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source: palm/trunk/SOURCE/diffusion_u.f90 @ 1948

Last change on this file since 1948 was 1874, checked in by maronga, 9 years ago
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[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	! -----------------
[1341]	21	!
[1851]	22	!
[1321]	23	! Former revisions:
	24	! -----------------
	25	! $Id: diffusion_u.f90 1874 2016-04-18 14:51:10Z maronga $
	26	!
[1874]	27	! 1873 2016-04-18 14:50:06Z maronga
	28	! Module renamed (removed _mod)
	29	!
	30	!
[1851]	31	! 1850 2016-04-08 13:29:27Z maronga
	32	! Module renamed
	33	!
	34	!
[1741]	35	! 1740 2016-01-13 08:19:40Z raasch
	36	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
	37	!
[1692]	38	! 1691 2015-10-26 16:17:44Z maronga
	39	! Formatting corrections.
	40	!
[1683]	41	! 1682 2015-10-07 23:56:08Z knoop
	42	! Code annotations made doxygen readable
	43	!
[1341]	44	! 1340 2014-03-25 19:45:13Z kanani
	45	! REAL constants defined as wp-kind
	46	!
[1321]	47	! 1320 2014-03-20 08:40:49Z raasch
[1320]	48	! ONLY-attribute added to USE-statements,
	49	! kind-parameters added to all INTEGER and REAL declaration statements,
	50	! kinds are defined in new module kinds,
	51	! revision history before 2012 removed,
	52	! comment fields (!:) to be used for variable explanations added to
	53	! all variable declaration statements
[1321]	54	!
[1258]	55	! 1257 2013-11-08 15:18:40Z raasch
	56	! openacc loop and loop vector clauses removed, declare create moved after
	57	! the FORTRAN declaration statement
	58	!
[1132]	59	! 1128 2013-04-12 06:19:32Z raasch
	60	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	61	! j_north
	62	!
[1037]	63	! 1036 2012-10-22 13:43:42Z raasch
	64	! code put under GPL (PALM 3.9)
	65	!
[1017]	66	! 1015 2012-09-27 09:23:24Z raasch
	67	! accelerator version (*_acc) added
	68	!
[1002]	69	! 1001 2012-09-13 14:08:46Z raasch
	70	! arrays comunicated by module instead of parameter list
	71	!
[979]	72	! 978 2012-08-09 08:28:32Z fricke
	73	! outflow damping layer removed
	74	! kmym_x/_y and kmyp_x/_y change to kmym and kmyp
	75	!
[1]	76	! Revision 1.1 1997/09/12 06:23:51 raasch
	77	! Initial revision
	78	!
	79	!
	80	! Description:
	81	! ------------
[1682]	82	!> Diffusion term of the u-component
	83	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
	84	!> and slows down the speed on NEC about 5-10%
[1]	85	!------------------------------------------------------------------------------!
[1682]	86	MODULE diffusion_u_mod
	87
[1]	88
[56]	89	USE wall_fluxes_mod
	90
[1]	91	PRIVATE
[1015]	92	PUBLIC diffusion_u, diffusion_u_acc
[1]	93
	94	INTERFACE diffusion_u
	95	MODULE PROCEDURE diffusion_u
	96	MODULE PROCEDURE diffusion_u_ij
	97	END INTERFACE diffusion_u
	98
[1015]	99	INTERFACE diffusion_u_acc
	100	MODULE PROCEDURE diffusion_u_acc
	101	END INTERFACE diffusion_u_acc
	102
[1]	103	CONTAINS
	104
	105
	106	!------------------------------------------------------------------------------!
[1682]	107	! Description:
	108	! ------------
	109	!> Call for all grid points
[1]	110	!------------------------------------------------------------------------------!
