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source: palm/trunk/SOURCE/diffusion_u.f90 @ 1320

Last change on this file since 1320 was 1320, checked in by raasch, 11 years ago
ONLY-attribute added to USE-statements, kind-parameters added to all INTEGER and REAL declaration statements, kinds are defined in new module kinds, old module precision_kind is removed, revision history before 2012 removed, comment fields (!:) to be used for variable explanations added to all variable declaration statements
Property svn:keywords set to `Id`
File size: 27.1 KB

Rev	Line
[1]	1	MODULE diffusion_u_mod
	2
[1036]	3	!--------------------------------------------------------------------------------!
	4	! This file is part of PALM.
	5	!
	6	! PALM is free software: you can redistribute it and/or modify it under the terms
	7	! of the GNU General Public License as published by the Free Software Foundation,
	8	! either version 3 of the License, or (at your option) any later version.
	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	!
[1310]	17	! Copyright 1997-2014 Leibniz Universitaet Hannover
[1036]	18	!--------------------------------------------------------------------------------!
	19	!
[484]	20	! Current revisions:
[1]	21	! -----------------
[1320]	22	! ONLY-attribute added to USE-statements,
	23	! kind-parameters added to all INTEGER and REAL declaration statements,
	24	! kinds are defined in new module kinds,
	25	! old module precision_kind is removed,
	26	! revision history before 2012 removed,
	27	! comment fields (!:) to be used for variable explanations added to
	28	! all variable declaration statements
[106]	29	!
[1]	30	! Former revisions:
	31	! -----------------
[3]	32	! $Id: diffusion_u.f90 1320 2014-03-20 08:40:49Z raasch $
[39]	33	!
[1258]	34	! 1257 2013-11-08 15:18:40Z raasch
	35	! openacc loop and loop vector clauses removed, declare create moved after
	36	! the FORTRAN declaration statement
	37	!
[1132]	38	! 1128 2013-04-12 06:19:32Z raasch
	39	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	40	! j_north
	41	!
[1037]	42	! 1036 2012-10-22 13:43:42Z raasch
	43	! code put under GPL (PALM 3.9)
	44	!
[1017]	45	! 1015 2012-09-27 09:23:24Z raasch
	46	! accelerator version (*_acc) added
	47	!
[1002]	48	! 1001 2012-09-13 14:08:46Z raasch
	49	! arrays comunicated by module instead of parameter list
	50	!
[979]	51	! 978 2012-08-09 08:28:32Z fricke
	52	! outflow damping layer removed
	53	! kmym_x/_y and kmyp_x/_y change to kmym and kmyp
	54	!
[1]	55	! Revision 1.1 1997/09/12 06:23:51 raasch
	56	! Initial revision
	57	!
	58	!
	59	! Description:
	60	! ------------
	61	! Diffusion term of the u-component
[51]	62	! To do: additional damping (needed for non-cyclic bc) causes bad vectorization
	63	! and slows down the speed on NEC about 5-10%
[1]	64	!------------------------------------------------------------------------------!
	65
[56]	66	USE wall_fluxes_mod
	67
[1]	68	PRIVATE
[1015]	69	PUBLIC diffusion_u, diffusion_u_acc
[1]	70
	71	INTERFACE diffusion_u
	72	MODULE PROCEDURE diffusion_u
	73	MODULE PROCEDURE diffusion_u_ij
	74	END INTERFACE diffusion_u
	75
[1015]	76	INTERFACE diffusion_u_acc
	77	MODULE PROCEDURE diffusion_u_acc
	78	END INTERFACE diffusion_u_acc
	79
[1]	80	CONTAINS
	81
	82
	83	!------------------------------------------------------------------------------!
	84	! Call for all grid points
	85	!------------------------------------------------------------------------------!
