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source: palm/trunk/SOURCE/diffusion_u.f90 @ 1364

Last change on this file since 1364 was 1341, checked in by kanani, 11 years ago
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[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	! -----------------
[1341]	22	!
	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: diffusion_u.f90 1341 2014-03-25 19:48:09Z keck $
	27	!
[1341]	28	! 1340 2014-03-25 19:45:13Z kanani
	29	! REAL constants defined as wp-kind
	30	!
[1321]	31	! 1320 2014-03-20 08:40:49Z raasch
[1320]	32	! ONLY-attribute added to USE-statements,
	33	! kind-parameters added to all INTEGER and REAL declaration statements,
	34	! kinds are defined in new module kinds,
	35	! revision history before 2012 removed,
	36	! comment fields (!:) to be used for variable explanations added to
	37	! all variable declaration statements
[1321]	38	!
[1258]	39	! 1257 2013-11-08 15:18:40Z raasch
	40	! openacc loop and loop vector clauses removed, declare create moved after
	41	! the FORTRAN declaration statement
	42	!
[1132]	43	! 1128 2013-04-12 06:19:32Z raasch
	44	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	45	! j_north
	46	!
[1037]	47	! 1036 2012-10-22 13:43:42Z raasch
	48	! code put under GPL (PALM 3.9)
	49	!
[1017]	50	! 1015 2012-09-27 09:23:24Z raasch
	51	! accelerator version (*_acc) added
	52	!
[1002]	53	! 1001 2012-09-13 14:08:46Z raasch
	54	! arrays comunicated by module instead of parameter list
	55	!
[979]	56	! 978 2012-08-09 08:28:32Z fricke
	57	! outflow damping layer removed
	58	! kmym_x/_y and kmyp_x/_y change to kmym and kmyp
	59	!
[1]	60	! Revision 1.1 1997/09/12 06:23:51 raasch
	61	! Initial revision
	62	!
	63	!
	64	! Description:
	65	! ------------
	66	! Diffusion term of the u-component
[51]	67	! To do: additional damping (needed for non-cyclic bc) causes bad vectorization
	68	! and slows down the speed on NEC about 5-10%
[1]	69	!------------------------------------------------------------------------------!
	70
[56]	71	USE wall_fluxes_mod
	72
[1]	73	PRIVATE
[1015]	74	PUBLIC diffusion_u, diffusion_u_acc
[1]	75
	76	INTERFACE diffusion_u
	77	MODULE PROCEDURE diffusion_u
	78	MODULE PROCEDURE diffusion_u_ij
	79	END INTERFACE diffusion_u
	80
[1015]	81	INTERFACE diffusion_u_acc
	82	MODULE PROCEDURE diffusion_u_acc
	83	END INTERFACE diffusion_u_acc
	84
[1]	85	CONTAINS
	86
	87
	88	!------------------------------------------------------------------------------!
	89	! Call for all grid points
	90	!------------------------------------------------------------------------------!
[1001]	91	SUBROUTINE diffusion_u
[1]	92
[1320]	93	USE arrays_3d, &
	94	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w
	95
	96	USE control_parameters, &
	97	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	98	use_top_fluxes
	99
	100	USE grid_variables, &
	101	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	102
	103	USE indices, &
	104	ONLY: nxl, nxlu, nxr, nyn, nys, nzb, nzb_diff_u, nzb_u_inner, &
	105	nzb_u_outer, nzt, nzt_diff
	106
	107	USE kinds
[1]	108
	109	IMPLICIT NONE
	110
[1320]	111	INTEGER(iwp) :: i !:
	112	INTEGER(iwp) :: j !:
	113	INTEGER(iwp) :: k !:
	114	REAL(wp) :: kmym !:
	115	REAL(wp) :: kmyp !:
	116	REAL(wp) :: kmzm !:
	117	REAL(wp) :: kmzp !:
[1001]	118
[1320]	119	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs !:
[1]	120
[56]	121	!
	122	!-- First calculate horizontal momentum flux u'v' at vertical walls,
	123	!-- if neccessary
	124	IF ( topography /= 'flat' ) THEN
[1320]	125	CALL wall_fluxes( usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, nzb_u_inner, &
[56]	126	nzb_u_outer, wall_u )
	127	ENDIF
	128
[106]	129	DO i = nxlu, nxr
[1001]	130	DO j = nys, nyn
[1]	131	!
	132	!-- Compute horizontal diffusion
	133	DO k = nzb_u_outer(j,i)+1, nzt
	134	!
	135	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	136	kmyp = 0.25_wp * &
[978]	137	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	138	kmym = 0.25_wp * &
[978]	139	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	140
[1320]	141	tend(k,j,i) = tend(k,j,i) &
[1340]	142	& + 2.0_wp * ( &
[1320]	143	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	144	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	145	& ) * ddx2 &
[1320]	146	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	147	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	148	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	149	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	150	& ) * ddy
	151	ENDDO
	152
	153	!