[1001]	111	SUBROUTINE diffusion_u
[1]	112
[1320]	113	USE arrays_3d, &
	114	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w
	115
	116	USE control_parameters, &
	117	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	118	use_top_fluxes
	119
	120	USE grid_variables, &
	121	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	122
	123	USE indices, &
	124	ONLY: nxl, nxlu, nxr, nyn, nys, nzb, nzb_diff_u, nzb_u_inner, &
	125	nzb_u_outer, nzt, nzt_diff
	126
	127	USE kinds
[1]	128
	129	IMPLICIT NONE
	130
[1682]	131	INTEGER(iwp) :: i !<
	132	INTEGER(iwp) :: j !<
	133	INTEGER(iwp) :: k !<
	134	REAL(wp) :: kmym !<
	135	REAL(wp) :: kmyp !<
	136	REAL(wp) :: kmzm !<
	137	REAL(wp) :: kmzp !<
[1001]	138
[1682]	139	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs !<
[1]	140
[56]	141	!
	142	!-- First calculate horizontal momentum flux u'v' at vertical walls,
	143	!-- if neccessary
	144	IF ( topography /= 'flat' ) THEN
[1320]	145	CALL wall_fluxes( usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, nzb_u_inner, &
[56]	146	nzb_u_outer, wall_u )
	147	ENDIF
	148
[106]	149	DO i = nxlu, nxr
[1001]	150	DO j = nys, nyn
[1]	151	!
	152	!-- Compute horizontal diffusion
	153	DO k = nzb_u_outer(j,i)+1, nzt
	154	!
	155	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	156	kmyp = 0.25_wp * &
[978]	157	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	158	kmym = 0.25_wp * &
[978]	159	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	160
[1320]	161	tend(k,j,i) = tend(k,j,i) &
[1340]	162	& + 2.0_wp * ( &
[1320]	163	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	164	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	165	& ) * ddx2 &
[1320]	166	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	167	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	168	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	169	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	170	& ) * ddy
	171	ENDDO
	172
	173	!
	174	!-- Wall functions at the north and south walls, respectively
[1340]	175	IF ( wall_u(j,i) /= 0.0_wp ) THEN
[51]	176
[1]	177	DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i)
[1340]	178	kmyp = 0.25_wp * &
[978]	179	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	180	kmym = 0.25_wp * &
[978]	181	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	182
	183	tend(k,j,i) = tend(k,j,i) &
[1340]	184	+ 2.0_wp * ( &
[1]	185	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	186	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	187	) * ddx2 &
[1]	188	+ ( fyp(j,i) * ( &
[978]	189	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	190	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
[1]	191	) &
	192	- fym(j,i) * ( &
[978]	193	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	194	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	195	) &
[56]	196	+ wall_u(j,i) * usvs(k,j,i) &
[1]	197	) * ddy
	198	ENDDO
	199	ENDIF
	200
	201	!
	202	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	203	!-- index k starts at nzb_u_inner+2.
[102]	204	DO k = nzb_diff_u(j,i), nzt_diff
[1]	205	!
	206	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	207	kmzp = 0.25_wp * &
[1]	208	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	209	kmzm = 0.25_wp * &
[1]	210	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	211
[1320]	212	tend(k,j,i) = tend(k,j,i) &
	213	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	214	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	215	& ) &
	216	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	217	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	218	& ) &
[1]	219	& ) * ddzw(k)
	220	ENDDO
	221
	222	!
	223	!-- Vertical diffusion at the first grid point above the surface,
	224	!-- if the momentum flux at the bottom is given by the Prandtl law or
	225	!-- if it is prescribed by the user.
	226	!-- Difference quotient of the momentum flux is not formed over half
	227	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	228	!-- with other (LES) models showed that the values of the momentum
[1]	229	!-- flux becomes too large in this case.
	230	!-- The term containing w(k-1,..) (see above equation) is removed here
	231	!-- because the vertical velocity is assumed to be zero at the surface.
	232	IF ( use_surface_fluxes ) THEN
	233	k = nzb_u_inner(j,i)+1
	234	!