[1001]	86	SUBROUTINE diffusion_u
[1]	87
[1320]	88	USE arrays_3d, &
	89	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w
	90
	91	USE control_parameters, &
	92	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	93	use_top_fluxes
	94
	95	USE grid_variables, &
	96	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	97
	98	USE indices, &
	99	ONLY: nxl, nxlu, nxr, nyn, nys, nzb, nzb_diff_u, nzb_u_inner, &
	100	nzb_u_outer, nzt, nzt_diff
	101
	102	USE kinds
[1]	103
	104	IMPLICIT NONE
	105
[1320]	106	INTEGER(iwp) :: i !:
	107	INTEGER(iwp) :: j !:
	108	INTEGER(iwp) :: k !:
	109	REAL(wp) :: kmym !:
	110	REAL(wp) :: kmyp !:
	111	REAL(wp) :: kmzm !:
	112	REAL(wp) :: kmzp !:
[1001]	113
[1320]	114	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs !:
[1]	115
[56]	116	!
	117	!-- First calculate horizontal momentum flux u'v' at vertical walls,
	118	!-- if neccessary
	119	IF ( topography /= 'flat' ) THEN
[1320]	120	CALL wall_fluxes( usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, nzb_u_inner, &
[56]	121	nzb_u_outer, wall_u )
	122	ENDIF
	123
[106]	124	DO i = nxlu, nxr
[1001]	125	DO j = nys, nyn
[1]	126	!
	127	!-- Compute horizontal diffusion
	128	DO k = nzb_u_outer(j,i)+1, nzt
	129	!
	130	!-- Interpolate eddy diffusivities on staggered gridpoints
[1320]	131	kmyp = 0.25 * &
[978]	132	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1320]	133	kmym = 0.25 * &
[978]	134	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	135
[1320]	136	tend(k,j,i) = tend(k,j,i) &
	137	& + 2.0 * ( &
	138	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	139	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
	140	& ) * ddx2 &
	141	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	142	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	143	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	144	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	145	& ) * ddy
	146	ENDDO
	147
	148	!
	149	!-- Wall functions at the north and south walls, respectively
	150	IF ( wall_u(j,i) /= 0.0 ) THEN
[51]	151
[1]	152	DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i)
[1320]	153	kmyp = 0.25 * &
[978]	154	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1320]	155	kmym = 0.25 * &
[978]	156	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	157
	158	tend(k,j,i) = tend(k,j,i) &
	159	+ 2.0 * ( &
	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) ) &
	162	) * ddx2 &
	163	+ ( fyp(j,i) * ( &
[978]	164	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	165	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
[1]	166	) &
	167	- fym(j,i) * ( &
[978]	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	) &
[56]	171	+ wall_u(j,i) * usvs(k,j,i) &
[1]	172	) * ddy
	173	ENDDO
	174	ENDIF
	175
	176	!
	177	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	178	!-- index k starts at nzb_u_inner+2.
[102]	179	DO k = nzb_diff_u(j,i), nzt_diff
[1]	180	!
	181	!-- Interpolate eddy diffusivities on staggered gridpoints
[1320]	182	kmzp = 0.25 * &
[1]	183	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1320]	184	kmzm = 0.25 * &
[1]	185	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	186
[1320]	187	tend(k,j,i) = tend(k,j,i) &
	188	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	189	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	190	& ) &
	191	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	192	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	193	& ) &
[1]	194	& ) * ddzw(k)
	195	ENDDO
	196
	197	!
	198	!-- Vertical diffusion at the first grid point above the surface,
	199	!-- if the momentum flux at the bottom is given by the Prandtl law or
	200	!-- if it is prescribed by the user.
	201	!-- Difference quotient of the momentum flux is not formed over half
	202	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	203	!-- with other (LES) models showed that the values of the momentum
[1]	204	!-- flux becomes too large in this case.
	205	!-- The term containing w(k-1,..) (see above equation) is removed here
	206	!-- because the vertical velocity is assumed to be zero at the surface.
	207	IF ( use_surface_fluxes ) THEN
	208	k = nzb_u_inner(j,i)+1
	209	!
	210	!-- Interpolate eddy diffusivities on staggered gridpoints
[1320]	211	kmzp = 0.25 * &
[1]	212	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1320]	213	kmzm = 0.25 * &
[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 * ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	218	& ) * ddzw(k) &
	219	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	220	& + usws(j,i) &
[1]	221	& ) * ddzw(k)
	222	ENDIF
	223
[102]	224	!
