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source: palm/trunk/SOURCE/diffusion_s.f90 @ 1935

Last change on this file since 1935 was 1874, checked in by maronga, 9 years ago
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[1873]	1	!> @file diffusion_s.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:
[1001]	20	! ------------------
[1341]	21	!
[1692]	22	!
[1321]	23	! Former revisions:
	24	! -----------------
	25	! $Id: diffusion_s.f90 1874 2016-04-18 14:51:10Z hellstea $
	26	!
[1874]	27	! 1873 2016-04-18 14:50:06Z maronga
	28	! Module renamed (removed _mod)
	29	!
	30	!
[1851]	31	! 1850 2016-04-08 13:29:27Z maronga
	32	! Module renamed
	33	!
	34	!
[1692]	35	! 1691 2015-10-26 16:17:44Z maronga
	36	! Formatting corrections.
	37	!
[1683]	38	! 1682 2015-10-07 23:56:08Z knoop
	39	! Code annotations made doxygen readable
	40	!
[1375]	41	! 1374 2014-04-25 12:55:07Z raasch
	42	! missing variables added to ONLY list
	43	!
[1341]	44	! 1340 2014-03-25 19:45:13Z kanani
	45	! REAL constants defined as wp-kind
	46	!
[1321]	47	! 1320 2014-03-20 08:40:49Z raasch
[1320]	48	! ONLY-attribute added to USE-statements,
	49	! kind-parameters added to all INTEGER and REAL declaration statements,
	50	! kinds are defined in new module kinds,
	51	! revision history before 2012 removed,
	52	! comment fields (!:) to be used for variable explanations added to
	53	! all variable declaration statements
[1321]	54	!
[1258]	55	! 1257 2013-11-08 15:18:40Z raasch
	56	! openacc loop and loop vector clauses removed
	57	!
[1132]	58	! 1128 2013-04-12 06:19:32Z raasch
	59	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	60	! j_north
	61	!
[1093]	62	! 1092 2013-02-02 11:24:22Z raasch
	63	! unused variables removed
	64	!
[1037]	65	! 1036 2012-10-22 13:43:42Z raasch
	66	! code put under GPL (PALM 3.9)
	67	!
[1017]	68	! 1015 2012-09-27 09:23:24Z raasch
	69	! accelerator version (*_acc) added
	70	!
[1011]	71	! 1010 2012-09-20 07:59:54Z raasch
	72	! cpp switch __nopointer added for pointer free version
	73	!
[1002]	74	! 1001 2012-09-13 14:08:46Z raasch
	75	! some arrays comunicated by module instead of parameter list
	76	!
[1]	77	! Revision 1.1 2000/04/13 14:54:02 schroeter
	78	! Initial revision
	79	!
	80	!
	81	! Description:
	82	! ------------
[1682]	83	!> Diffusion term of scalar quantities (temperature and water content)
[1]	84	!------------------------------------------------------------------------------!
[1682]	85	MODULE diffusion_s_mod
	86
[1]	87
	88	PRIVATE
[1015]	89	PUBLIC diffusion_s, diffusion_s_acc
[1]	90
	91	INTERFACE diffusion_s
	92	MODULE PROCEDURE diffusion_s
	93	MODULE PROCEDURE diffusion_s_ij
	94	END INTERFACE diffusion_s
	95
[1015]	96	INTERFACE diffusion_s_acc
	97	MODULE PROCEDURE diffusion_s_acc
	98	END INTERFACE diffusion_s_acc
	99
[1]	100	CONTAINS
	101
	102
	103	!------------------------------------------------------------------------------!
[1682]	104	! Description:
	105	! ------------
	106	!> Call for all grid points
[1]	107	!------------------------------------------------------------------------------!
