source: palm/trunk/SOURCE/diffusion_v.f90 @ 392

Last change on this file since 392 was 392, checked in by raasch, 12 years ago

New:
---

Adapted for machine lck
(mrun, mbuild, subjob)

bc_lr/bc_ns in most subroutines replaced by LOGICAL variables bc_lr_cyc,
bc_ns_cyc for speed optimization
(check_parameters, diffusion_u, diffusion_v, diffusion_w, modules)

Additional timestep criterion in case of simulations with plant canopy (timestep)

Check for illegal entries in section_xy|xz|yz that exceed nz+1|ny+1|nx+1
(check_parameters)

Clipping of dvrp output implemented. Default colourtable for particles
implemented, particle attributes (color, dvrp_size) can be set with new
parameters particle_color, particle_dvrpsize, color_interval,
dvrpsize_interval (init_dvrp, data_output_dvrp, modules, user_data_output_dvrp).
Slicer attributes (dvrp) are set with new routine set_slicer_attributes_dvrp
and are controlled with existing parameters slicer_range_limits.
(set_slicer_attributes_dvrp)

Ocean atmosphere coupling allows to use independent precursor runs in order
to account for different spin-up times. The time when coupling has to be
started is given by new inipar parameter coupling_start_time. The precursor
ocean run has to be started using new mrun option "-y" in order to add
appendix "_O" to all output files.
(check_for_restart, check_parameters, data_output_2d, data_output_3d,
data_output_profiles, data_output_ptseries, data_output_spectra,
data_output_tseries, header, init_coupling, modules, mrun,
parin, read_var_list, surface_coupler, time_integration, write_var_list)

Polygon reduction for topography and ground plate isosurface. Reduction level
for buildings can be chosen with parameter cluster_size. (init_dvrp)

External pressure gradient (check_parameters, header, init_3d_model, modules,
parin, prognostic_equations, read_var_list, write_var_list)

New topography case 'single_street_canyon' (header, init_grid, modules, parin,
read_var_list, user_check_parameters, user_header, user_init_grid, write_var_list)

Option to predefine a target bulk velocity for conserve_volume_flow
(check_parameters, header, init_3d_model, modules, parin, read_var_list,
write_var_list)

Option for user defined 2D data output in xy cross sections at z=nzb+1
(data_output_2d, user_data_output_2d)

xy cross section output of surface heatfluxes (latent, sensible)
(average_3d_data, check_parameters, data_output_2d, modules, read_3d_binary,
sum_up_3d_data, write_3d_binary)

average_3d_data, check_for_restart, check_parameters, data_output_2d, data_output_3d, data_output_dvrp, data_output_profiles, data_output_ptseries, data_output_spectra, data_output_tseries, init_coupling, init_dvrp, init_grid, init_3d_model, header, mbuild, modules, mrun, package_parin, parin, prognostic_equations, read_3d_binary, read_var_list, subjob, surface_coupler, timestep, time_integration, user_check_parameters, user_data_output_2d, user_data_output_dvrp, user_header, user_init_grid, write_3d_binary, write_var_list

New: set_particle_attributes, set_slicer_attributes_dvrp

Changed:


lcmuk changed to lc to avoid problems with Intel compiler on sgi-ice
(poisfft)

For extended NetCDF files, the updated title attribute includes an update of
time_average_text where appropriate. (netcdf)

In case of restart runs without extension, initial profiles are not written
to NetCDF-file anymore. (data_output_profiles, modules, read_var_list, write_var_list)

Small change in formatting of the message handling routine concering the output in the
job protocoll. (message)

initializing_actions='read_data_for_recycling' renamed to 'cyclic_fill', now
independent of turbulent_inflow (check_parameters, header, init_3d_model)

2 NetCDF error numbers changed. (data_output_3d)

A Link to the website appendix_a.html is printed for further information
about the possible errors. (message)

Temperature gradient criterion for estimating the boundary layer height
replaced by the gradient criterion of Sullivan et al. (1998). (flow_statistics)

