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source: palm/trunk/SOURCE/diffusion_u.f90 @ 1801

Last change on this file since 1801 was 1741, checked in by raasch, 9 years ago
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[1682]	1	!> @file diffusion_u.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	!
[1691]	16	! Copyright 1997-2015 Leibniz Universitaet Hannover
[1036]	17	!--------------------------------------------------------------------------------!
	18	!
[484]	19	! Current revisions:
[1]	20	! -----------------
[1341]	21	!
[1741]	22	!
[1321]	23	! Former revisions:
	24	! -----------------
	25	! $Id: diffusion_u.f90 1741 2016-01-13 08:32:52Z raasch $
	26	!
[1741]	27	! 1740 2016-01-13 08:19:40Z raasch
	28	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
	29	!
[1692]	30	! 1691 2015-10-26 16:17:44Z maronga
	31	! Formatting corrections.
	32	!
[1683]	33	! 1682 2015-10-07 23:56:08Z knoop
	34	! Code annotations made doxygen readable
	35	!
[1341]	36	! 1340 2014-03-25 19:45:13Z kanani
	37	! REAL constants defined as wp-kind
	38	!
[1321]	39	! 1320 2014-03-20 08:40:49Z raasch
[1320]	40	! ONLY-attribute added to USE-statements,
	41	! kind-parameters added to all INTEGER and REAL declaration statements,
	42	! kinds are defined in new module kinds,
	43	! revision history before 2012 removed,
	44	! comment fields (!:) to be used for variable explanations added to
	45	! all variable declaration statements
[1321]	46	!
[1258]	47	! 1257 2013-11-08 15:18:40Z raasch
	48	! openacc loop and loop vector clauses removed, declare create moved after
	49	! the FORTRAN declaration statement
	50	!
[1132]	51	! 1128 2013-04-12 06:19:32Z raasch
	52	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	53	! j_north
	54	!
[1037]	55	! 1036 2012-10-22 13:43:42Z raasch
	56	! code put under GPL (PALM 3.9)
	57	!
[1017]	58	! 1015 2012-09-27 09:23:24Z raasch
	59	! accelerator version (*_acc) added
	60	!
[1002]	61	! 1001 2012-09-13 14:08:46Z raasch
	62	! arrays comunicated by module instead of parameter list
	63	!
[979]	64	! 978 2012-08-09 08:28:32Z fricke
	65	! outflow damping layer removed
	66	! kmym_x/_y and kmyp_x/_y change to kmym and kmyp
	67	!
[1]	68	! Revision 1.1 1997/09/12 06:23:51 raasch
	69	! Initial revision
	70	!
	71	!
	72	! Description:
	73	! ------------
[1682]	74	!> Diffusion term of the u-component
	75	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
	76	!> and slows down the speed on NEC about 5-10%
[1]	77	!------------------------------------------------------------------------------!
[1682]	78	MODULE diffusion_u_mod
	79
[1]	80
[56]	81	USE wall_fluxes_mod
	82
[1]	83	PRIVATE
[1015]	84	PUBLIC diffusion_u, diffusion_u_acc
[1]	85
	86	INTERFACE diffusion_u
	87	MODULE PROCEDURE diffusion_u
	88	MODULE PROCEDURE diffusion_u_ij
	89	END INTERFACE diffusion_u
	90
[1015]	91	INTERFACE diffusion_u_acc
	92	MODULE PROCEDURE diffusion_u_acc
	93	END INTERFACE diffusion_u_acc
	94
[1]	95	CONTAINS
	96
	97
	98	!------------------------------------------------------------------------------!
[1682]	99	! Description:
	100	! ------------
	101	!> Call for all grid points
[1]	102	!------------------------------------------------------------------------------!
