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source: palm/trunk/SOURCE/diffusion_u.f90 @ 1691

Last change on this file since 1691 was 1691, checked in by maronga, 9 years ago
various bugfixes and modifications of the atmosphere-land-surface-radiation interaction. Completely re-written routine to calculate surface fluxes (surface_layer_fluxes.f90) that replaces prandtl_fluxes. Minor formatting corrections and renamings
Property svn:keywords set to `Id`
File size: 27.4 KB

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