NetCDF unit attribute in timeseries output in case of statistic regions added
(netcdf)

Output of NetCDF messages with aid of message handling routine.
(check_open, close_file, data_output_2d, data_output_3d,
data_output_profiles, data_output_ptseries, data_output_spectra,
data_output_tseries, netcdf, output_particles_netcdf)

Output of messages replaced by message handling routine.
(advec_particles, advec_s_bc, buoyancy, calc_spectra, check_for_restart,
check_open, coriolis, cpu_log, data_output_2d, data_output_3d, data_output_dvrp,
data_output_profiles, data_output_spectra, fft_xy, flow_statistics, header,
init_1d_model, init_3d_model, init_dvrp, init_grid, init_particles, init_pegrid,
netcdf, parin, plant_canopy_model, poisfft_hybrid, poismg, read_3d_binary,
read_var_list, surface_coupler, temperton_fft, timestep, user_actions,
user_data_output_dvrp, user_dvrp_coltab, user_init_grid, user_init_plant_canopy,
user_parin, user_read_restart_data, user_spectra )

Maximum number of tails is calculated from maximum number of particles and
skip_particles_for_tail (init_particles)

Value of vertical_particle_advection may differ for each particle group
(advec_particles, header, modules)

First constant in array den also defined as type double. (eqn_state_seawater)

Parameter dvrp_psize moved from particles_par to dvrp_graphics_par. (package_parin)

topography_grid_convention moved from userpar to inipar (check_parameters,
header, parin, read_var_list, user_check_parameters, user_header,
user_init_grid, user_parin, write_var_list)

Default value of grid_matching changed to strict.

Adjustments for runs on lcxt4 (necessary due to an software update on CRAY) and
for coupled runs on ibmy (mrun, subjob)

advec_particles, advec_s_bc, buoyancy, calc_spectra, check_for_restart, check_open, check_parameters, close_file, coriolis, cpu_log, data_output_2d, data_output_3d, data_output_dvrp, data_output_profiles, data_output_ptseries, data_output_spectra, data_output_tseries, eqn_state_seawater, fft_xy, flow_statistics, header, init_1d_model, init_3d_model, init_dvrp, init_grid, init_particles, init_pegrid, message, mrun, netcdf, output_particles_netcdf, package_parin, parin, plant_canopy_model, poisfft, poisfft_hybrid, poismg, read_3d_binary, read_var_list, sort_particles, subjob, user_check_parameters, user_header, user_init_grid, user_parin, surface_coupler, temperton_fft, timestep, user_actions, user_data_output_dvrp, user_dvrp_coltab, user_init_grid, user_init_plant_canopy, user_parin, user_read_restart_data, user_spectra, write_var_list

Errors:


Bugfix: Initial hydrostatic pressure profile in case of ocean runs is now
calculated in 5 iteration steps. (init_ocean)

Bugfix: wrong sign in buoyancy production of ocean part in case of not using
the reference density (only in 3D routine production_e) (production_e)

Bugfix: output of averaged 2d/3d quantities requires that an avaraging
interval has been set, respective error message is included (check_parameters)

Bugfix: Output on unit 14 only if requested by write_binary.
(user_last_actions)

Bugfix to avoid zero division by km_neutral (production_e)

Bugfix for extended NetCDF files: In order to avoid 'data mode' errors if
updated attributes are larger than their original size, NF90_PUT_ATT is called
in 'define mode' enclosed by NF90_REDEF and NF90_ENDDEF calls. This implies a
possible performance loss; an alternative strategy would be to ensure equal
attribute size in a job chain. (netcdf)

Bugfix: correction of initial volume flow for non-flat topography (init_3d_model)
Bugfix: zero initialization of arrays within buildings for 'cyclic_fill' (init_3d_model)

Bugfix: to_be_resorted => s_av for time-averaged scalars (data_output_2d, data_output_3d)

Bugfix: error in formatting the output (message)

Bugfix: avoid that ngp_2dh_s_inner becomes zero (init_3_model)

