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source: palm/trunk/SOURCE/diffusion_u_mod.f90 @ 1850

Last change on this file since 1850 was 1850, checked in by maronga, 8 years ago
added _mod string to several filenames to meet the naming convection for modules
Property svn:keywords set to `Id`
File size: 26.8 KB

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

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