	154	!-- Wall functions at the north and south walls, respectively
[1340]	155	IF ( wall_u(j,i) /= 0.0_wp ) THEN
[51]	156
[1]	157	DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i)
[1340]	158	kmyp = 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) )
[1340]	160	kmym = 0.25_wp * &
[978]	161	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	162
	163	tend(k,j,i) = tend(k,j,i) &
[1340]	164	+ 2.0_wp * ( &
[1]	165	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	166	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	167	) * ddx2 &
[1]	168	+ ( fyp(j,i) * ( &
[978]	169	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	170	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
[1]	171	) &
	172	- fym(j,i) * ( &
[978]	173	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	174	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	175	) &
[56]	176	+ wall_u(j,i) * usvs(k,j,i) &
[1]	177	) * ddy
	178	ENDDO
	179	ENDIF
	180
	181	!
	182	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	183	!-- index k starts at nzb_u_inner+2.
[102]	184	DO k = nzb_diff_u(j,i), nzt_diff
[1]	185	!
	186	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	187	kmzp = 0.25_wp * &
[1]	188	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	189	kmzm = 0.25_wp * &
[1]	190	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	191
[1320]	192	tend(k,j,i) = tend(k,j,i) &
	193	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	194	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	195	& ) &
	196	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	197	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	198	& ) &
[1]	199	& ) * ddzw(k)
	200	ENDDO
	201
	202	!
	203	!-- Vertical diffusion at the first grid point above the surface,
	204	!-- if the momentum flux at the bottom is given by the Prandtl law or
	205	!-- if it is prescribed by the user.
	206	!-- Difference quotient of the momentum flux is not formed over half
	207	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	208	!-- with other (LES) models showed that the values of the momentum
[1]	209	!-- flux becomes too large in this case.
	210	!-- The term containing w(k-1,..) (see above equation) is removed here
	211	!-- because the vertical velocity is assumed to be zero at the surface.
	212	IF ( use_surface_fluxes ) THEN
	213	k = nzb_u_inner(j,i)+1
	214	!
	215	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	216	kmzp = 0.25_wp * &
[1]	217	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	218	kmzm = 0.25_wp * &
[1]	219	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	220
[1320]	221	tend(k,j,i) = tend(k,j,i) &
	222	& + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	223	& ) * ddzw(k) &
	224	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	225	& + usws(j,i) &
[1]	226	& ) * ddzw(k)
	227	ENDIF
	228
[102]	229	!
	230	!-- Vertical diffusion at the first gridpoint below the top boundary,
	231	!-- if the momentum flux at the top is prescribed by the user
[103]	232	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	233	k = nzt
	234	!
	235	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	236	kmzp = 0.25_wp * &
[102]	237	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	238	kmzm = 0.25_wp * &
[102]	239	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	240
[1320]	241	tend(k,j,i) = tend(k,j,i) &
	242	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	243	& ) * ddzw(k) &
	244	& + ( -uswst(j,i) &
	245	& - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
[102]	246	& ) * ddzw(k)
	247	ENDIF
	248
[1]	249	ENDDO
	250	ENDDO
	251
	252	END SUBROUTINE diffusion_u
	253
	254
	255	!------------------------------------------------------------------------------!
[1015]	256	! Call for all grid points - accelerator version
	257	!------------------------------------------------------------------------------!
	258	SUBROUTINE diffusion_u_acc
	259
[1320]	260	USE arrays_3d, &
	261	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w
	262
	263	USE control_parameters, &
	264	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	265	use_top_fluxes
	266
	267	USE grid_variables, &
	268	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	269
	270	USE indices, &
	271	ONLY: i_left, i_right, j_north, j_south, nxl, nxr, nyn, nys, nzb, &
	272	nzb_diff_u, nzb_u_inner, nzb_u_outer, nzt, nzt_diff
	273
	274	USE kinds
[1015]	275
	276	IMPLICIT NONE
	277
[1320]	278	INTEGER(iwp) :: i !:
	279	INTEGER(iwp) :: j !:
	280	INTEGER(iwp) :: k !:
	281	REAL(wp) :: kmym !:
	282	REAL(wp) :: kmyp !:
	283	REAL(wp) :: kmzm !:
	284	REAL(wp) :: kmzp !:
[1015]	285
[1320]	286	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs !:
[1015]	287	!$acc declare create ( usvs )
	288
	289	!