Typographical error: unit of wpt in dots_unit (modules)

Bugfix: error in check, if particles moved further than one subdomain length.
This check must not be applied for newly released particles. (advec_particles)

Bugfix: several tail counters are initialized, particle_tail_coordinates is
only written to file if its third index is > 0, arrays for tails are allocated
with a minimum size of 10 tails if there is no tail initially (init_particles,
advec_particles)

Bugfix: pressure included for profile output (check_parameters)

Bugfix: Type of count and count_rate changed to default INTEGER on NEC machines
(cpu_log)

Bugfix: output if particle time series only if particle advection is switched
on. (time_integration)

Bugfix: qsws was calculated in case of constant heatflux = .FALSE. (prandtl_fluxes)

Bugfix: averaging along z is not allowed for 2d quantities (e.g. u* and z0) (data_output_2d)

Typographical errors (netcdf)

If the inversion height calculated by the prerun is zero, inflow_damping_height
must be explicitly specified (init_3d_model)

Small bugfix concerning 3d 64bit netcdf output format (header)

Bugfix: dt_fixed removed from the restart file, because otherwise, no change
from a fixed to a variable timestep would be possible in restart runs.
(read_var_list, write_var_list)

Bugfix: initial setting of time_coupling in coupled restart runs (time_integration)

advec_particles, check_parameters, cpu_log, data_output_2d, data_output_3d, header, init_3d_model, init_particles, init_ocean, modules, netcdf, prandtl_fluxes, production_e, read_var_list, time_integration, user_last_actions, write_var_list

