source: palm/trunk/SOURCE/diffusion_s.f90 @ 667

Last change on this file since 667 was 667, checked in by suehring, 11 years ago

summary:


Gryschka:

  • Coupling with different resolution and different numbers of PEs in ocean and atmosphere is available
  • Exchange of u and v from ocean surface to atmosphere surface
  • Mirror boundary condition for u and v at the bottom are replaced by dirichlet boundary conditions
  • Inflow turbulence is now defined by flucuations around spanwise mean
  • Bugfixes for cyclic_fill and constant_volume_flow

Suehring:

  • New advection added ( Wicker and Skamarock 5th order ), therefore:
    • New module advec_ws.f90
    • Modified exchange of ghost boundaries.
    • Modified evaluation of turbulent fluxes
    • New index bounds nxlg, nxrg, nysg, nyng

advec_ws.f90


Advection scheme for scalars and momentum using the flux formulation of
Wicker and Skamarock 5th order.
Additionally the module contains of a routine using for initialisation and
steering of the statical evaluation. The computation of turbulent fluxes takes
place inside the advection routines.
In case of vector architectures Dirichlet and Radiation boundary conditions are
outstanding and not available. Furthermore simulations within topography are
not possible so far. A further routine local_diss_ij is available and is used
if a control of dissipative fluxes is desired.

check_parameters.f90


Exchange of parameters between ocean and atmosphere via PE0
Check for illegal combination of ws-scheme and timestep scheme.
Check for topography and ws-scheme.
Check for not cyclic boundary conditions in combination with ws-scheme and
loop_optimization = 'vector'.
Check for call_psolver_at_all_substeps and ws-scheme for momentum_advec.

Different processor/grid topology in atmosphere and ocean is now allowed!
Bugfixes in checking for conserve_volume_flow_mode.

exchange_horiz.f90


Dynamic exchange of ghost points with nbgp_local to ensure that no useless
ghost points exchanged in case of multigrid. type_yz(0) and type_xz(0) used for
normal grid, the remaining types used for the several grid levels.
Exchange is done via MPI-Vectors with a dynamic value of ghost points which
depend on the advection scheme. Exchange of left and right PEs is 10% faster
with MPI-Vectors than without.

flow_statistics.f90


When advection is computed with ws-scheme, turbulent fluxes are already
computed in the respective advection routines and buffered in arrays
sums_xxxx_ws_l(). This is due to a consistent treatment of statistics
with the numerics and to avoid unphysical kinks near the surface. So some if-
requests has to be done to dicern between fluxes from ws-scheme other advection
schemes. Furthermore the computation of z_i is only done if the heat flux
exceeds a minimum value. This affects only simulations of a neutral boundary
layer and is due to reasons of computations in the advection scheme.

inflow_turbulence.f90


Using nbgp recycling planes for a better resolution of the turbulent flow near
the inflow.

init_grid.f90


Definition of new array bounds nxlg, nxrg, nysg, nyng on each PE.
Furthermore the allocation of arrays and steering of loops is done with these
parameters. Call of exchange_horiz are modified.
In case of dirichlet bounday condition at the bottom zu(0)=0.0
dzu_mg has to be set explicitly for a equally spaced grid near bottom.
ddzu_pres added to use a equally spaced grid near bottom.

init_pegrid.f90


Moved determination of target_id's from init_coupling
Determination of parameters needed for coupling (coupling_topology, ngp_a, ngp_o)
with different grid/processor-topology in ocean and atmosphere

Adaption of ngp_xy, ngp_y to a dynamic number of ghost points.
The maximum_grid_level changed from 1 to 0. 0 is the normal grid, 1 to
maximum_grid_level the grids for multigrid, in which 0 and 1 are normal grids.
This distinction is due to reasons of data exchange and performance for the
normal grid and grids in poismg.
The definition of MPI-Vectors adapted to a dynamic numer of ghost points.
New MPI-Vectors for data exchange between left and right boundaries added.
This is due to reasons of performance (10% faster).

ATTENTION: nnz_x undefined problem still has to be solved!!!!!!!!
TEST OUTPUT (TO BE REMOVED) logging mpi2 ierr values

parin.f90


Steering parameter dissipation_control added in inipar.

Makefile


Module advec_ws added.