[1001]	103	SUBROUTINE diffusion_u
[1]	104
[1320]	105	USE arrays_3d, &
	106	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w
	107
	108	USE control_parameters, &
	109	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	110	use_top_fluxes
	111
	112	USE grid_variables, &
	113	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	114
	115	USE indices, &
	116	ONLY: nxl, nxlu, nxr, nyn, nys, nzb, nzb_diff_u, nzb_u_inner, &
	117	nzb_u_outer, nzt, nzt_diff
	118
	119	USE kinds
[1]	120
	121	IMPLICIT NONE
	122
[1682]	123	INTEGER(iwp) :: i !<
	124	INTEGER(iwp) :: j !<
	125	INTEGER(iwp) :: k !<
	126	REAL(wp) :: kmym !<
	127	REAL(wp) :: kmyp !<
	128	REAL(wp) :: kmzm !<
	129	REAL(wp) :: kmzp !<
[1001]	130
[1682]	131	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs !<
[1]	132
[56]	133	!
	134	!-- First calculate horizontal momentum flux u'v' at vertical walls,
	135	!-- if neccessary
	136	IF ( topography /= 'flat' ) THEN
[1320]	137	CALL wall_fluxes( usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, nzb_u_inner, &
[56]	138	nzb_u_outer, wall_u )
	139	ENDIF
	140
[106]	141	DO i = nxlu, nxr
[1001]	142	DO j = nys, nyn
[1]	143	!
	144	!-- Compute horizontal diffusion
	145	DO k = nzb_u_outer(j,i)+1, nzt
	146	!
	147	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	148	kmyp = 0.25_wp * &
[978]	149	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	150	kmym = 0.25_wp * &
[978]	151	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	152
[1320]	153	tend(k,j,i) = tend(k,j,i) &
[1340]	154	& + 2.0_wp * ( &
[1320]	155	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	156	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	157	& ) * ddx2 &
[1320]	158	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	159	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	160	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	161	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	162	& ) * ddy
	163	ENDDO
	164
	165	!
	166	!-- Wall functions at the north and south walls, respectively
[1340]	167	IF ( wall_u(j,i) /= 0.0_wp ) THEN
[51]	168
[1]	169	DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i)
[1340]	170	kmyp = 0.25_wp * &
[978]	171	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	172	kmym = 0.25_wp * &
[978]	173	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	174
	175	tend(k,j,i) = tend(k,j,i) &
[1340]	176	+ 2.0_wp * ( &
[1]	177	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	178	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	179	) * ddx2 &
[1]	180	+ ( fyp(j,i) * ( &
[978]	181	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	182	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
[1]	183	) &
	184	- fym(j,i) * ( &
[978]	185	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	186	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	187	) &
[56]	188	+ wall_u(j,i) * usvs(k,j,i) &
[1]	189	) * ddy
	190	ENDDO
	191	ENDIF
	192
	193	!
	194	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	195	!-- index k starts at nzb_u_inner+2.
[102]	196	DO k = nzb_diff_u(j,i), nzt_diff
[1]	197	!
	198	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	199	kmzp = 0.25_wp * &
[1]	200	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	201	kmzm = 0.25_wp * &
[1]	202	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	203
[1320]	204	tend(k,j,i) = tend(k,j,i) &
	205	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	206	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	207	& ) &
	208	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	209	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	210	& ) &
[1]	211	& ) * ddzw(k)
	212	ENDDO
	213
	214	!
	215	!-- Vertical diffusion at the first grid point above the surface,
	216	!-- if the momentum flux at the bottom is given by the Prandtl law or
	217	!-- if it is prescribed by the user.
	218	!-- Difference quotient of the momentum flux is not formed over half
	219	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	220	!-- with other (LES) models showed that the values of the momentum
[1]	221	!-- flux becomes too large in this case.
	222	!-- The term containing w(k-1,..) (see above equation) is removed here
	223	!-- because the vertical velocity is assumed to be zero at the surface.
	224	IF ( use_surface_fluxes ) THEN
	225	k = nzb_u_inner(j,i)+1
	226	!
