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source: palm/trunk/SOURCE/diffusion_u.f90 @ 2076

Last change on this file since 2076 was 2038, checked in by knoop, 8 years ago
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[1873]	1	!> @file diffusion_u.f90
[2000]	2	!------------------------------------------------------------------------------!
[1036]	3	! This file is part of PALM.
	4	!
[2000]	5	! PALM is free software: you can redistribute it and/or modify it under the
	6	! terms of the GNU General Public License as published by the Free Software
	7	! Foundation, either version 3 of the License, or (at your option) any later
	8	! version.
[1036]	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	!
[1818]	17	! Copyright 1997-2016 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[484]	20	! Current revisions:
[1]	21	! -----------------
[1341]	22	!
[2038]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: diffusion_u.f90 2038 2016-10-26 11:16:56Z raasch $
	27	!
[2038]	28	! 2037 2016-10-26 11:15:40Z knoop
	29	! Anelastic approximation implemented
	30	!
[2001]	31	! 2000 2016-08-20 18:09:15Z knoop
	32	! Forced header and separation lines into 80 columns
	33	!
[1874]	34	! 1873 2016-04-18 14:50:06Z maronga
	35	! Module renamed (removed _mod)
	36	!
	37	!
[1851]	38	! 1850 2016-04-08 13:29:27Z maronga
	39	! Module renamed
	40	!
	41	!
[1741]	42	! 1740 2016-01-13 08:19:40Z raasch
	43	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
	44	!
[1692]	45	! 1691 2015-10-26 16:17:44Z maronga
	46	! Formatting corrections.
	47	!
[1683]	48	! 1682 2015-10-07 23:56:08Z knoop
	49	! Code annotations made doxygen readable
	50	!
[1341]	51	! 1340 2014-03-25 19:45:13Z kanani
	52	! REAL constants defined as wp-kind
	53	!
[1321]	54	! 1320 2014-03-20 08:40:49Z raasch
[1320]	55	! ONLY-attribute added to USE-statements,
	56	! kind-parameters added to all INTEGER and REAL declaration statements,
	57	! kinds are defined in new module kinds,
	58	! revision history before 2012 removed,
	59	! comment fields (!:) to be used for variable explanations added to
	60	! all variable declaration statements
[1321]	61	!
[1258]	62	! 1257 2013-11-08 15:18:40Z raasch
	63	! openacc loop and loop vector clauses removed, declare create moved after
	64	! the FORTRAN declaration statement
	65	!
[1132]	66	! 1128 2013-04-12 06:19:32Z raasch
	67	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	68	! j_north
	69	!
[1037]	70	! 1036 2012-10-22 13:43:42Z raasch
	71	! code put under GPL (PALM 3.9)
	72	!
[1017]	73	! 1015 2012-09-27 09:23:24Z raasch
	74	! accelerator version (*_acc) added
	75	!
[1002]	76	! 1001 2012-09-13 14:08:46Z raasch
	77	! arrays comunicated by module instead of parameter list
	78	!
[979]	79	! 978 2012-08-09 08:28:32Z fricke
	80	! outflow damping layer removed
	81	! kmym_x/_y and kmyp_x/_y change to kmym and kmyp
	82	!
[1]	83	! Revision 1.1 1997/09/12 06:23:51 raasch
	84	! Initial revision
	85	!
	86	!
	87	! Description:
	88	! ------------
[1682]	89	!> Diffusion term of the u-component
	90	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
	91	!> and slows down the speed on NEC about 5-10%
[1]	92	!------------------------------------------------------------------------------!
[1682]	93	MODULE diffusion_u_mod
	94
[1]	95
[56]	96	USE wall_fluxes_mod
	97
[1]	98	PRIVATE
[1015]	99	PUBLIC diffusion_u, diffusion_u_acc
[1]	100
	101	INTERFACE diffusion_u
	102	MODULE PROCEDURE diffusion_u
	103	MODULE PROCEDURE diffusion_u_ij
	104	END INTERFACE diffusion_u
	105
[1015]	106	INTERFACE diffusion_u_acc
	107	MODULE PROCEDURE diffusion_u_acc
	108	END INTERFACE diffusion_u_acc
	109
[1]	110	CONTAINS
	111
	112
	113	!------------------------------------------------------------------------------!