Modules


Removed u_nzb_p1_for_vfc and v_nzb_p1_for_vfc

For coupling with different resolution in ocean and atmophere:
+nx_a, +nx_o, ny_a, +ny_o, ngp_a, ngp_o, +total_2d_o, +total_2d_a,
+coupling_topology

Buffer arrays for the left sided advective fluxes added in arrays_3d.
+flux_s_u, +flux_s_v, +flux_s_w, +diss_s_u, +diss_s_v, +diss_s_w,
+flux_s_pt, +diss_s_pt, +flux_s_e, +diss_s_e, +flux_s_q, +diss_s_q,
+flux_s_sa, +diss_s_sa
3d arrays for dissipation control added. (only necessary for vector arch.)
+var_x, +var_y, +var_z, +gamma_x, +gamma_y, +gamma_z
Default of momentum_advec and scalar_advec changed to 'ws-scheme' .
+exchange_mg added in control_parameters to steer the data exchange.
Parameters +nbgp, +nxlg, +nxrg, +nysg, +nyng added in indices.
flag array +boundary_flags added in indices to steer the degradation of order
of the advective fluxes when non-cyclic boundaries are used.
MPI-datatypes +type_y, +type_y_int and +type_yz for data_exchange added in
pegrid.
+sums_wsus_ws_l, +sums_wsvs_ws_l, +sums_us2_ws_l, +sums_vs2_ws_l,
+sums_ws2_ws_l, +sums_wspts_ws_l, +sums_wssas_ws_l, +sums_wsqs_ws_l
and +weight_substep added in statistics to steer the statistical evaluation
of turbulent fluxes in the advection routines.
LOGICALS +ws_scheme_sca and +ws_scheme_mom added to get a better performance
in prognostic_equations.
LOGICAL +dissipation_control control added to steer numerical dissipation
in ws-scheme.

Changed length of string run_description_header

pres.f90


New allocation of tend when ws-scheme and multigrid is used. This is due to
reasons of perforance of the data_exchange. The same is done with p after
poismg is called.
nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng when no
multigrid is used. Calls of exchange_horiz are modified.

bugfix: After pressure correction no volume flow correction in case of
non-cyclic boundary conditions
(has to be done only before pressure correction)

Call of SOR routine is referenced with ddzu_pres.

prognostic_equations.f90


Calls of the advection routines with WS5 added.
Calls of ws_statistics added to set the statistical arrays to zero after each
time step.

advec_particles.f90


Declaration of de_dx, de_dy, de_dz adapted to additional ghost points.
Furthermore the calls of exchange_horiz were modified.

asselin_filter.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

average_3d_data.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

boundary_conds.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng
Removed mirror boundary conditions for u and v at the bottom in case of
ibc_uv_b == 0. Instead, dirichelt boundary conditions (u=v=0) are set
in init_3d_model

calc_liquid_water_content.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

calc_spectra.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng for
allocation of tend.

check_open.f90


Output of total array size was adapted to nbgp.

data_output_2d.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng in loops and
allocation of arrays local_2d and total_2d.
Calls of exchange_horiz are modified.

data_output_2d.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng in loops and
allocation of arrays. Calls of exchange_horiz are modified.
Skip-value skip_do_avs changed to a dynamic adaption of ghost points.

data_output_mask.f90


Calls of exchange_horiz are modified.

diffusion_e.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusion_s.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusion_u.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusion_v.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusion_w.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusivities.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusivities.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.
Calls of exchange_horiz are modified.

exchange_horiz_2d.f90


Dynamic exchange of ghost points with nbgp, which depends on the advection
scheme. Exchange between left and right PEs is now done with MPI-vectors.

global_min_max.f90


Adapting of the index arrays, because MINLOC assumes lowerbound
at 1 and not at nbgp.

init_3d_model.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng in loops and
allocation of arrays. Calls of exchange_horiz are modified.
Call ws_init to initialize arrays needed for statistical evaluation and
optimization when ws-scheme is used.
Initial volume flow is now calculated by using the variable hom_sum.
Therefore the correction of initial volume flow for non-flat topography
removed (removed u_nzb_p1_for_vfc and v_nzb_p1_for_vfc)
Changed surface boundary conditions for u and v in case of ibc_uv_b == 0 from
mirror bc to dirichlet boundary conditions (u=v=0), so that k=nzb is
representative for the height z0

Bugfix: type conversion of '1' to 64bit for the MAX function (ngp_3d_inner)

init_coupling.f90


determination of target_id's moved to init_pegrid

init_pt_anomaly.f90


Call of exchange_horiz are modified.

init_rankine.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.
Calls of exchange_horiz are modified.

init_slope.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

header.f90


Output of advection scheme.

poismg.f90


Calls of exchange_horiz are modified.

prandtl_fluxes.f90


Changed surface boundary conditions for u and v from mirror bc to dirichelt bc,
therefore u(uzb,:,:) and v(nzb,:,:) is now representative for the height z0
nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

production_e.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

read_3d_binary.f90


+/- 1 replaced with +/- nbgp when swapping and allocating variables.