	235	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	236	kmzp = 0.25_wp * &
[1]	237	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	238
[1320]	239	tend(k,j,i) = tend(k,j,i) &
	240	& + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	241	& ) * ddzw(k) &
	242	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	243	& + usws(j,i) &
[1]	244	& ) * ddzw(k)
	245	ENDIF
	246
[102]	247	!
	248	!-- Vertical diffusion at the first gridpoint below the top boundary,
	249	!-- if the momentum flux at the top is prescribed by the user
[103]	250	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	251	k = nzt
	252	!
	253	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	254	kmzm = 0.25_wp * &
[102]	255	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	256
[1320]	257	tend(k,j,i) = tend(k,j,i) &
	258	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	259	& ) * ddzw(k) &
	260	& + ( -uswst(j,i) &
	261	& - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
[102]	262	& ) * ddzw(k)
	263	ENDIF
	264
[1]	265	ENDDO
	266	ENDDO
	267
	268	END SUBROUTINE diffusion_u
	269
	270
	271	!------------------------------------------------------------------------------!
[1682]	272	! Description:
	273	! ------------
	274	!> Call for all grid points - accelerator version
[1015]	275	!------------------------------------------------------------------------------!
	276	SUBROUTINE diffusion_u_acc
	277
[1320]	278	USE arrays_3d, &
	279	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w
	280
	281	USE control_parameters, &
	282	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	283	use_top_fluxes
	284
	285	USE grid_variables, &
	286	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	287
	288	USE indices, &
	289	ONLY: i_left, i_right, j_north, j_south, nxl, nxr, nyn, nys, nzb, &
	290	nzb_diff_u, nzb_u_inner, nzb_u_outer, nzt, nzt_diff
	291
	292	USE kinds
[1015]	293
	294	IMPLICIT NONE
	295
[1682]	296	INTEGER(iwp) :: i !<
	297	INTEGER(iwp) :: j !<
	298	INTEGER(iwp) :: k !<
	299	REAL(wp) :: kmym !<
	300	REAL(wp) :: kmyp !<
	301	REAL(wp) :: kmzm !<
	302	REAL(wp) :: kmzp !<
[1015]	303
[1682]	304	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs !<
[1015]	305	!$acc declare create ( usvs )
	306
	307	!
	308	!-- First calculate horizontal momentum flux u'v' at vertical walls,
	309	!-- if neccessary
	310	IF ( topography /= 'flat' ) THEN
[1320]	311	CALL wall_fluxes_acc( usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
	312	nzb_u_inner, nzb_u_outer, wall_u )
[1015]	313	ENDIF
	314
[1320]	315	!$acc kernels present ( u, v, w, km, tend, usws, uswst ) &
	316	!$acc present ( ddzu, ddzw, fym, fyp, wall_u ) &
[1015]	317	!$acc present ( nzb_u_inner, nzb_u_outer, nzb_diff_u )
[1128]	318	DO i = i_left, i_right
	319	DO j = j_south, j_north
[1015]	320	!
	321	!-- Compute horizontal diffusion
	322	DO k = 1, nzt
	323	IF ( k > nzb_u_outer(j,i) ) THEN
	324	!
	325	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	326	kmyp = 0.25_wp * &
[1015]	327	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	328	kmym = 0.25_wp * &
[1015]	329	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
	330
	331	tend(k,j,i) = tend(k,j,i) &
[1340]	332	& + 2.0_wp * ( &
[1015]	333	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	334	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	335	& ) * ddx2 &
[1015]	336	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	337	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	338	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	339	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	340	& ) * ddy
	341	ENDIF
	342	ENDDO
	343
	344	!