	227	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	228	kmzp = 0.25_wp * &
[1]	229	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	230
[1320]	231	tend(k,j,i) = tend(k,j,i) &
	232	& + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	233	& ) * ddzw(k) &
	234	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	235	& + usws(j,i) &
[1]	236	& ) * ddzw(k)
	237	ENDIF
	238
[102]	239	!
	240	!-- Vertical diffusion at the first gridpoint below the top boundary,
	241	!-- if the momentum flux at the top is prescribed by the user
[103]	242	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	243	k = nzt
	244	!
	245	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	246	kmzm = 0.25_wp * &
[102]	247	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	248
[1320]	249	tend(k,j,i) = tend(k,j,i) &
	250	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	251	& ) * ddzw(k) &
	252	& + ( -uswst(j,i) &
	253	& - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
[102]	254	& ) * ddzw(k)
	255	ENDIF
	256
[1]	257	ENDDO
	258	ENDDO
	259
	260	END SUBROUTINE diffusion_u
	261
	262
	263	!------------------------------------------------------------------------------!
[1682]	264	! Description:
	265	! ------------
	266	!> Call for all grid points - accelerator version
[1015]	267	!------------------------------------------------------------------------------!
	268	SUBROUTINE diffusion_u_acc
	269
[1320]	270	USE arrays_3d, &
	271	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w
	272
	273	USE control_parameters, &
	274	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	275	use_top_fluxes
	276
	277	USE grid_variables, &
	278	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	279
	280	USE indices, &
	281	ONLY: i_left, i_right, j_north, j_south, nxl, nxr, nyn, nys, nzb, &
	282	nzb_diff_u, nzb_u_inner, nzb_u_outer, nzt, nzt_diff
	283
	284	USE kinds
[1015]	285
	286	IMPLICIT NONE
	287
[1682]	288	INTEGER(iwp) :: i !<
	289	INTEGER(iwp) :: j !<
	290	INTEGER(iwp) :: k !<
	291	REAL(wp) :: kmym !<
	292	REAL(wp) :: kmyp !<
	293	REAL(wp) :: kmzm !<
	294	REAL(wp) :: kmzp !<
[1015]	295
[1682]	296	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs !<
[1015]	297	!$acc declare create ( usvs )
	298
	299	!
	300	!-- First calculate horizontal momentum flux u'v' at vertical walls,
	301	!-- if neccessary
	302	IF ( topography /= 'flat' ) THEN
[1320]	303	CALL wall_fluxes_acc( usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
	304	nzb_u_inner, nzb_u_outer, wall_u )
[1015]	305	ENDIF
	306
[1320]	307	!$acc kernels present ( u, v, w, km, tend, usws, uswst ) &
	308	!$acc present ( ddzu, ddzw, fym, fyp, wall_u ) &
[1015]	309	!$acc present ( nzb_u_inner, nzb_u_outer, nzb_diff_u )
[1128]	310	DO i = i_left, i_right
	311	DO j = j_south, j_north
[1015]	312	!
	313	!-- Compute horizontal diffusion
	314	DO k = 1, nzt
	315	IF ( k > nzb_u_outer(j,i) ) THEN
	316	!
	317	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	318	kmyp = 0.25_wp * &
[1015]	319	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	320	kmym = 0.25_wp * &
[1015]	321	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
	322
	323	tend(k,j,i) = tend(k,j,i) &
[1340]	324	& + 2.0_wp * ( &
[1015]	325	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	326	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	327	& ) * ddx2 &
[1015]	328	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	329	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	330	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	331	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	332	& ) * ddy
	333	ENDIF
	334	ENDDO
	335
	336	!