[1001]	108	SUBROUTINE diffusion_s( s, s_flux_b, s_flux_t, wall_s_flux )
[1]	109
[1320]	110	USE arrays_3d, &
	111	ONLY: ddzu, ddzw, kh, tend
	112
	113	USE control_parameters, &
	114	ONLY: use_surface_fluxes, use_top_fluxes
	115
	116	USE grid_variables, &
	117	ONLY: ddx2, ddy2, fwxm, fwxp, fwym, fwyp, wall_w_x, wall_w_y
	118
	119	USE indices, &
[1374]	120	ONLY: nxl, nxlg, nxr, nxrg, nyn, nyng, nys, nysg, nzb, &
[1320]	121	nzb_diff_s_inner, nzb_s_inner, nzb_s_outer, nzt, nzt_diff
	122
	123	USE kinds
[1]	124
	125	IMPLICIT NONE
	126
[1682]	127	INTEGER(iwp) :: i !<
	128	INTEGER(iwp) :: j !<
	129	INTEGER(iwp) :: k !<
	130	REAL(wp) :: wall_s_flux(0:4) !<
	131	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: s_flux_b, s_flux_t !<
[1010]	132	#if defined( __nopointer )
[1682]	133	REAL(wp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: s !<
[1010]	134	#else
[1682]	135	REAL(wp), DIMENSION(:,:,:), POINTER :: s !<
[1010]	136	#endif
[1]	137
	138	DO i = nxl, nxr
	139	DO j = nys,nyn
	140	!
	141	!-- Compute horizontal diffusion
[19]	142	DO k = nzb_s_outer(j,i)+1, nzt
[1]	143
[1320]	144	tend(k,j,i) = tend(k,j,i) &
[1340]	145	+ 0.5_wp * ( &
[1320]	146	( kh(k,j,i) + kh(k,j,i+1) ) * ( s(k,j,i+1)-s(k,j,i) ) &
	147	- ( kh(k,j,i) + kh(k,j,i-1) ) * ( s(k,j,i)-s(k,j,i-1) ) &
[1340]	148	) * ddx2 &
	149	+ 0.5_wp * ( &
[1320]	150	( kh(k,j,i) + kh(k,j+1,i) ) * ( s(k,j+1,i)-s(k,j,i) ) &
	151	- ( kh(k,j,i) + kh(k,j-1,i) ) * ( s(k,j,i)-s(k,j-1,i) ) &
[1340]	152	) * ddy2
[1]	153	ENDDO
	154
	155	!
	156	!-- Apply prescribed horizontal wall heatflux where necessary
[1691]	157	IF ( ( wall_w_x(j,i) /= 0.0_wp ) .OR. ( wall_w_y(j,i) /= 0.0_wp ) &
	158	) THEN
[1]	159	DO k = nzb_s_inner(j,i)+1, nzb_s_outer(j,i)
	160
[1320]	161	tend(k,j,i) = tend(k,j,i) &
[1340]	162	+ ( fwxp(j,i) * 0.5_wp * &
[1320]	163	( kh(k,j,i) + kh(k,j,i+1) ) * ( s(k,j,i+1)-s(k,j,i) ) &
[1340]	164	+ ( 1.0_wp - fwxp(j,i) ) * wall_s_flux(1) &
	165	-fwxm(j,i) * 0.5_wp * &
[1320]	166	( kh(k,j,i) + kh(k,j,i-1) ) * ( s(k,j,i)-s(k,j,i-1) ) &
[1340]	167	+ ( 1.0_wp - fwxm(j,i) ) * wall_s_flux(2) &
[1320]	168	) * ddx2 &
[1340]	169	+ ( fwyp(j,i) * 0.5_wp * &
[1320]	170	( kh(k,j,i) + kh(k,j+1,i) ) * ( s(k,j+1,i)-s(k,j,i) ) &
[1340]	171	+ ( 1.0_wp - fwyp(j,i) ) * wall_s_flux(3) &
	172	-fwym(j,i) * 0.5_wp * &
[1320]	173	( kh(k,j,i) + kh(k,j-1,i) ) * ( s(k,j,i)-s(k,j-1,i) ) &
[1340]	174	+ ( 1.0_wp - fwym(j,i) ) * wall_s_flux(4) &
[1]	175	) * ddy2
	176	ENDDO
	177	ENDIF
	178
	179	!