	225	!-- Vertical diffusion at the first gridpoint below the top boundary,
	226	!-- if the momentum flux at the top is prescribed by the user
[103]	227	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	228	k = nzt
	229	!
	230	!-- Interpolate eddy diffusivities on staggered gridpoints
[1320]	231	kmzp = 0.25 * &
[102]	232	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1320]	233	kmzm = 0.25 * &
[102]	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	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	238	& ) * ddzw(k) &
	239	& + ( -uswst(j,i) &
	240	& - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
[102]	241	& ) * ddzw(k)
	242	ENDIF
	243
[1]	244	ENDDO
	245	ENDDO
	246
	247	END SUBROUTINE diffusion_u
	248
	249
	250	!------------------------------------------------------------------------------!
[1015]	251	! Call for all grid points - accelerator version
	252	!------------------------------------------------------------------------------!
	253	SUBROUTINE diffusion_u_acc
	254
[1320]	255	USE arrays_3d, &
	256	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w
	257
	258	USE control_parameters, &
	259	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	260	use_top_fluxes
	261
	262	USE grid_variables, &
	263	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	264
	265	USE indices, &
	266	ONLY: i_left, i_right, j_north, j_south, nxl, nxr, nyn, nys, nzb, &
	267	nzb_diff_u, nzb_u_inner, nzb_u_outer, nzt, nzt_diff
	268
	269	USE kinds
[1015]	270
	271	IMPLICIT NONE
	272
[1320]	273	INTEGER(iwp) :: i !:
	274	INTEGER(iwp) :: j !:
	275	INTEGER(iwp) :: k !:
	276	REAL(wp) :: kmym !:
	277	REAL(wp) :: kmyp !:
	278	REAL(wp) :: kmzm !:
	279	REAL(wp) :: kmzp !:
[1015]	280
[1320]	281	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs !:
[1015]	282	!$acc declare create ( usvs )
	283
	284	!
	285	!-- First calculate horizontal momentum flux u'v' at vertical walls,
	286	!-- if neccessary
	287	IF ( topography /= 'flat' ) THEN
[1320]	288	CALL wall_fluxes_acc( usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
	289	nzb_u_inner, nzb_u_outer, wall_u )
[1015]	290	ENDIF
	291
[1320]	292	!$acc kernels present ( u, v, w, km, tend, usws, uswst ) &
	293	!$acc present ( ddzu, ddzw, fym, fyp, wall_u ) &
[1015]	294	!$acc present ( nzb_u_inner, nzb_u_outer, nzb_diff_u )
[1128]	295	DO i = i_left, i_right
	296	DO j = j_south, j_north
[1015]	297	!
	298	!-- Compute horizontal diffusion
	299	DO k = 1, nzt
	300	IF ( k > nzb_u_outer(j,i) ) THEN
	301	!
	302	!-- Interpolate eddy diffusivities on staggered gridpoints
[1320]	303	kmyp = 0.25 * &
[1015]	304	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1320]	305	kmym = 0.25 * &
[1015]	306	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
	307
	308	tend(k,j,i) = tend(k,j,i) &
	309	& + 2.0 * ( &
	310	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	311	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
	312	& ) * ddx2 &
	313	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	314	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	315	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	316	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	317	& ) * ddy
	318	ENDIF
	319	ENDDO
	320
	321	!
	322	!-- Wall functions at the north and south walls, respectively
	323	DO k = 1, nzt
[1320]	324	IF( k > nzb_u_inner(j,i) .AND. k <= nzb_u_outer(j,i) .AND. &
[1015]	325	wall_u(j,i) /= 0.0 ) THEN
	326
[1320]	327	kmyp = 0.25 * &
[1015]	328	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1320]	329	kmym = 0.25 * &
[1015]	330	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
	331
	332	tend(k,j,i) = tend(k,j,i) &
	333	+ 2.0 * ( &
	334	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	335	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
	336	) * ddx2 &
	337	+ ( fyp(j,i) * ( &
	338	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	339	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	340	) &
	341	- fym(j,i) * ( &
	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	) &
	345	+ wall_u(j,i) * usvs(k,j,i) &
	346	) * ddy
	347	ENDIF
	348	ENDDO
	349
	350	!