sor.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.
Call of exchange_horiz are modified.
bug removed in declaration of ddzw(), nz replaced by nzt+1

subsidence.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

sum_up_3d_data.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

surface_coupler.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng in
MPI_SEND() and MPI_RECV.
additional case for nonequivalent processor and grid topopolgy in ocean and
atmosphere added (coupling_topology = 1)

Added exchange of u and v from Ocean to Atmosphere

time_integration.f90


Calls of exchange_horiz are modified.
Adaption to slooping surface.

timestep.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

user_3d_data_averaging.f90, user_data_output_2d.f90, user_data_output_3d.f90,
user_actions.f90, user_init.f90, user_init_plant_canopy.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

user_read_restart_data.f90


Allocation with nbgp.

wall_fluxes.f90


nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

write_compressed.f90


Array bounds and nx, ny adapted with nbgp.

sor.f90


bug removed in declaration of ddzw(), nz replaced by nzt+1

  • Property svn:keywords set to Id
File size: 10.9 KB
Line 
1 MODULE diffusion_s_mod
2
3!------------------------------------------------------------------------------!
4! Current revisions:
5! -----------------
6! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng
7!
8! Former revisions:
9! -----------------
10! $Id: diffusion_s.f90 667 2010-12-23 12:06:00Z suehring $
11!
12! 183 2008-08-04 15:39:12Z letzel
13! bugfix: calculation of fluxes at vertical surfaces
14!
15! 129 2007-10-30 12:12:24Z letzel
16! replace wall_heatflux by wall_s_flux that is now included in the parameter
17! list, bugfix for assignment of fluxes at walls
18!
19! 20 2007-02-26 00:12:32Z raasch
20! Bugfix: ddzw dimensioned 1:nzt"+1"
21! Calculation extended for gridpoint nzt, fluxes can be given at top,
22! +s_flux_t in parameter list, s_flux renamed s_flux_b
23!
24! RCS Log replace by Id keyword, revision history cleaned up
25!
26! Revision 1.8  2006/02/23 10:34:17  raasch
27! nzb_2d replaced by nzb_s_outer in horizontal diffusion and by nzb_s_inner
28! or nzb_diff_s_inner, respectively, in vertical diffusion, prescribed surface
29! fluxes at vertically oriented topography
30!
31! Revision 1.1  2000/04/13 14:54:02  schroeter
32! Initial revision
33!
34!
35! Description:
36! ------------
37! Diffusion term of scalar quantities (temperature and water content)
38!------------------------------------------------------------------------------!
39
40    PRIVATE
41    PUBLIC diffusion_s
42
43    INTERFACE diffusion_s
44       MODULE PROCEDURE diffusion_s
45       MODULE PROCEDURE diffusion_s_ij
46    END INTERFACE diffusion_s
47
48 CONTAINS
49
50
51!------------------------------------------------------------------------------!
52! Call for all grid points
53!------------------------------------------------------------------------------!
54    SUBROUTINE diffusion_s( ddzu, ddzw, kh, s, s_flux_b, s_flux_t, &
55                            wall_s_flux, tend )
56
57       USE control_parameters
58       USE grid_variables
59       USE indices
60
61       IMPLICIT NONE
62
63       INTEGER ::  i, j, k
64       REAL    ::  vertical_gridspace
65       REAL    ::  ddzu(1:nzt+1), ddzw(1:nzt+1)
66       REAL    ::  tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg)
67       REAL    ::  wall_s_flux(0:4)
68       REAL, DIMENSION(:,:),   POINTER ::  s_flux_b, s_flux_t
69       REAL, DIMENSION(:,:,:), POINTER ::  kh, s
70
71       DO  i = nxl, nxr
72          DO  j = nys,nyn
73!
74!--          Compute horizontal diffusion
75             DO  k = nzb_s_outer(j,i)+1, nzt
76
77                tend(k,j,i) = tend(k,j,i)                                     &
78                                          + 0.5 * (                           &
79                        ( kh(k,j,i) + kh(k,j,i+1) ) * ( s(k,j,i+1)-s(k,j,i) ) &
80                      - ( kh(k,j,i) + kh(k,j,i-1) ) * ( s(k,j,i)-s(k,j,i-1) ) &
81                                                  ) * ddx2                    &
82                                          + 0.5 * (                           &
83                        ( kh(k,j,i) + kh(k,j+1,i) ) * ( s(k,j+1,i)-s(k,j,i) ) &
84                      - ( kh(k,j,i) + kh(k,j-1,i) ) * ( s(k,j,i)-s(k,j-1,i) ) &
