,i) * ( &
[978]	193	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	194	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
[1]	195	) &
	196	- fym(j,i) * ( &
[978]	197	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	198	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	199	) &
[56]	200	+ wall_u(j,i) * usvs(k,j,i) &
[1]	201	) * ddy
	202	ENDDO
	203	ENDIF
	204
	205	!
	206	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	207	!-- index k starts at nzb_u_inner+2.
[102]	208	DO k = nzb_diff_u(j,i), nzt_diff
[1]	209	!
	210	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	211	kmzp = 0.25_wp * &
[1]	212	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	213	kmzm = 0.25_wp * &
[1]	214	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	215
[1320]	216	tend(k,j,i) = tend(k,j,i) &
	217	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	218	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	219	& ) &
	220	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	221	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	222	& ) &
[1]	223	& ) * ddzw(k)
	224	ENDDO
	225
	226	!
	227	!-- Vertical diffusion at the first grid point above the surface,
	228	!-- if the momentum flux at the bottom is given by the Prandtl law or
	229	!-- if it is prescribed by the user.
	230	!-- Difference quotient of the momentum flux is not formed over half
	231	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	232	!-- with other (LES) models showed that the values of the momentum
[1]	233	!-- flux becomes too large in this case.
	234	!-- The term containing w(k-1,..) (see above equation) is removed here
	235	!-- because the vertical velocity is assumed to be zero at the surface.
	236	IF ( use_surface_fluxes ) THEN
	237	k = nzb_u_inner(j,i)+1
	238	!
	239	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	240	kmzp = 0.25_wp * &
[1]	241	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	242
[1320]	243	tend(k,j,i) = tend(k,j,i) &
	244	& + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	245	& ) * ddzw(k) &
	246	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	247	& + usws(j,i) &
[1]	248	& ) * ddzw(k)
	249	ENDIF
	250
[102]	251	!
	252	!-- Vertical diffusion at the first gridpoint below the top boundary,
	253	!-- if the momentum flux at the top is prescribed by the user
[103]	254	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	255	k = nzt
	256	!
	257	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	258	kmzm = 0.25_wp * &
[102]	259	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	260
[1320]	261	tend(k,j,i) = tend(k,j,i) &
	262	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	263	& ) * ddzw(k) &
	264	& + ( -uswst(j,i) &
	265	& - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
[102]	266	& ) * ddzw(k)
	267	ENDIF
	268
[1]	269	ENDDO
	270	ENDDO
	271
	272	END SUBROUTINE diffusion_u
	273
	274
	275	!------------------------------------------------------------------------------!
[1682]	276	! Description:
	277	! ------------
	278	!> Call for all grid points - accelerator version
[1015]	279	!------------------------------------------------------------------------------!
	280	SUBROUTINE diffusion_u_acc
	281
[1320]	282	USE arrays_3d, &
	283	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w
	284
	285	USE control_parameters, &
	286	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	287	use_top_fluxes
	288
	289	USE grid_variables, &
	290	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	291
	292	USE indices, &
	293	ONLY: i_left, i_right, j_north, j_south, nxl, nxr, nyn, nys, nzb, &
	294	nzb_diff_u, nzb_u_inner, nzb_u_outer, nzt, nzt_diff
	295
	296	USE kinds
[1015]	297
	298	IMPLICIT NONE
	299
[1682]	300	INTEGER(iwp) :: i !<
	301	INTEGER(iwp) :: j !<
	302	INTEGER(iwp) :: k !<
	303	REAL(wp) :: kmym !<
	304	REAL(wp) :: kmyp !<
	305	REAL(wp) :: kmzm !<
	306	REAL(wp) :: kmzp !<
[1015]	307
[1682]	308	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs !<
[1015]	309	!$acc declare create ( usvs )
	310
	311	!
	312	!-- First calculate horizontal momentum flux u'v' at vertical walls,
	313	!-- if neccessary
	314	IF ( topography /= 'flat' ) THEN
[1320]	315	CALL wall_fluxes_acc( usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
	316	nzb_u_inner, nzb_u_outer, wall_u )
[1015]	317	ENDIF
	318
[1320]	319	!$acc kernels present ( u, v, w, km, tend, usws, uswst ) &
	320	!$acc present ( ddzu, ddzw, fym, fyp, wall_u ) &
[1015]	321	!$acc present ( nzb_u_inner, nzb_u_outer, nzb_diff_u )
[1128]	322	DO i = i_left, i_right
	323	DO j = j_south, j_north
[1015]	324	!