	337	!-- Wall functions at the north and south walls, respectively
	338	DO k = 1, nzt
[1320]	339	IF( k > nzb_u_inner(j,i) .AND. k <= nzb_u_outer(j,i) .AND. &
[1340]	340	wall_u(j,i) /= 0.0_wp ) THEN
[1015]	341
[1340]	342	kmyp = 0.25_wp * &
[1015]	343	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	344	kmym = 0.25_wp * &
[1015]	345	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
	346
	347	tend(k,j,i) = tend(k,j,i) &
[1340]	348	+ 2.0_wp * ( &
[1015]	349	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	350	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	351	) * ddx2 &
[1015]	352	+ ( fyp(j,i) * ( &
	353	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	354	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	355	) &
	356	- fym(j,i) * ( &
	357	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	358	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	359	) &
	360	+ wall_u(j,i) * usvs(k,j,i) &
	361	) * ddy
	362	ENDIF
	363	ENDDO
	364
	365	!
	366	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	367	!-- index k starts at nzb_u_inner+2.
	368	DO k = 1, nzt_diff
	369	IF ( k >= nzb_diff_u(j,i) ) THEN
	370	!
	371	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	372	kmzp = 0.25_wp * &
[1015]	373	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	374	kmzm = 0.25_wp * &
[1015]	375	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	376
	377	tend(k,j,i) = tend(k,j,i) &
	378	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1)&
	379	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	380	& ) &
	381	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k)&
	382	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	383	& ) &
	384	& ) * ddzw(k)
	385	ENDIF
	386	ENDDO
	387
	388	ENDDO
	389	ENDDO
	390
	391	!
	392	!-- Vertical diffusion at the first grid point above the surface,
	393	!-- if the momentum flux at the bottom is given by the Prandtl law or
	394	!-- if it is prescribed by the user.
	395	!-- Difference quotient of the momentum flux is not formed over half
	396	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	397	!-- with other (LES) models showed that the values of the momentum
[1015]	398	!-- flux becomes too large in this case.
	399	!-- The term containing w(k-1,..) (see above equation) is removed here
	400	!-- because the vertical velocity is assumed to be zero at the surface.
	401	IF ( use_surface_fluxes ) THEN
	402
[1128]	403	DO i = i_left, i_right
	404	DO j = j_south, j_north
[1015]	405
	406	k = nzb_u_inner(j,i)+1
	407	!
	408	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	409	kmzp = 0.25_wp * &
[1015]	410	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	411
[1320]	412	tend(k,j,i) = tend(k,j,i) &
	413	& + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	414	& ) * ddzw(k) &
	415	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	416	& + usws(j,i) &
[1015]	417	& ) * ddzw(k)
	418	ENDDO
	419	ENDDO
	420
	421	ENDIF
	422
	423	!
	424	!-- Vertical diffusion at the first gridpoint below the top boundary,
	425	!-- if the momentum flux at the top is prescribed by the user
	426	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
	427
	428	k = nzt
	429
[1128]	430	DO i = i_left, i_right
	431	DO j = j_south, j_north
[1015]	432
	433	!
	434	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	435	kmzm = 0.25_wp * &
[1015]	436	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	437
[1320]	438	tend(k,j,i) = tend(k,j,i) &
	439	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	440	& ) * ddzw(k) &
	441	& + ( -uswst(j,i) &
	442	& - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
[1015]	443	& ) * ddzw(k)
	444	ENDDO
	445	ENDDO
	446
	447	ENDIF
	448	!$acc end kernels
	449
	450	END SUBROUTINE diffusion_u_acc
	451
	452
	453	!------------------------------------------------------------------------------!
[1682]	454	! Description:
	455	! ------------
	456	!> Call for grid point i,j
[1]	457	!------------------------------------------------------------------------------!