	180	!-- Compute vertical diffusion. In case that surface fluxes have been
[19]	181	!-- prescribed or computed at bottom and/or top, index k starts/ends at
	182	!-- nzb+2 or nzt-1, respectively.
	183	DO k = nzb_diff_s_inner(j,i), nzt_diff
[1]	184
[1320]	185	tend(k,j,i) = tend(k,j,i) &
[1340]	186	+ 0.5_wp * ( &
[1320]	187	( kh(k,j,i) + kh(k+1,j,i) ) * ( s(k+1,j,i)-s(k,j,i) ) * ddzu(k+1) &
	188	- ( kh(k,j,i) + kh(k-1,j,i) ) * ( s(k,j,i)-s(k-1,j,i) ) * ddzu(k) &
[1340]	189	) * ddzw(k)
[1]	190	ENDDO
	191
	192	!
[19]	193	!-- Vertical diffusion at the first computational gridpoint along
[1]	194	!-- z-direction
	195	IF ( use_surface_fluxes ) THEN
	196
	197	k = nzb_s_inner(j,i)+1
	198
[1320]	199	tend(k,j,i) = tend(k,j,i) &
[1340]	200	+ ( 0.5_wp * ( kh(k,j,i)+kh(k+1,j,i) ) &
	201	* ( s(k+1,j,i)-s(k,j,i) ) &
	202	* ddzu(k+1) &
[1320]	203	+ s_flux_b(j,i) &
[1]	204	) * ddzw(k)
	205
	206	ENDIF
	207
[19]	208	!
	209	!-- Vertical diffusion at the last computational gridpoint along
	210	!-- z-direction
	211	IF ( use_top_fluxes ) THEN
	212
	213	k = nzt
	214
[1320]	215	tend(k,j,i) = tend(k,j,i) &
	216	+ ( - s_flux_t(j,i) &
[1340]	217	- 0.5_wp * ( kh(k-1,j,i)+kh(k,j,i) )&
	218	* ( s(k,j,i)-s(k-1,j,i) ) &
	219	* ddzu(k) &
[19]	220	) * ddzw(k)
	221
	222	ENDIF
	223
[1]	224	ENDDO
	225	ENDDO
	226
	227	END SUBROUTINE diffusion_s
	228
	229
	230	!------------------------------------------------------------------------------!
[1682]	231	! Description:
	232	! ------------
	233	!> Call for all grid points - accelerator version
[1015]	234	!------------------------------------------------------------------------------!
	235	SUBROUTINE diffusion_s_acc( s, s_flux_b, s_flux_t, wall_s_flux )
	236
[1320]	237	USE arrays_3d, &
	238	ONLY: ddzu, ddzw, kh, tend
	239
	240	USE control_parameters, &
	241	ONLY: use_surface_fluxes, use_top_fluxes
	242
	243	USE grid_variables, &
	244	ONLY: ddx2, ddy2, fwxm, fwxp, fwym, fwyp, wall_w_x, wall_w_y
	245
	246	USE indices, &
	247	ONLY: i_left, i_right, j_north, j_south, nxlg, nxrg, nyng, nysg, &
[1374]	248	nzb, nzb_diff_s_inner, nzb_s_inner, nzb_s_outer, nzt, nzt_diff
[1320]	249
	250	USE kinds
[1015]	251
	252	IMPLICIT NONE
	253
[1682]	254	INTEGER(iwp) :: i !<
	255	INTEGER(iwp) :: j !<
	256	INTEGER(iwp) :: k !<
	257	REAL(wp) :: wall_s_flux(0:4) !<
	258	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: s_flux_b !<
	259	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: s_flux_t !<
[1015]	260	#if defined( __nopointer )
[1682]	261	REAL(wp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: s !<
[1015]	262	#else
[1682]	263	REAL(wp), DIMENSION(:,:,:), POINTER :: s !<
[1015]	264	#endif
	265
	266	!$acc kernels present( ddzu, ddzw, fwxm, fwxp, fwym, fwyp, kh ) &
	267	!$acc present( nzb_diff_s_inner, nzb_s_inner, nzb_s_outer, s ) &
	268	!$acc present( s_flux_b, s_flux_t, tend, wall_s_flux ) &
	269	!$acc present( wall_w_x, wall_w_y )
[1128]	270	DO i = i_left, i_right
	271	DO j = j_south, j_north
[1015]	272	!