	345	!-- Wall functions at the north and south walls, respectively
	346	DO k = 1, nzt
[1320]	347	IF( k > nzb_u_inner(j,i) .AND. k <= nzb_u_outer(j,i) .AND. &
[1340]	348	wall_u(j,i) /= 0.0_wp ) THEN
[1015]	349
[1340]	350	kmyp = 0.25_wp * &
[1015]	351	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	352	kmym = 0.25_wp * &
[1015]	353	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
	354
	355	tend(k,j,i) = tend(k,j,i) &
[1340]	356	+ 2.0_wp * ( &
[1015]	357	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	358	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	359	) * ddx2 &
[1015]	360	+ ( fyp(j,i) * ( &
	361	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	362	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	363	) &
	364	- fym(j,i) * ( &
	365	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	366	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	367	) &
	368	+ wall_u(j,i) * usvs(k,j,i) &
	369	) * ddy
	370	ENDIF
	371	ENDDO
	372
	373	!
	374	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	375	!-- index k starts at nzb_u_inner+2.
	376	DO k = 1, nzt_diff
	377	IF ( k >= nzb_diff_u(j,i) ) THEN
	378	!
	379	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	380	kmzp = 0.25_wp * &
[1015]	381	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	382	kmzm = 0.25_wp * &
[1015]	383	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	384
	385	tend(k,j,i) = tend(k,j,i) &
	386	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1)&
	387	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	388	& ) &
	389	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k)&
	390	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	391	& ) &
	392	& ) * ddzw(k)
	393	ENDIF
	394	ENDDO
	395
	396	ENDDO
	397	ENDDO
	398
	399	!
	400	!-- Vertical diffusion at the first grid point above the surface,
	401	!-- if the momentum flux at the bottom is given by the Prandtl law or
	402	!-- if it is prescribed by the user.
	403	!-- Difference quotient of the momentum flux is not formed over half
	404	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	405	!-- with other (LES) models showed that the values of the momentum
[1015]	406	!-- flux becomes too large in this case.
	407	!-- The term containing w(k-1,..) (see above equation) is removed here
	408	!-- because the vertical velocity is assumed to be zero at the surface.
	409	IF ( use_surface_fluxes ) THEN
	410
[1128]	411	DO i = i_left, i_right
	412	DO j = j_south, j_north
[1015]	413
	414	k = nzb_u_inner(j,i)+1
	415	!
	416	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	417	kmzp = 0.25_wp * &
[1015]	418	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	419
[1320]	420	tend(k,j,i) = tend(k,j,i) &
	421	& + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	422	& ) * ddzw(k) &
	423	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	424	& + usws(j,i) &
[1015]	425	& ) * ddzw(k)
	426	ENDDO
	427	ENDDO
	428
	429	ENDIF
	430
	431	!
	432	!-- Vertical diffusion at the first gridpoint below the top boundary,
	433	!-- if the momentum flux at the top is prescribed by the user
	434	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
	435
	436	k = nzt
	437
[1128]	438	DO i = i_left, i_right
	439	DO j = j_south, j_north
[1015]	440
	441	!
	442	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	443	kmzm = 0.25_wp * &
[1015]	444	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	445
[1320]	446	tend(k,j,i) = tend(k,j,i) &
	447	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	448	& ) * ddzw(k) &
	449	& + ( -uswst(j,i) &
	450	& - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
[1015]	451	& ) * ddzw(k)
	452	ENDDO
	453	ENDDO
	454
	455	ENDIF
	456	!$acc end kernels
	457
	458	END SUBROUTINE diffusion_u_acc
	459
	460
	461	!------------------------------------------------------------------------------!
[1682]	462	! Description:
	463	! ------------
	464	!> Call for grid point i,j
[1]	465	!------------------------------------------------------------------------------!