	325	!-- Compute horizontal diffusion
	326	DO k = 1, nzt
	327	IF ( k > nzb_u_outer(j,i) ) THEN
	328	!
	329	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	330	kmyp = 0.25_wp * &
[1015]	331	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	332	kmym = 0.25_wp * &
[1015]	333	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
	334
	335	tend(k,j,i) = tend(k,j,i) &
[1340]	336	& + 2.0_wp * ( &
[1015]	337	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	338	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	339	& ) * ddx2 &
[1015]	340	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	341	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	342	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	343	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	344	& ) * ddy
	345	ENDIF
	346	ENDDO
	347
	348	!
	349	!-- Wall functions at the north and south walls, respectively
	350	DO k = 1, nzt
[1320]	351	IF( k > nzb_u_inner(j,i) .AND. k <= nzb_u_outer(j,i) .AND. &
[1340]	352	wall_u(j,i) /= 0.0_wp ) THEN
[1015]	353
[1340]	354	kmyp = 0.25_wp * &
[1015]	355	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	356	kmym = 0.25_wp * &
[1015]	357	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
	358
	359	tend(k,j,i) = tend(k,j,i) &
[1340]	360	+ 2.0_wp * ( &
[1015]	361	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	362	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	363	) * ddx2 &
[1015]	364	+ ( fyp(j,i) * ( &
	365	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	366	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	367	) &
	368	- fym(j,i) * ( &
	369	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	370	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	371	) &
	372	+ wall_u(j,i) * usvs(k,j,i) &
	373	) * ddy
	374	ENDIF
	375	ENDDO
	376
	377	!
	378	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	379	!-- index k starts at nzb_u_inner+2.
	380	DO k = 1, nzt_diff
	381	IF ( k >= nzb_diff_u(j,i) ) THEN
	382	!
	383	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	384	kmzp = 0.25_wp * &
[1015]	385	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	386	kmzm = 0.25_wp * &
[1015]	387	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	388
	389	tend(k,j,i) = tend(k,j,i) &
	390	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1)&
	391	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	392	& ) &
	393	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k)&
	394	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	395	& ) &
	396	& ) * ddzw(k)
	397	ENDIF
	398	ENDDO
	399
	400	ENDDO
	401	ENDDO
	402
	403	!
	404	!-- Vertical diffusion at the first grid point above the surface,
	405	!-- if the momentum flux at the bottom is given by the Prandtl law or
	406	!-- if it is prescribed by the user.
	407	!-- Difference quotient of the momentum flux is not formed over half
	408	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	409	!-- with other (LES) models showed that the values of the momentum
[1015]	410	!-- flux becomes too large in this case.
	411	!-- The term containing w(k-1,..) (see above equation) is removed here
	412	!-- because the vertical velocity is assumed to be zero at the surface.
	413	IF ( use_surface_fluxes ) THEN
	414
[1128]	415	DO i = i_left, i_right
	416	DO j = j_south, j_north
[1015]	417
	418	k = nzb_u_inner(j,i)+1
	419	!
	420	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	421	kmzp = 0.25_wp * &
[1015]	422	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	423
[1320]	424	tend(k,j,i) = tend(k,j,i) &
	425	& + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	426	& ) * ddzw(k) &
	427	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	428	& + usws(j,i) &
[1015]	429	& ) * ddzw(k)
	430	ENDDO
	431	ENDDO
	432
	433	ENDIF
	434
	435	!
	436	!-- Vertical diffusion at the first gridpoint below the top boundary,
	437	!-- if the momentum flux at the top is prescribed by the user
	438	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
	439
	440	k = nzt
	441
[1128]	442	DO i = i_left, i_right
	443	DO j = j_south, j_north
[1015]	444
	445	!
	446	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	447	kmzm = 0.25_wp * &
[1015]	448	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	449
[1320]	450	tend(k,j,i) = tend(k,j,i) &
	451	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	452	& ) * ddzw(k) &
	453	& + ( -uswst(j,i) &
	454	& - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
[1015]	455	& ) * ddzw(k)
	456	ENDDO
	457	ENDDO
	458
	459	ENDIF
	460	!$acc end kernels
	461
	462	END SUBROUTINE diffusion_u_acc
	463
	464
	465	!------------------------------------------------------------------------------!
[1682]	466	! Description:
	467	! ------------
	468	!> Call for grid point i,j
[1]	469	!------------------------------------------------------------------------------!