85                                                  ) * ddy2
86             ENDDO
87
88!
89!--          Apply prescribed horizontal wall heatflux where necessary
90             IF ( ( wall_w_x(j,i) .NE. 0.0 ) .OR. ( wall_w_y(j,i) .NE. 0.0 ) ) &
91             THEN
92                DO  k = nzb_s_inner(j,i)+1, nzb_s_outer(j,i)
93
94                   tend(k,j,i) = tend(k,j,i)                                  &
95                                                + ( fwxp(j,i) * 0.5 *         &
96                        ( kh(k,j,i) + kh(k,j,i+1) ) * ( s(k,j,i+1)-s(k,j,i) ) &
97                        + ( 1.0 - fwxp(j,i) ) * wall_s_flux(1)                &
98                                                   -fwxm(j,i) * 0.5 *         &
99                        ( kh(k,j,i) + kh(k,j,i-1) ) * ( s(k,j,i)-s(k,j,i-1) ) &
100                        + ( 1.0 - fwxm(j,i) ) * wall_s_flux(2)                &
101                                                  ) * ddx2                    &
102                                                + ( fwyp(j,i) * 0.5 *         &
103                        ( kh(k,j,i) + kh(k,j+1,i) ) * ( s(k,j+1,i)-s(k,j,i) ) &
104                        + ( 1.0 - fwyp(j,i) ) * wall_s_flux(3)                &
105                                                   -fwym(j,i) * 0.5 *         &
106                        ( kh(k,j,i) + kh(k,j-1,i) ) * ( s(k,j,i)-s(k,j-1,i) ) &
107                        + ( 1.0 - fwym(j,i) ) * wall_s_flux(4)                &
108                                                  ) * ddy2
109                ENDDO
110             ENDIF
111
112!
113!--          Compute vertical diffusion. In case that surface fluxes have been
114!--          prescribed or computed at bottom and/or top, index k starts/ends at
115!--          nzb+2 or nzt-1, respectively.
116             DO  k = nzb_diff_s_inner(j,i), nzt_diff
117
118                tend(k,j,i) = tend(k,j,i)                                     &
119                                       + 0.5 * (                              &
120            ( kh(k,j,i) + kh(k+1,j,i) ) * ( s(k+1,j,i)-s(k,j,i) ) * ddzu(k+1) &
121          - ( kh(k,j,i) + kh(k-1,j,i) ) * ( s(k,j,i)-s(k-1,j,i) ) * ddzu(k)   &
122                                               ) * ddzw(k)
123             ENDDO
124
125!
126!--          Vertical diffusion at the first computational gridpoint along
127!--          z-direction
128             IF ( use_surface_fluxes )  THEN
129
130                k = nzb_s_inner(j,i)+1
131
132                tend(k,j,i) = tend(k,j,i)                                     &
133                                       + ( 0.5 * ( kh(k,j,i)+kh(k+1,j,i) )    &
134                                               * ( s(k+1,j,i)-s(k,j,i) )      &
135                                               * ddzu(k+1)                    &
136                                           + s_flux_b(j,i)                    &
137                                         ) * ddzw(k)
138
139             ENDIF
140
141!
142!--          Vertical diffusion at the last computational gridpoint along
143!--          z-direction
144             IF ( use_top_fluxes )  THEN
145
146                k = nzt
147
148                tend(k,j,i) = tend(k,j,i)                                     &
149                                       + ( - s_flux_t(j,i)                    &
150                                           - 0.5 * ( kh(k-1,j,i)+kh(k,j,i) )  &
151                                                 * ( s(k,j,i)-s(k-1,j,i) )    &
152                                                 * ddzu(k)                    &
153                                         ) * ddzw(k)
154
155             ENDIF
156
157          ENDDO
158       ENDDO
159
160    END SUBROUTINE diffusion_s
161
162
163!------------------------------------------------------------------------------!
164! Call for grid point i,j
165!------------------------------------------------------------------------------!
166    SUBROUTINE diffusion_s_ij( i, j, ddzu, ddzw, kh, s, s_flux_b, s_flux_t, &
167                               wall_s_flux, tend )
168
169       USE control_parameters
170       USE grid_variables
171       USE indices
172
173       IMPLICIT NONE
174
175       INTEGER ::  i, j, k
176       REAL    ::  vertical_gridspace
177       REAL    ::  ddzu(1:nzt+1), ddzw(1:nzt+1)
178       REAL    ::  tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg)