[1682]	114	! Description:
	115	! ------------
	116	!> Call for all grid points
[1]	117	!------------------------------------------------------------------------------!
[1001]	118	SUBROUTINE diffusion_u
[1]	119
[1320]	120	USE arrays_3d, &
[2037]	121	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w, &
	122	drho_air, rho_air_zw
[1320]	123
	124	USE control_parameters, &
	125	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	126	use_top_fluxes
	127
	128	USE grid_variables, &
	129	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	130
	131	USE indices, &
	132	ONLY: nxl, nxlu, nxr, nyn, nys, nzb, nzb_diff_u, nzb_u_inner, &
	133	nzb_u_outer, nzt, nzt_diff
	134
	135	USE kinds
[1]	136
	137	IMPLICIT NONE
	138
[1682]	139	INTEGER(iwp) :: i !<
	140	INTEGER(iwp) :: j !<
	141	INTEGER(iwp) :: k !<
	142	REAL(wp) :: kmym !<
	143	REAL(wp) :: kmyp !<
	144	REAL(wp) :: kmzm !<
	145	REAL(wp) :: kmzp !<
[1001]	146
[1682]	147	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs !<
[1]	148
[56]	149	!
	150	!-- First calculate horizontal momentum flux u'v' at vertical walls,
	151	!-- if neccessary
	152	IF ( topography /= 'flat' ) THEN
[1320]	153	CALL wall_fluxes( usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, nzb_u_inner, &
[56]	154	nzb_u_outer, wall_u )
	155	ENDIF
	156
[106]	157	DO i = nxlu, nxr
[1001]	158	DO j = nys, nyn
[1]	159	!
	160	!-- Compute horizontal diffusion
	161	DO k = nzb_u_outer(j,i)+1, nzt
	162	!
	163	!-- Interpolate eddy diffusivities on staggered gridpoints
[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
[1320]	169	tend(k,j,i) = tend(k,j,i) &
[1340]	170	& + 2.0_wp * ( &
[1320]	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 &
[1320]	174	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	175	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	176	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	177	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	178	& ) * ddy
	179	ENDDO
	180
	181	!
	182	!-- Wall functions at the north and south walls, respectively
[1340]	183	IF ( wall_u(j,i) /= 0.0_wp ) THEN
[51]	184
[1]	185	DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i)
[1340]	186	kmyp = 0.25_wp * &
[978]	187	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	188	kmym = 0.25_wp * &
[978]	189	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	190
	191	tend(k,j,i) = tend(k,j,i) &
[1340]	192	+ 2.0_wp * ( &
[1]	193	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	194	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	195	) * ddx2 &
[1]	196	+ ( fyp(j,i) * ( &
[978]	197	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	198	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
[1]	199	) &
	200	- fym(j,i) * ( &
[978]	201	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	202	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	203	) &
[56]	204	+ wall_u(j,i) * usvs(k,j,i) &
[1]	205	) * ddy
	206	ENDDO
	207	ENDIF
	208
	209	!
	210	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	211	!-- index k starts at nzb_u_inner+2.
[102]	212	DO k = nzb_diff_u(j,i), nzt_diff
[1]	213	!
	214	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	215	kmzp = 0.25_wp * &
[1]	216	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	217	kmzm = 0.25_wp * &
[1]	218	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	219
[1320]	220	tend(k,j,i) = tend(k,j,i) &
	221	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	222	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
[2037]	223	& ) * rho_air_zw(k) &
[1320]	224	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	225	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
[2037]	226	& ) * rho_air_zw(k-1) &
	227	& ) * ddzw(k) * drho_air(k)
[1]	228	ENDDO
	229
	230	!
	231	!-- Vertical diffusion at the first grid point above the surface,
	232	!-- if the momentum flux at the bottom is given by the Prandtl law or
	233	!-- if it is prescribed by the user.
	234	!-- Difference quotient of the momentum flux is not formed over half
	235	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	236	!-- with other (LES) models showed that the values of the momentum
[1]	237	!-- flux becomes too large in this case.