[1001]	466	SUBROUTINE diffusion_u_ij( i, j )
[1]	467
[1320]	468	USE arrays_3d, &
	469	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w
	470
	471	USE control_parameters, &
	472	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
	473
	474	USE grid_variables, &
	475	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	476
	477	USE indices, &
	478	ONLY: nzb, nzb_diff_u, nzb_u_inner, nzb_u_outer, nzt, nzt_diff
	479
	480	USE kinds
[1]	481
	482	IMPLICIT NONE
	483
[1682]	484	INTEGER(iwp) :: i !<
	485	INTEGER(iwp) :: j !<
	486	INTEGER(iwp) :: k !<
	487	REAL(wp) :: kmym !<
	488	REAL(wp) :: kmyp !<
	489	REAL(wp) :: kmzm !<
	490	REAL(wp) :: kmzp !<
[1]	491
[1682]	492	REAL(wp), DIMENSION(nzb:nzt+1) :: usvs !<
[1001]	493
[1]	494	!
	495	!-- Compute horizontal diffusion
	496	DO k = nzb_u_outer(j,i)+1, nzt
	497	!
	498	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	499	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	500	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]	501
[1320]	502	tend(k,j,i) = tend(k,j,i) &
[1340]	503	& + 2.0_wp * ( &
[1320]	504	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	505	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	506	& ) * ddx2 &
[1320]	507	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	508	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	509	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	510	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	511	& ) * ddy
	512	ENDDO
	513
	514	!
	515	!-- Wall functions at the north and south walls, respectively
[1691]	516	IF ( wall_u(j,i) /= 0.0_wp ) THEN
[51]	517
	518	!
	519	!-- Calculate the horizontal momentum flux u'v'
[1320]	520	CALL wall_fluxes( i, j, nzb_u_inner(j,i)+1, nzb_u_outer(j,i), &
	521	usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
[51]	522
[1]	523	DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i)
[1340]	524	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	525	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]	526
	527	tend(k,j,i) = tend(k,j,i) &
[1340]	528	+ 2.0_wp * ( &
[1]	529	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	530	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	531	) * ddx2 &
[1]	532	+ ( fyp(j,i) * ( &
[978]	533	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	534	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
[1]	535	) &
	536	- fym(j,i) * ( &
[978]	537	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	538	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	539	) &
[51]	540	+ wall_u(j,i) * usvs(k) &
[1]	541	) * ddy
	542	ENDDO
	543	ENDIF
	544
	545	!
	546	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	547	!-- index k starts at nzb_u_inner+2.
[102]	548	DO k = nzb_diff_u(j,i), nzt_diff
[1]	549	!
	550	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	551	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	552	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]	553
[1320]	554	tend(k,j,i) = tend(k,j,i) &
	555	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	556	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	557	& ) &
	558	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	559	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	560	& ) &
[1]	561	& ) * ddzw(k)
	562	ENDDO
	563
	564	!
	565	!-- Vertical diffusion at the first grid point above the surface, if the
	566	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	567	!-- prescribed by the user.
	568	!-- Difference quotient of the momentum flux is not formed over half of
	569	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	570	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	571	!-- too large in this case.
	572	!-- The term containing w(k-1,..) (see above equation) is removed here
	573	!-- because the vertical velocity is assumed to be zero at the surface.
	574	IF ( use_surface_fluxes ) THEN
	575	k = nzb_u_inner(j,i)+1
	576	!
	577	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	578	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]	579
[1320]	580	tend(k,j,i) = tend(k,j,i) &
	581	& + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	582	& ) * ddzw(k) &
	583	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	584	& + usws(j,i) &
[1]	585	& ) * ddzw(k)
	586	ENDIF
	587
[102]	588	!
	589	!-- Vertical diffusion at the first gridpoint below the top boundary,
	590	!-- if the momentum flux at the top is prescribed by the user
[103]	591	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	592	k = nzt
	593	!
	594	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	595	kmzm = 0.25_wp * &
[102]	596	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	597
[1320]	598	tend(k,j,i) = tend(k,j,i) &
	599	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	600	& ) * ddzw(k) &
	601	& + ( -uswst(j,i) &
	602	& - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
[102]	603	& ) * ddzw(k)
	604	ENDIF
	605
[1]	606	END SUBROUTINE diffusion_u_ij
	607
	608	END MODULE diffusion_u_mod

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