	351	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	352	!-- index k starts at nzb_u_inner+2.
	353	DO k = 1, nzt_diff
	354	IF ( k >= nzb_diff_u(j,i) ) THEN
	355	!
	356	!-- Interpolate eddy diffusivities on staggered gridpoints
[1320]	357	kmzp = 0.25 * &
[1015]	358	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1320]	359	kmzm = 0.25 * &
[1015]	360	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	361
	362	tend(k,j,i) = tend(k,j,i) &
	363	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1)&
	364	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	365	& ) &
	366	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k)&
	367	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	368	& ) &
	369	& ) * ddzw(k)
	370	ENDIF
	371	ENDDO
	372
	373	ENDDO
	374	ENDDO
	375
	376	!
	377	!-- Vertical diffusion at the first grid point above the surface,
	378	!-- if the momentum flux at the bottom is given by the Prandtl law or
	379	!-- if it is prescribed by the user.
	380	!-- Difference quotient of the momentum flux is not formed over half
	381	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	382	!-- with other (LES) models showed that the values of the momentum
[1015]	383	!-- flux becomes too large in this case.
	384	!-- The term containing w(k-1,..) (see above equation) is removed here
	385	!-- because the vertical velocity is assumed to be zero at the surface.
	386	IF ( use_surface_fluxes ) THEN
	387
[1128]	388	DO i = i_left, i_right
	389	DO j = j_south, j_north
[1015]	390
	391	k = nzb_u_inner(j,i)+1
	392	!
	393	!-- Interpolate eddy diffusivities on staggered gridpoints
[1320]	394	kmzp = 0.25 * &
[1015]	395	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1320]	396	kmzm = 0.25 * &
[1015]	397	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	398
[1320]	399	tend(k,j,i) = tend(k,j,i) &
	400	& + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	401	& ) * ddzw(k) &
	402	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	403	& + usws(j,i) &
[1015]	404	& ) * ddzw(k)
	405	ENDDO
	406	ENDDO
	407
	408	ENDIF
	409
	410	!
	411	!-- Vertical diffusion at the first gridpoint below the top boundary,
	412	!-- if the momentum flux at the top is prescribed by the user
	413	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
	414
	415	k = nzt
	416
[1128]	417	DO i = i_left, i_right
	418	DO j = j_south, j_north
[1015]	419
	420	!
	421	!-- Interpolate eddy diffusivities on staggered gridpoints
[1320]	422	kmzp = 0.25 * &
[1015]	423	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1320]	424	kmzm = 0.25 * &
[1015]	425	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	426
[1320]	427	tend(k,j,i) = tend(k,j,i) &
	428	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	429	& ) * ddzw(k) &
	430	& + ( -uswst(j,i) &
	431	& - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
[1015]	432	& ) * ddzw(k)
	433	ENDDO
	434	ENDDO
	435
	436	ENDIF
	437	!$acc end kernels
	438
	439	END SUBROUTINE diffusion_u_acc
	440
	441
	442	!------------------------------------------------------------------------------!
[1]	443	! Call for grid point i,j
	444	!------------------------------------------------------------------------------!
[1001]	445	SUBROUTINE diffusion_u_ij( i, j )
[1]	446
[1320]	447	USE arrays_3d, &
	448	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w
	449
	450	USE control_parameters, &
	451	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
	452
	453	USE grid_variables, &
	454	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	455
	456	USE indices, &
	457	ONLY: nzb, nzb_diff_u, nzb_u_inner, nzb_u_outer, nzt, nzt_diff
	458
	459	USE kinds
[1]	460
	461	IMPLICIT NONE
	462
[1320]	463	INTEGER(iwp) :: i !:
	464	INTEGER(iwp) :: j !:
	465	INTEGER(iwp) :: k !:
	466	REAL(wp) :: kmym !:
	467	REAL(wp) :: kmyp !:
	468	REAL(wp) :: kmzm !:
	469	REAL(wp) :: kmzp !:
[1]	470
[1320]	471	REAL(wp), DIMENSION(nzb:nzt+1) :: usvs !:
[1001]	472
[1]	473	!