[1001]	470	SUBROUTINE diffusion_u_ij( i, j )
[1]	471
[1320]	472	USE arrays_3d, &
	473	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w
	474
	475	USE control_parameters, &
	476	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
	477
	478	USE grid_variables, &
	479	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	480
	481	USE indices, &
	482	ONLY: nzb, nzb_diff_u, nzb_u_inner, nzb_u_outer, nzt, nzt_diff
	483
	484	USE kinds
[1]	485
	486	IMPLICIT NONE
	487
[1682]	488	INTEGER(iwp) :: i !<
	489	INTEGER(iwp) :: j !<
	490	INTEGER(iwp) :: k !<
	491	REAL(wp) :: kmym !<
	492	REAL(wp) :: kmyp !<
	493	REAL(wp) :: kmzm !<
	494	REAL(wp) :: kmzp !<
[1]	495
[1682]	496	REAL(wp), DIMENSION(nzb:nzt+1) :: usvs !<
[1001]	497
[1]	498	!
	499	!-- Compute horizontal diffusion
	500	DO k = nzb_u_outer(j,i)+1, nzt
	501	!
	502	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	503	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	504	kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	505
[1320]	506	tend(k,j,i) = tend(k,j,i) &
[1340]	507	& + 2.0_wp * ( &
[1320]	508	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	509	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	510	& ) * ddx2 &
[1320]	511	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	512	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	513	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	514	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	515	& ) * ddy
	516	ENDDO
	517
	518	!
	519	!-- Wall functions at the north and south walls, respectively
[1691]	520	IF ( wall_u(j,i) /= 0.0_wp ) THEN
[51]	521
	522	!
	523	!-- Calculate the horizontal momentum flux u'v'
[1320]	524	CALL wall_fluxes( i, j, nzb_u_inner(j,i)+1, nzb_u_outer(j,i), &
	525	usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
[51]	526
[1]	527	DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i)
[1340]	528	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	529	kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	530
	531	tend(k,j,i) = tend(k,j,i) &
[1340]	532	+ 2.0_wp * ( &
[1]	533	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	534	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	535	) * ddx2 &
[1]	536	+ ( fyp(j,i) * ( &
[978]	537	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	538	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
[1]	539	) &
	540	- fym(j,i) * ( &
[978]	541	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	542	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	543	) &
[51]	544	+ wall_u(j,i) * usvs(k) &
[1]	545	) * ddy
	546	ENDDO
	547	ENDIF
	548
	549	!
	550	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	551	!-- index k starts at nzb_u_inner+2.
[102]	552	DO k = nzb_diff_u(j,i), nzt_diff
[1]	553	!
	554	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	555	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	556	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
[1]	557
[1320]	558	tend(k,j,i) = tend(k,j,i) &
	559	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	560	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	561	& ) &
	562	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	563	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	564	& ) &
[1]	565	& ) * ddzw(k)
	566	ENDDO
	567
	568	!
	569	!-- Vertical diffusion at the first grid point above the surface, if the
	570	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	571	!-- prescribed by the user.
	572	!-- Difference quotient of the momentum flux is not formed over half of
	573	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	574	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	575	!-- too large in this case.
	576	!-- The term containing w(k-1,..) (see above equation) is removed here
	577	!-- because the vertical velocity is assumed to be zero at the surface.
	578	IF ( use_surface_fluxes ) THEN
	579	k = nzb_u_inner(j,i)+1
	580	!
	581	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	582	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1]	583
[1320]	584	tend(k,j,i) = tend(k,j,i) &
	585	& + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	586	& ) * ddzw(k) &
	587	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	588	& + usws(j,i) &
[1]	589	& ) * ddzw(k)
	590	ENDIF
	591
[102]	592	!
	593	!-- Vertical diffusion at the first gridpoint below the top boundary,
	594	!-- if the momentum flux at the top is prescribed by the user
[103]	595	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	596	k = nzt
	597	!
	598	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	599	kmzm = 0.25_wp * &
[102]	600	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	601
[1320]	602	tend(k,j,i) = tend(k,j,i) &
	603	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	604	& ) * ddzw(k) &
	605	& + ( -uswst(j,i) &
	606	& - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
[102]	607	& ) * ddzw(k)
	608	ENDIF
	609
[1]	610	END SUBROUTINE diffusion_u_ij
	611
	612	END MODULE diffusion_u_mod

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