	238	!-- The term containing w(k-1,..) (see above equation) is removed here
	239	!-- because the vertical velocity is assumed to be zero at the surface.
	240	IF ( use_surface_fluxes ) THEN
	241	k = nzb_u_inner(j,i)+1
	242	!
	243	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	244	kmzp = 0.25_wp * &
[1]	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) &
[2037]	248	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	249	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	250	& ) * rho_air_zw(k) &
	251	& - ( -usws(j,i) ) &
	252	& ) * ddzw(k) * drho_air(k)
[1]	253	ENDIF
	254
[102]	255	!
	256	!-- Vertical diffusion at the first gridpoint below the top boundary,
	257	!-- if the momentum flux at the top is prescribed by the user
[103]	258	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	259	k = nzt
	260	!
	261	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	262	kmzm = 0.25_wp * &
[102]	263	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	264
[1320]	265	tend(k,j,i) = tend(k,j,i) &
[2037]	266	& + ( ( -uswst(j,i) ) &
	267	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	268	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	269	& ) * rho_air_zw(k-1) &
	270	& ) * ddzw(k) * drho_air(k)
[102]	271	ENDIF
	272
[1]	273	ENDDO
	274	ENDDO
	275
	276	END SUBROUTINE diffusion_u
	277
	278
	279	!------------------------------------------------------------------------------!
[1682]	280	! Description:
	281	! ------------
	282	!> Call for all grid points - accelerator version
[1015]	283	!------------------------------------------------------------------------------!
	284	SUBROUTINE diffusion_u_acc
	285
[1320]	286	USE arrays_3d, &
[2037]	287	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w, &
	288	drho_air, rho_air_zw
[1320]	289
	290	USE control_parameters, &
	291	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	292	use_top_fluxes
	293
	294	USE grid_variables, &
	295	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	296
	297	USE indices, &
	298	ONLY: i_left, i_right, j_north, j_south, nxl, nxr, nyn, nys, nzb, &
	299	nzb_diff_u, nzb_u_inner, nzb_u_outer, nzt, nzt_diff
	300
	301	USE kinds
[1015]	302
	303	IMPLICIT NONE
	304
[1682]	305	INTEGER(iwp) :: i !<
	306	INTEGER(iwp) :: j !<
	307	INTEGER(iwp) :: k !<
	308	REAL(wp) :: kmym !<
	309	REAL(wp) :: kmyp !<
	310	REAL(wp) :: kmzm !<
	311	REAL(wp) :: kmzp !<
[1015]	312
[1682]	313	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs !<
[1015]	314	!$acc declare create ( usvs )
	315
	316	!
	317	!-- First calculate horizontal momentum flux u'v' at vertical walls,
	318	!-- if neccessary
	319	IF ( topography /= 'flat' ) THEN
[1320]	320	CALL wall_fluxes_acc( usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
	321	nzb_u_inner, nzb_u_outer, wall_u )
[1015]	322	ENDIF
	323
[1320]	324	!$acc kernels present ( u, v, w, km, tend, usws, uswst ) &
	325	!$acc present ( ddzu, ddzw, fym, fyp, wall_u ) &
[1015]	326	!$acc present ( nzb_u_inner, nzb_u_outer, nzb_diff_u )
[1128]	327	DO i = i_left, i_right
	328	DO j = j_south, j_north
[1015]	329	!
	330	!-- Compute horizontal diffusion
	331	DO k = 1, nzt
	332	IF ( k > nzb_u_outer(j,i) ) THEN
	333	!
	334	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	335	kmyp = 0.25_wp * &
[1015]	336	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	337	kmym = 0.25_wp * &
[1015]	338	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
	339
	340	tend(k,j,i) = tend(k,j,i) &
[1340]	341	& + 2.0_wp * ( &
[1015]	342	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	343	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	344	& ) * ddx2 &
[1015]	345	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	346	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	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	& ) * ddy
	350	ENDIF
	351	ENDDO
	352
	353	!