	290	!-- First calculate horizontal momentum flux u'v' at vertical walls,
	291	!-- if neccessary
	292	IF ( topography /= 'flat' ) THEN
[1320]	293	CALL wall_fluxes_acc( usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
	294	nzb_u_inner, nzb_u_outer, wall_u )
[1015]	295	ENDIF
	296
[1320]	297	!$acc kernels present ( u, v, w, km, tend, usws, uswst ) &
	298	!$acc present ( ddzu, ddzw, fym, fyp, wall_u ) &
[1015]	299	!$acc present ( nzb_u_inner, nzb_u_outer, nzb_diff_u )
[1128]	300	DO i = i_left, i_right
	301	DO j = j_south, j_north
[1015]	302	!
	303	!-- Compute horizontal diffusion
	304	DO k = 1, nzt
	305	IF ( k > nzb_u_outer(j,i) ) THEN
	306	!
	307	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	308	kmyp = 0.25_wp * &
[1015]	309	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	310	kmym = 0.25_wp * &
[1015]	311	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
	312
	313	tend(k,j,i) = tend(k,j,i) &
[1340]	314	& + 2.0_wp * ( &
[1015]	315	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	316	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	317	& ) * ddx2 &
[1015]	318	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	319	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	320	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	321	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	322	& ) * ddy
	323	ENDIF
	324	ENDDO
	325
	326	!
	327	!-- Wall functions at the north and south walls, respectively
	328	DO k = 1, nzt
[1320]	329	IF( k > nzb_u_inner(j,i) .AND. k <= nzb_u_outer(j,i) .AND. &
[1340]	330	wall_u(j,i) /= 0.0_wp ) THEN
[1015]	331
[1340]	332	kmyp = 0.25_wp * &
[1015]	333	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	334	kmym = 0.25_wp * &
[1015]	335	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
	336
	337	tend(k,j,i) = tend(k,j,i) &
[1340]	338	+ 2.0_wp * ( &
[1015]	339	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	340	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	341	) * ddx2 &
[1015]	342	+ ( fyp(j,i) * ( &
	343	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	344	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	345	) &
	346	- fym(j,i) * ( &
	347	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	348	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	349	) &
	350	+ wall_u(j,i) * usvs(k,j,i) &
	351	) * ddy
	352	ENDIF
	353	ENDDO
	354
	355	!
	356	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	357	!-- index k starts at nzb_u_inner+2.
	358	DO k = 1, nzt_diff
	359	IF ( k >= nzb_diff_u(j,i) ) THEN
	360	!
	361	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	362	kmzp = 0.25_wp * &
[1015]	363	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	364	kmzm = 0.25_wp * &
[1015]	365	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	366
	367	tend(k,j,i) = tend(k,j,i) &
	368	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1)&
	369	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	370	& ) &
	371	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k)&
	372	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	373	& ) &
	374	& ) * ddzw(k)
	375	ENDIF
	376	ENDDO
	377
	378	ENDDO
	379	ENDDO
	380
	381	!
	382	!-- Vertical diffusion at the first grid point above the surface,
	383	!-- if the momentum flux at the bottom is given by the Prandtl law or
	384	!-- if it is prescribed by the user.
	385	!-- Difference quotient of the momentum flux is not formed over half
	386	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	387	!-- with other (LES) models showed that the values of the momentum
[1015]	388	!-- flux becomes too large in this case.
	389	!-- The term containing w(k-1,..) (see above equation) is removed here
	390	!-- because the vertical velocity is assumed to be zero at the surface.
	391	IF ( use_surface_fluxes ) THEN
	392
[1128]	393	DO i = i_left, i_right
	394	DO j = j_south, j_north
[1015]	395
	396	k = nzb_u_inner(j,i)+1
	397	!
	398	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	399	kmzp = 0.25_wp * &
[1015]	400	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	401	kmzm = 0.25_wp * &
[1015]	402	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	403
[1320]	404	tend(k,j,i) = tend(k,j,i) &
	405	& + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	406	& ) * ddzw(k) &
	407	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	408	& + usws(j,i) &
[1015]	409	& ) * ddzw(k)
	410	ENDDO
	411	ENDDO
	412
	413	ENDIF
	414
	415	!
	416	!-- Vertical diffusion at the first gridpoint below the top boundary,
	417	!-- if the momentum flux at the top is prescribed by the user
	418	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
	419
	420	k = nzt
	421
[1128]	422	DO i = i_left, i_right
	423	DO j = j_south, j_north
[1015]	424
	425	!
	426	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	427	kmzp = 0.25_wp * &
[1015]	428	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	429	kmzm = 0.25_wp * &
[1015]	430	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	431
[1320]	432	tend(k,j,i) = tend(k,j,i) &
	433	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	434	& ) * ddzw(k) &
	435	& + ( -uswst(j,i) &
	436	& - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
[1015]	437	& ) * ddzw(k)
	438	ENDDO
	439	ENDDO
	440
	441	ENDIF
	442	!$acc end kernels
	443
	444	END SUBROUTINE diffusion_u_acc
	445
	446
	447	!------------------------------------------------------------------------------!