	273	!-- Compute horizontal diffusion
	274	DO k = 1, nzt
	275	IF ( k > nzb_s_outer(j,i) ) THEN
	276
[1320]	277	tend(k,j,i) = tend(k,j,i) &
[1340]	278	+ 0.5_wp * ( &
[1320]	279	( kh(k,j,i) + kh(k,j,i+1) ) * ( s(k,j,i+1)-s(k,j,i) ) &
	280	- ( kh(k,j,i) + kh(k,j,i-1) ) * ( s(k,j,i)-s(k,j,i-1) ) &
[1340]	281	) * ddx2 &
	282	+ 0.5_wp * ( &
[1320]	283	( kh(k,j,i) + kh(k,j+1,i) ) * ( s(k,j+1,i)-s(k,j,i) ) &
	284	- ( kh(k,j,i) + kh(k,j-1,i) ) * ( s(k,j,i)-s(k,j-1,i) ) &
[1340]	285	) * ddy2
[1015]	286	ENDIF
	287	ENDDO
	288
	289	!
	290	!-- Apply prescribed horizontal wall heatflux where necessary
	291	DO k = 1, nzt
	292	IF ( k > nzb_s_inner(j,i) .AND. k <= nzb_s_outer(j,i) .AND. &
[1340]	293	( wall_w_x(j,i) /= 0.0_wp .OR. wall_w_y(j,i) /= 0.0_wp ) ) &
[1015]	294	THEN
[1320]	295	tend(k,j,i) = tend(k,j,i) &
[1340]	296	+ ( fwxp(j,i) * 0.5_wp * &
[1320]	297	( kh(k,j,i) + kh(k,j,i+1) ) * ( s(k,j,i+1)-s(k,j,i) ) &
[1340]	298	+ ( 1.0_wp - fwxp(j,i) ) * wall_s_flux(1) &
	299	-fwxm(j,i) * 0.5_wp * &
[1320]	300	( kh(k,j,i) + kh(k,j,i-1) ) * ( s(k,j,i)-s(k,j,i-1) ) &
[1340]	301	+ ( 1.0_wp - fwxm(j,i) ) * wall_s_flux(2) &
[1320]	302	) * ddx2 &
[1340]	303	+ ( fwyp(j,i) * 0.5_wp * &
[1320]	304	( kh(k,j,i) + kh(k,j+1,i) ) * ( s(k,j+1,i)-s(k,j,i) ) &
[1340]	305	+ ( 1.0_wp - fwyp(j,i) ) * wall_s_flux(3) &
	306	-fwym(j,i) * 0.5_wp * &
[1320]	307	( kh(k,j,i) + kh(k,j-1,i) ) * ( s(k,j,i)-s(k,j-1,i) ) &
[1340]	308	+ ( 1.0_wp - fwym(j,i) ) * wall_s_flux(4) &
[1015]	309	) * ddy2
	310	ENDIF
	311	ENDDO
	312
	313	!
	314	!-- Compute vertical diffusion. In case that surface fluxes have been
	315	!-- prescribed or computed at bottom and/or top, index k starts/ends at
	316	!-- nzb+2 or nzt-1, respectively.
	317	DO k = 1, nzt_diff
	318	IF ( k >= nzb_diff_s_inner(j,i) ) THEN
[1320]	319	tend(k,j,i) = tend(k,j,i) &
[1340]	320	+ 0.5_wp * ( &
[1320]	321	( kh(k,j,i) + kh(k+1,j,i) ) * ( s(k+1,j,i)-s(k,j,i) ) * ddzu(k+1) &
	322	- ( kh(k,j,i) + kh(k-1,j,i) ) * ( s(k,j,i)-s(k-1,j,i) ) * ddzu(k) &
[1340]	323	) * ddzw(k)
[1015]	324	ENDIF
	325	ENDDO
	326
	327	!