	474	!-- Compute horizontal diffusion
	475	DO k = nzb_u_outer(j,i)+1, nzt
	476	!
	477	!-- Interpolate eddy diffusivities on staggered gridpoints
[978]	478	kmyp = 0.25 * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	479	kmym = 0.25 * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	480
[1320]	481	tend(k,j,i) = tend(k,j,i) &
	482	& + 2.0 * ( &
	483	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	484	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
	485	& ) * ddx2 &
	486	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	487	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	488	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	489	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	490	& ) * ddy
	491	ENDDO
	492
	493	!
	494	!-- Wall functions at the north and south walls, respectively
	495	IF ( wall_u(j,i) .NE. 0.0 ) THEN
[51]	496
	497	!
	498	!-- Calculate the horizontal momentum flux u'v'
[1320]	499	CALL wall_fluxes( i, j, nzb_u_inner(j,i)+1, nzb_u_outer(j,i), &
	500	usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
[51]	501
[1]	502	DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i)
[978]	503	kmyp = 0.25 * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	504	kmym = 0.25 * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	505
	506	tend(k,j,i) = tend(k,j,i) &
	507	+ 2.0 * ( &
	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) ) &
	510	) * ddx2 &
	511	+ ( fyp(j,i) * ( &
[978]	512	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	513	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
[1]	514	) &
	515	- fym(j,i) * ( &
[978]	516	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	517	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	518	) &
[51]	519	+ wall_u(j,i) * usvs(k) &
[1]	520	) * ddy
	521	ENDDO
	522	ENDIF
	523
	524	!
	525	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	526	!-- index k starts at nzb_u_inner+2.
[102]	527	DO k = nzb_diff_u(j,i), nzt_diff
[1]	528	!
	529	!-- Interpolate eddy diffusivities on staggered gridpoints
	530	kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	531	kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	532
[1320]	533	tend(k,j,i) = tend(k,j,i) &
	534	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	535	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	536	& ) &
	537	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	538	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	539	& ) &
[1]	540	& ) * ddzw(k)
	541	ENDDO
	542
	543	!
	544	!-- Vertical diffusion at the first grid point above the surface, if the
	545	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	546	!-- prescribed by the user.
	547	!-- Difference quotient of the momentum flux is not formed over half of
	548	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	549	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	550	!-- too large in this case.
	551	!-- The term containing w(k-1,..) (see above equation) is removed here
	552	!-- because the vertical velocity is assumed to be zero at the surface.
	553	IF ( use_surface_fluxes ) THEN
	554	k = nzb_u_inner(j,i)+1
	555	!
	556	!-- Interpolate eddy diffusivities on staggered gridpoints
	557	kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	558	kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	559
[1320]	560	tend(k,j,i) = tend(k,j,i) &
	561	& + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	562	& ) * ddzw(k) &
	563	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	564	& + usws(j,i) &
[1]	565	& ) * ddzw(k)
	566	ENDIF
	567
[102]	568	!
	569	!-- Vertical diffusion at the first gridpoint below the top boundary,
	570	!-- if the momentum flux at the top is prescribed by the user
[103]	571	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	572	k = nzt
	573	!
	574	!-- Interpolate eddy diffusivities on staggered gridpoints
[1320]	575	kmzp = 0.25 * &
[102]	576	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1320]	577	kmzm = 0.25 * &
[102]	578	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	579
[1320]	580	tend(k,j,i) = tend(k,j,i) &
	581	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	582	& ) * ddzw(k) &
	583	& + ( -uswst(j,i) &
	584	& - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
[102]	585	& ) * ddzw(k)
	586	ENDIF
	587
[1]	588	END SUBROUTINE diffusion_u_ij
	589
	590	END MODULE diffusion_u_mod

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