[1]	448	! Call for grid point i,j
	449	!------------------------------------------------------------------------------!
[1001]	450	SUBROUTINE diffusion_u_ij( i, j )
[1]	451
[1320]	452	USE arrays_3d, &
	453	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w
	454
	455	USE control_parameters, &
	456	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
	457
	458	USE grid_variables, &
	459	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	460
	461	USE indices, &
	462	ONLY: nzb, nzb_diff_u, nzb_u_inner, nzb_u_outer, nzt, nzt_diff
	463
	464	USE kinds
[1]	465
	466	IMPLICIT NONE
	467
[1320]	468	INTEGER(iwp) :: i !:
	469	INTEGER(iwp) :: j !:
	470	INTEGER(iwp) :: k !:
	471	REAL(wp) :: kmym !:
	472	REAL(wp) :: kmyp !:
	473	REAL(wp) :: kmzm !:
	474	REAL(wp) :: kmzp !:
[1]	475
[1320]	476	REAL(wp), DIMENSION(nzb:nzt+1) :: usvs !:
[1001]	477
[1]	478	!
	479	!-- Compute horizontal diffusion
	480	DO k = nzb_u_outer(j,i)+1, nzt
	481	!
	482	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	483	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	484	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]	485
[1320]	486	tend(k,j,i) = tend(k,j,i) &
[1340]	487	& + 2.0_wp * ( &
[1320]	488	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	489	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	490	& ) * ddx2 &
[1320]	491	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	492	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	493	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	494	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	495	& ) * ddy
	496	ENDDO
	497
	498	!
	499	!-- Wall functions at the north and south walls, respectively
[1340]	500	IF ( wall_u(j,i) .NE. 0.0_wp ) THEN
[51]	501
	502	!
	503	!-- Calculate the horizontal momentum flux u'v'
[1320]	504	CALL wall_fluxes( i, j, nzb_u_inner(j,i)+1, nzb_u_outer(j,i), &
	505	usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
[51]	506
[1]	507	DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i)
[1340]	508	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	509	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]	510
	511	tend(k,j,i) = tend(k,j,i) &
[1340]	512	+ 2.0_wp * ( &
[1]	513	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	514	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	515	) * ddx2 &
[1]	516	+ ( fyp(j,i) * ( &
[978]	517	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	518	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
[1]	519	) &
	520	- fym(j,i) * ( &
[978]	521	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	522	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	523	) &
[51]	524	+ wall_u(j,i) * usvs(k) &
[1]	525	) * ddy
	526	ENDDO
	527	ENDIF
	528
	529	!
	530	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	531	!-- index k starts at nzb_u_inner+2.
[102]	532	DO k = nzb_diff_u(j,i), nzt_diff
[1]	533	!
	534	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	535	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	536	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]	537
[1320]	538	tend(k,j,i) = tend(k,j,i) &
	539	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	540	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	541	& ) &
	542	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	543	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	544	& ) &
[1]	545	& ) * ddzw(k)
	546	ENDDO
	547
	548	!
	549	!-- Vertical diffusion at the first grid point above the surface, if the
	550	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	551	!-- prescribed by the user.
	552	!-- Difference quotient of the momentum flux is not formed over half of
	553	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	554	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	555	!-- too large in this case.
	556	!-- The term containing w(k-1,..) (see above equation) is removed here
	557	!-- because the vertical velocity is assumed to be zero at the surface.
	558	IF ( use_surface_fluxes ) THEN
	559	k = nzb_u_inner(j,i)+1
	560	!
	561	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	562	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	563	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]	564
[1320]	565	tend(k,j,i) = tend(k,j,i) &
	566	& + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	567	& ) * ddzw(k) &
	568	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	569	& + usws(j,i) &
[1]	570	& ) * ddzw(k)
	571	ENDIF
	572
[102]	573	!
	574	!-- Vertical diffusion at the first gridpoint below the top boundary,
	575	!-- if the momentum flux at the top is prescribed by the user
[103]	576	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	577	k = nzt
	578	!
	579	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	580	kmzp = 0.25_wp * &
[102]	581	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	582	kmzm = 0.25_wp * &
[102]	583	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	584
[1320]	585	tend(k,j,i) = tend(k,j,i) &
	586	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	587	& ) * ddzw(k) &
	588	& + ( -uswst(j,i) &
	589	& - kmzm * ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
[102]	590	& ) * ddzw(k)
	591	ENDIF
	592
[1]	593	END SUBROUTINE diffusion_u_ij
	594
	595	END MODULE diffusion_u_mod

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