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source: palm/trunk/SOURCE/diffusion_u.f90 @ 1873

Last change on this file since 1873 was 1873, checked in by maronga, 8 years ago
revised renaming of modules
Property svn:keywords set to `Id`
File size: 26.8 KB

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

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