	354	!-- Wall functions at the north and south walls, respectively
	355	DO k = 1, nzt
[1320]	356	IF( k > nzb_u_inner(j,i) .AND. k <= nzb_u_outer(j,i) .AND. &
[1340]	357	wall_u(j,i) /= 0.0_wp ) THEN
[1015]	358
[1340]	359	kmyp = 0.25_wp * &
[1015]	360	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	361	kmym = 0.25_wp * &
[1015]	362	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
	363
	364	tend(k,j,i) = tend(k,j,i) &
[1340]	365	+ 2.0_wp * ( &
[1015]	366	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	367	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	368	) * ddx2 &
[1015]	369	+ ( fyp(j,i) * ( &
	370	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	371	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	372	) &
	373	- fym(j,i) * ( &
	374	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	375	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	376	) &
	377	+ wall_u(j,i) * usvs(k,j,i) &
	378	) * ddy
	379	ENDIF
	380	ENDDO
	381
	382	!
	383	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	384	!-- index k starts at nzb_u_inner+2.
	385	DO k = 1, nzt_diff
	386	IF ( k >= nzb_diff_u(j,i) ) THEN
	387	!
	388	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	389	kmzp = 0.25_wp * &
[1015]	390	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	391	kmzm = 0.25_wp * &
[1015]	392	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	393
	394	tend(k,j,i) = tend(k,j,i) &
	395	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1)&
	396	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
[2037]	397	& ) * rho_air_zw(k) &
[1015]	398	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k)&
	399	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
[2037]	400	& ) * rho_air_zw(k-1) &
	401	& ) * ddzw(k) * drho_air(k)
[1015]	402	ENDIF
	403	ENDDO
	404
	405	ENDDO
	406	ENDDO
	407
	408	!
	409	!-- Vertical diffusion at the first grid point above the surface,
	410	!-- if the momentum flux at the bottom is given by the Prandtl law or
	411	!-- if it is prescribed by the user.
	412	!-- Difference quotient of the momentum flux is not formed over half
	413	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	414	!-- with other (LES) models showed that the values of the momentum
[1015]	415	!-- flux becomes too large in this case.
	416	!-- The term containing w(k-1,..) (see above equation) is removed here
	417	!-- because the vertical velocity is assumed to be zero at the surface.
	418	IF ( use_surface_fluxes ) THEN
	419
[1128]	420	DO i = i_left, i_right
	421	DO j = j_south, j_north
[1015]	422
	423	k = nzb_u_inner(j,i)+1
	424	!
	425	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	426	kmzp = 0.25_wp * &
[1015]	427	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	428
[1320]	429	tend(k,j,i) = tend(k,j,i) &
[2037]	430	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	431	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	432	& ) * rho_air_zw(k) &
	433	& - ( -usws(j,i) ) &
	434	& ) * ddzw(k) * drho_air(k)
[1015]	435	ENDDO
	436	ENDDO
	437
	438	ENDIF
	439
	440	!
	441	!-- Vertical diffusion at the first gridpoint below the top boundary,
	442	!-- if the momentum flux at the top is prescribed by the user
	443	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
	444
	445	k = nzt
	446
[1128]	447	DO i = i_left, i_right
	448	DO j = j_south, j_north
[1015]	449
	450	!
	451	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	452	kmzm = 0.25_wp * &
[1015]	453	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	454
[1320]	455	tend(k,j,i) = tend(k,j,i) &
[2037]	456	& + ( ( -uswst(j,i) ) &
	457	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	458	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	459	& ) * rho_air_zw(k-1) &
	460	& ) * ddzw(k) * drho_air(k)
[1015]	461	ENDDO
	462	ENDDO
	463
	464	ENDIF
	465	!$acc end kernels
	466
	467	END SUBROUTINE diffusion_u_acc
	468
	469
	470	!------------------------------------------------------------------------------!
[1682]	471	! Description:
	472	! ------------
	473	!> Call for grid point i,j
[1]	474	!------------------------------------------------------------------------------!