[1001]	458	SUBROUTINE diffusion_u_ij( i, j )
[1]	459
[1320]	460	USE arrays_3d, &
	461	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w
	462
	463	USE control_parameters, &
	464	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
	465
	466	USE grid_variables, &
	467	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	468
	469	USE indices, &
	470	ONLY: nzb, nzb_diff_u, nzb_u_inner, nzb_u_outer, nzt, nzt_diff
	471
	472	USE kinds
[1]	473
	474	IMPLICIT NONE
	475
[1682]	476	INTEGER(iwp) :: i !<
	477	INTEGER(iwp) :: j !<
	478	INTEGER(iwp) :: k !<
	479	REAL(wp) :: kmym !<
	480	REAL(wp) :: kmyp !<
	481	REAL(wp) :: kmzm !<
	482	REAL(wp) :: kmzp !<
[1]	483
[1682]	484	REAL(wp), DIMENSION(nzb:nzt+1) :: usvs !<
[1001]	485
[1]	486	!
	487	!-- Compute horizontal diffusion
	488	DO k = nzb_u_outer(j,i)+1, nzt
	489	!
	490	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	491	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	492	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]	493
[1320]	494	tend(k,j,i) = tend(k,j,i) &
[1340]	495	& + 2.0_wp * ( &
[1320]	496	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	497	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	498	& ) * ddx2 &
[1320]	499	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	500	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	501	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	502	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	503	& ) * ddy
	504	ENDDO
	505
	506	!
	507	!-- Wall functions at the north and south walls, respectively
[1691]	508	IF ( wall_u(j,i) /= 0.0_wp ) THEN
[51]	509
	510	!
	511	!-- Calculate the horizontal momentum flux u'v'
[1320]	512	CALL wall_fluxes( i, j, nzb_u_inner(j,i)+1, nzb_u_outer(j,i), &
	513	usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
[51]	514
[1]	515	DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i)
[1340]	516	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	517	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]	518
	519	tend(k,j,i) = tend(k,j,i) &
[1340]	520	+ 2.0_wp * ( &
[1]	521	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	522	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	523	) * ddx2 &
[1]	524	+ ( fyp(j,i) * ( &
[978]	525	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	526	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
[1]	527	) &
	528	- fym(j,i) * ( &
[978]	529	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	530	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	531	) &
[51]	532	+ wall_u(j,i) * usvs(k) &
[1]	533	) * ddy
	534	ENDDO
	535	ENDIF
	536
	537	!
	538	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	539	!-- index k starts at nzb_u_inner+2.
[102]	540	DO k = nzb_diff_u(j,i), nzt_diff
[1]	541	!
	542	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	543	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	544	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]	545
[1320]	546	tend(k,j,i) = tend(k,j,i) &
	547	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	548	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	549	& ) &
	550	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	551	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	552	& ) &
[1]	553	& ) * ddzw(k)
	554	ENDDO
	555
	556	!
	557	!-- Vertical diffusion at the first grid point above the surface, if the
	558	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	559	!-- prescribed by the user.
	560	!-- Difference quotient of the momentum flux is not formed over half of
	561	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	562	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	563	!-- too large in this case.
	564	!-- The term containing w(k-1,..) (see above equation) is removed here
	565	!-- because the vertical velocity is assumed to be zero at the surface.
	566	IF ( use_surface_fluxes ) THEN
	567	k = nzb_u_inner(j,i)+1
	568	!
	569	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	570	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]	571
[1320]	572	tend(k,j,i) = tend(k,j,i) &
	573	& + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	574	& ) * ddzw(k) &
	575	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	576	& + usws(j,i) &
[1]	577	& ) * ddzw(k)
	578	ENDIF
	579
[102]	580	!
	581	!-- Vertical diffusion at the first gridpoint below the top boundary,
	582	!-- if the momentum flux at the top is prescribed by the user
[103]	583	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	584	k = nzt
	585	!
	586	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	587	kmzm = 0.25_wp * &
[102]	588	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	589
[1320]	590	tend(k,j,i) = tend(k,j,i) &
	591	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	592	& ) * ddzw(k) &
	593	& + ( -uswst(j,i) &
	594	& - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
[102]	595	& ) * ddzw(k)
	596	ENDIF
	597
[1]	598	END SUBROUTINE diffusion_u_ij
	599
	600	END MODULE diffusion_u_mod

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