	328	!-- Vertical diffusion at the first computational gridpoint along
	329	!-- z-direction
	330	DO k = 1, nzt
	331	IF ( use_surface_fluxes .AND. k == nzb_s_inner(j,i)+1 ) THEN
[1320]	332	tend(k,j,i) = tend(k,j,i) &
[1340]	333	+ ( 0.5_wp * ( kh(k,j,i)+kh(k+1,j,i) )&
	334	* ( s(k+1,j,i)-s(k,j,i) ) &
	335	* ddzu(k+1) &
[1320]	336	+ s_flux_b(j,i) &
[1015]	337	) * ddzw(k)
	338	ENDIF
	339
	340	!
	341	!-- Vertical diffusion at the last computational gridpoint along
	342	!-- z-direction
	343	IF ( use_top_fluxes .AND. k == nzt ) THEN
	344	tend(k,j,i) = tend(k,j,i) &
	345	+ ( - s_flux_t(j,i) &
[1340]	346	- 0.5_wp * ( kh(k-1,j,i)+kh(k,j,i) )&
	347	* ( s(k,j,i)-s(k-1,j,i) ) &
	348	* ddzu(k) &
[1015]	349	) * ddzw(k)
	350	ENDIF
	351	ENDDO
	352
	353	ENDDO
	354	ENDDO
	355	!$acc end kernels
	356
	357	END SUBROUTINE diffusion_s_acc
	358
	359
	360	!------------------------------------------------------------------------------!
[1682]	361	! Description:
	362	! ------------
	363	!> Call for grid point i,j
[1]	364	!------------------------------------------------------------------------------!
[1001]	365	SUBROUTINE diffusion_s_ij( i, j, s, s_flux_b, s_flux_t, wall_s_flux )
[1]	366
[1320]	367	USE arrays_3d, &
	368	ONLY: ddzu, ddzw, kh, tend
	369
	370	USE control_parameters, &
	371	ONLY: use_surface_fluxes, use_top_fluxes
	372
	373	USE grid_variables, &
	374	ONLY: ddx2, ddy2, fwxm, fwxp, fwym, fwyp, wall_w_x, wall_w_y
	375
	376	USE indices, &
[1374]	377	ONLY: nxlg, nxrg, nyng, nysg, nzb, nzb_diff_s_inner, nzb_s_inner, &
[1320]	378	nzb_s_outer, nzt, nzt_diff
	379
	380	USE kinds
[1]	381
	382	IMPLICIT NONE
	383
[1682]	384	INTEGER(iwp) :: i !<
	385	INTEGER(iwp) :: j !<
	386	INTEGER(iwp) :: k !<
	387	REAL(wp) :: wall_s_flux(0:4) !<
	388	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: s_flux_b !<
	389	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: s_flux_t !<
[1010]	390	#if defined( __nopointer )
[1682]	391	REAL(wp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: s !<
[1010]	392	#else
[1682]	393	REAL(wp), DIMENSION(:,:,:), POINTER :: s !<
[1010]	394	#endif
[1]	395
	396	!
	397	!-- Compute horizontal diffusion
[19]	398	DO k = nzb_s_outer(j,i)+1, nzt
[1]	399
[1320]	400	tend(k,j,i) = tend(k,j,i) &
[1340]	401	+ 0.5_wp * ( &
[1320]	402	( kh(k,j,i) + kh(k,j,i+1) ) * ( s(k,j,i+1)-s(k,j,i) ) &
	403	- ( kh(k,j,i) + kh(k,j,i-1) ) * ( s(k,j,i)-s(k,j,i-1) ) &
[1340]	404	) * ddx2 &
	405	+ 0.5_wp * ( &
[1320]	406	( kh(k,j,i) + kh(k,j+1,i) ) * ( s(k,j+1,i)-s(k,j,i) ) &
	407	- ( kh(k,j,i) + kh(k,j-1,i) ) * ( s(k,j,i)-s(k,j-1,i) ) &
[1340]	408	) * ddy2
[1]	409	ENDDO
	410
	411	!