[1001]	475	SUBROUTINE diffusion_u_ij( i, j )
[1]	476
[1320]	477	USE arrays_3d, &
[2037]	478	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w, &
	479	drho_air, rho_air_zw
[1320]	480
	481	USE control_parameters, &
	482	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
	483
	484	USE grid_variables, &
	485	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	486
	487	USE indices, &
	488	ONLY: nzb, nzb_diff_u, nzb_u_inner, nzb_u_outer, nzt, nzt_diff
	489
	490	USE kinds
[1]	491
	492	IMPLICIT NONE
	493
[1682]	494	INTEGER(iwp) :: i !<
	495	INTEGER(iwp) :: j !<
	496	INTEGER(iwp) :: k !<
	497	REAL(wp) :: kmym !<
	498	REAL(wp) :: kmyp !<
	499	REAL(wp) :: kmzm !<
	500	REAL(wp) :: kmzp !<
[1]	501
[1682]	502	REAL(wp), DIMENSION(nzb:nzt+1) :: usvs !<
[1001]	503
[1]	504	!
	505	!-- Compute horizontal diffusion
	506	DO k = nzb_u_outer(j,i)+1, nzt
	507	!
	508	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	509	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	510	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]	511
[1320]	512	tend(k,j,i) = tend(k,j,i) &
[1340]	513	& + 2.0_wp * ( &
[1320]	514	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	515	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	516	& ) * ddx2 &
[1320]	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 &
	519	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	520	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	521	& ) * ddy
	522	ENDDO
	523
	524	!
	525	!-- Wall functions at the north and south walls, respectively
[1691]	526	IF ( wall_u(j,i) /= 0.0_wp ) THEN
[51]	527
	528	!
	529	!-- Calculate the horizontal momentum flux u'v'
[1320]	530	CALL wall_fluxes( i, j, nzb_u_inner(j,i)+1, nzb_u_outer(j,i), &
	531	usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
[51]	532
[1]	533	DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i)
[1340]	534	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	535	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]	536
	537	tend(k,j,i) = tend(k,j,i) &
[1340]	538	+ 2.0_wp * ( &
[1]	539	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	540	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	541	) * ddx2 &
[1]	542	+ ( fyp(j,i) * ( &
[978]	543	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	544	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
[1]	545	) &
	546	- fym(j,i) * ( &
[978]	547	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	548	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	549	) &
[51]	550	+ wall_u(j,i) * usvs(k) &
[1]	551	) * ddy
	552	ENDDO
	553	ENDIF
	554
	555	!
	556	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	557	!-- index k starts at nzb_u_inner+2.
[102]	558	DO k = nzb_diff_u(j,i), nzt_diff
[1]	559	!
	560	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	561	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	562	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]	563
[1320]	564	tend(k,j,i) = tend(k,j,i) &
	565	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	566	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
[2037]	567	& ) * rho_air_zw(k) &
[1320]	568	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	569	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
[2037]	570	& ) * rho_air_zw(k-1) &
	571	& ) * ddzw(k) * drho_air(k)
[1]	572	ENDDO
	573
	574	!
	575	!-- Vertical diffusion at the first grid point above the surface, if the
	576	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	577	!-- prescribed by the user.
	578	!-- Difference quotient of the momentum flux is not formed over half of
	579	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	580	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	581	!-- too large in this case.
	582	!-- The term containing w(k-1,..) (see above equation) is removed here
	583	!-- because the vertical velocity is assumed to be zero at the surface.
	584	IF ( use_surface_fluxes ) THEN
	585	k = nzb_u_inner(j,i)+1
	586	!
	587	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	588	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]	589
[1320]	590	tend(k,j,i) = tend(k,j,i) &
[2037]	591	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	592	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	593	& ) * rho_air_zw(k) &
	594	& - ( -usws(j,i) ) &
	595	& ) * ddzw(k) * drho_air(k)
[1]	596	ENDIF
	597
[102]	598	!
	599	!-- Vertical diffusion at the first gridpoint below the top boundary,
	600	!-- if the momentum flux at the top is prescribed by the user
[103]	601	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	602	k = nzt
	603	!
	604	!-- Interpolate eddy diffusivities on staggered gridpoints
[2037]	605	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
[102]	606
[1320]	607	tend(k,j,i) = tend(k,j,i) &
[2037]	608	& + ( ( -uswst(j,i) ) &
	609	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	610	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	611	& ) * rho_air_zw(k-1) &
	612	& ) * ddzw(k) * drho_air(k)
[102]	613	ENDIF
	614
[1]	615	END SUBROUTINE diffusion_u_ij
	616
	617	END MODULE diffusion_u_mod

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