179       REAL    ::  wall_s_flux(0:4)
180       REAL, DIMENSION(:,:),   POINTER ::  s_flux_b, s_flux_t
181       REAL, DIMENSION(:,:,:), POINTER ::  kh, s
182
183!
184!--    Compute horizontal diffusion
185       DO  k = nzb_s_outer(j,i)+1, nzt
186
187          tend(k,j,i) = tend(k,j,i)                                           &
188                                          + 0.5 * (                           &
189                        ( kh(k,j,i) + kh(k,j,i+1) ) * ( s(k,j,i+1)-s(k,j,i) ) &
190                      - ( kh(k,j,i) + kh(k,j,i-1) ) * ( s(k,j,i)-s(k,j,i-1) ) &
191                                                  ) * ddx2                    &
192                                          + 0.5 * (                           &
193                        ( kh(k,j,i) + kh(k,j+1,i) ) * ( s(k,j+1,i)-s(k,j,i) ) &
194                      - ( kh(k,j,i) + kh(k,j-1,i) ) * ( s(k,j,i)-s(k,j-1,i) ) &
195                                                  ) * ddy2
196       ENDDO
197
198!
199!--    Apply prescribed horizontal wall heatflux where necessary
200       IF ( ( wall_w_x(j,i) .NE. 0.0 ) .OR. ( wall_w_y(j,i) .NE. 0.0 ) ) &
201       THEN
202          DO  k = nzb_s_inner(j,i)+1, nzb_s_outer(j,i)
203
204             tend(k,j,i) = tend(k,j,i)                                        &
205                                                + ( fwxp(j,i) * 0.5 *         &
206                        ( kh(k,j,i) + kh(k,j,i+1) ) * ( s(k,j,i+1)-s(k,j,i) ) &
207                        + ( 1.0 - fwxp(j,i) ) * wall_s_flux(1)                &
208                                                   -fwxm(j,i) * 0.5 *         &
209                        ( kh(k,j,i) + kh(k,j,i-1) ) * ( s(k,j,i)-s(k,j,i-1) ) &
210                        + ( 1.0 - fwxm(j,i) ) * wall_s_flux(2)                &
211                                                  ) * ddx2                    &
212                                                + ( fwyp(j,i) * 0.5 *         &
213                        ( kh(k,j,i) + kh(k,j+1,i) ) * ( s(k,j+1,i)-s(k,j,i) ) &
214                        + ( 1.0 - fwyp(j,i) ) * wall_s_flux(3)                &
215                                                   -fwym(j,i) * 0.5 *         &
216                        ( kh(k,j,i) + kh(k,j-1,i) ) * ( s(k,j,i)-s(k,j-1,i) ) &
217                        + ( 1.0 - fwym(j,i) ) * wall_s_flux(4)                &
218                                                  ) * ddy2
219          ENDDO
220       ENDIF
221
222!
223!--    Compute vertical diffusion. In case that surface fluxes have been
224!--    prescribed or computed at bottom and/or top, index k starts/ends at
225!--    nzb+2 or nzt-1, respectively.
226       DO  k = nzb_diff_s_inner(j,i), nzt_diff
227
228          tend(k,j,i) = tend(k,j,i)                                           &
229                                       + 0.5 * (                              &
230            ( kh(k,j,i) + kh(k+1,j,i) ) * ( s(k+1,j,i)-s(k,j,i) ) * ddzu(k+1) &
231          - ( kh(k,j,i) + kh(k-1,j,i) ) * ( s(k,j,i)-s(k-1,j,i) ) * ddzu(k)   &
232                                               ) * ddzw(k)
233       ENDDO
234
235!
236!--    Vertical diffusion at the first computational gridpoint along z-direction
237       IF ( use_surface_fluxes )  THEN
238
239          k = nzb_s_inner(j,i)+1
240
241          tend(k,j,i) = tend(k,j,i) + ( 0.5 * ( kh(k,j,i)+kh(k+1,j,i) )  &
242                                            * ( s(k+1,j,i)-s(k,j,i) )    &
243                                            * ddzu(k+1)                  &
244                                        + s_flux_b(j,i)                  &
245                                      ) * ddzw(k)
246
247       ENDIF
248
249!
250!--    Vertical diffusion at the last computational gridpoint along z-direction
251       IF ( use_top_fluxes )  THEN
252
253          k = nzt
254
255          tend(k,j,i) = tend(k,j,i) + ( - s_flux_t(j,i)                  &
256                                      - 0.5 * ( kh(k-1,j,i)+kh(k,j,i) )  &
257                                            * ( s(k,j,i)-s(k-1,j,i) )    &
258                                            * ddzu(k)                    &
259                                      ) * ddzw(k)
260
261       ENDIF
262
263    END SUBROUTINE diffusion_s_ij
264
265 END MODULE diffusion_s_mod
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