	412	!-- Apply prescribed horizontal wall heatflux where necessary
[1691]	413	IF ( ( wall_w_x(j,i) /= 0.0_wp ) .OR. ( wall_w_y(j,i) /= 0.0_wp ) ) &
[1]	414	THEN
	415	DO k = nzb_s_inner(j,i)+1, nzb_s_outer(j,i)
	416
[1320]	417	tend(k,j,i) = tend(k,j,i) &
[1340]	418	+ ( fwxp(j,i) * 0.5_wp * &
[1320]	419	( kh(k,j,i) + kh(k,j,i+1) ) * ( s(k,j,i+1)-s(k,j,i) ) &
[1340]	420	+ ( 1.0_wp - fwxp(j,i) ) * wall_s_flux(1) &
	421	-fwxm(j,i) * 0.5_wp * &
[1320]	422	( kh(k,j,i) + kh(k,j,i-1) ) * ( s(k,j,i)-s(k,j,i-1) ) &
[1340]	423	+ ( 1.0_wp - fwxm(j,i) ) * wall_s_flux(2) &
[1320]	424	) * ddx2 &
[1340]	425	+ ( fwyp(j,i) * 0.5_wp * &
[1320]	426	( kh(k,j,i) + kh(k,j+1,i) ) * ( s(k,j+1,i)-s(k,j,i) ) &
[1340]	427	+ ( 1.0_wp - fwyp(j,i) ) * wall_s_flux(3) &
	428	-fwym(j,i) * 0.5_wp * &
[1320]	429	( kh(k,j,i) + kh(k,j-1,i) ) * ( s(k,j,i)-s(k,j-1,i) ) &
[1340]	430	+ ( 1.0_wp - fwym(j,i) ) * wall_s_flux(4) &
[1]	431	) * ddy2
	432	ENDDO
	433	ENDIF
	434
	435	!
	436	!-- Compute vertical diffusion. In case that surface fluxes have been
[19]	437	!-- prescribed or computed at bottom and/or top, index k starts/ends at
	438	!-- nzb+2 or nzt-1, respectively.
	439	DO k = nzb_diff_s_inner(j,i), nzt_diff
[1]	440
[1320]	441	tend(k,j,i) = tend(k,j,i) &
[1340]	442	+ 0.5_wp * ( &
[1320]	443	( kh(k,j,i) + kh(k+1,j,i) ) * ( s(k+1,j,i)-s(k,j,i) ) * ddzu(k+1) &
	444	- ( kh(k,j,i) + kh(k-1,j,i) ) * ( s(k,j,i)-s(k-1,j,i) ) * ddzu(k) &
[1340]	445	) * ddzw(k)
[1]	446	ENDDO
	447
	448	!
[19]	449	!-- Vertical diffusion at the first computational gridpoint along z-direction
[1]	450	IF ( use_surface_fluxes ) THEN
	451
	452	k = nzb_s_inner(j,i)+1
	453
[1340]	454	tend(k,j,i) = tend(k,j,i) + ( 0.5_wp * ( kh(k,j,i)+kh(k+1,j,i) ) &
	455	* ( s(k+1,j,i)-s(k,j,i) ) &
	456	* ddzu(k+1) &
[1320]	457	+ s_flux_b(j,i) &
[19]	458	) * ddzw(k)
[1]	459
	460	ENDIF
	461
[19]	462	!
	463	!-- Vertical diffusion at the last computational gridpoint along z-direction
	464	IF ( use_top_fluxes ) THEN
	465
	466	k = nzt
	467
[1320]	468	tend(k,j,i) = tend(k,j,i) + ( - s_flux_t(j,i) &
[1340]	469	- 0.5_wp * ( kh(k-1,j,i)+kh(k,j,i) ) &
	470	* ( s(k,j,i)-s(k-1,j,i) ) &
	471	* ddzu(k) &
[19]	472	) * ddzw(k)
	473
	474	ENDIF
	475
[1]	476	END SUBROUTINE diffusion_s_ij
	477
	478	END MODULE diffusion_s_mod

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