  • Property svn:keywords set to Id
File size: 17.7 KB
Line 
1 MODULE diffusion_v_mod
2
3!------------------------------------------------------------------------------!
4! Actual revisions:
5! -----------------
6!
7!
8! Former revisions:
9! -----------------
10! $Id: diffusion_v.f90 392 2009-09-24 10:39:14Z raasch $
11!
12! 366 2009-08-25 08:06:27Z raasch
13! bc_lr replaced by bc_lr_cyc
14!
15! 106 2007-08-16 14:30:26Z raasch
16! Momentumflux at top (vswst) included as boundary condition,
17! j loop is starting from nysv (needed for non-cyclic boundary conditions)
18!
19! 75 2007-03-22 09:54:05Z raasch
20! Wall functions now include diabatic conditions, call of routine wall_fluxes,
21! z0 removed from argument list, vynp eliminated
22!
23! 20 2007-02-26 00:12:32Z raasch
24! Bugfix: ddzw dimensioned 1:nzt"+1"
25!
26! RCS Log replace by Id keyword, revision history cleaned up
27!
28! Revision 1.15  2006/02/23 10:36:00  raasch
29! nzb_2d replaced by nzb_v_outer in horizontal diffusion and by nzb_v_inner
30! or nzb_diff_v, respectively, in vertical diffusion,
31! wall functions added for north and south walls, +z0 in argument list,
32! terms containing w(k-1,..) are removed from the Prandtl-layer equation
33! because they cause errors at the edges of topography
34! WARNING: loops containing the MAX function are still not properly vectorized!
35!
36! Revision 1.1  1997/09/12 06:24:01  raasch
37! Initial revision
38!
39!
40! Description:
41! ------------
42! Diffusion term of the v-component
43!------------------------------------------------------------------------------!
44
45    USE wall_fluxes_mod
46
47    PRIVATE
48    PUBLIC diffusion_v
49
50    INTERFACE diffusion_v
51       MODULE PROCEDURE diffusion_v
52       MODULE PROCEDURE diffusion_v_ij
53    END INTERFACE diffusion_v
54
55 CONTAINS
56
57
58!------------------------------------------------------------------------------!
59! Call for all grid points
60!------------------------------------------------------------------------------!
61    SUBROUTINE diffusion_v( ddzu, ddzw, km, km_damp_x, tend, u, v, vsws, &
62                            vswst, w )
63
64       USE control_parameters
65       USE grid_variables
66       USE indices
67
68       IMPLICIT NONE
69
70       INTEGER ::  i, j, k
71       REAL    ::  kmxm_x, kmxm_y, kmxp_x, kmxp_y, kmzm, kmzp
72       REAL    ::  ddzu(1:nzt+1), ddzw(1:nzt+1), km_damp_x(nxl-1:nxr+1)
73       REAL    ::  tend(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1)
74       REAL, DIMENSION(:,:),   POINTER ::  vsws, vswst
75       REAL, DIMENSION(:,:,:), POINTER ::  km, u, v, w
76       REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) ::  vsus
77
78!
79!--    First calculate horizontal momentum flux v'u' at vertical walls,
80!--    if neccessary
81       IF ( topography /= 'flat' )  THEN
82          CALL wall_fluxes( vsus, 0.0, 1.0, 0.0, 0.0, nzb_v_inner, &
83                            nzb_v_outer, wall_v )
84       ENDIF
85
86       DO  i = nxl, nxr
87          DO  j = nysv, nyn
88!
89!--          Compute horizontal diffusion
90             DO  k = nzb_v_outer(j,i)+1, nzt
91!
92!--             Interpolate eddy diffusivities on staggered gridpoints
93                kmxp_x = 0.25 * &
94                         ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
95                kmxm_x = 0.25 * &
96                         ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
97                kmxp_y = kmxp_x
98                kmxm_y = kmxm_x
99!
100!--             Increase diffusion at the outflow boundary in case of
101!--             non-cyclic lateral boundaries. Damping is only needed for
102!--             velocity components parallel to the outflow boundary in
103!--             the direction normal to the outflow boundary.
104                IF ( .NOT. bc_lr_cyc )  THEN
105                   kmxp_x = MAX( kmxp_x, km_damp_x(i) )
106                   kmxm_x = MAX( kmxm_x, km_damp_x(i) )
107                ENDIF
108
109                tend(k,j,i) = tend(k,j,i)                                    &
110                      & + ( kmxp_x * ( v(k,j,i+1) - v(k,j,i)     ) * ddx     &
111                      &   + kmxp_y * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy     &
112                      &   - kmxm_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx         &
113                      &   - kmxm_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy         &
114                      &   ) * ddx                                            &
115                      & + 2.0 * (                                            &
116                      &           km(k,j,i)   * ( v(k,j+1,i) - v(k,j,i) )    &
117                      &         - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) )    &
118                      &         ) * ddy2
119             ENDDO
120
121!
122!--          Wall functions at the left and right walls, respectively
123             IF ( wall_v(j,i) /= 0.0 )  THEN
124
125                DO  k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
126                   kmxp_x = 0.25 * &
127                            ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
128                   kmxm_x = 0.25 * &
129                            ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
130                   kmxp_y = kmxp_x
131                   kmxm_y = kmxm_x
132!
133!--                Increase diffusion at the outflow boundary in case of
134!--                non-cyclic lateral boundaries. Damping is only needed for
135!--                velocity components parallel to the outflow boundary in
136!--                the direction normal to the outflow boundary.
137                   IF ( .NOT. bc_lr_cyc )  THEN
138                      kmxp_x = MAX( kmxp_x, km_damp_x(i) )
139                      kmxm_x = MAX( kmxm_x, km_damp_x(i) )
140                   ENDIF
141
142                   tend(k,j,i) = tend(k,j,i)                                   &
143                                 + 2.0 * (                                     &
144                                       km(k,j,i)   * ( v(k,j+1,i) - v(k,j,i) ) &
145                                     - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
146                                         ) * ddy2                              &
147                                 + (   fxp(j,i) * (                            &
148                                  kmxp_x * ( v(k,j,i+1) - v(k,j,i)     ) * ddx &
149                                + kmxp_y * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
150                                                  )                            &
151                                     - fxm(j,i) * (                            &
152                                  kmxm_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx     &
153                                + kmxm_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy     &
154                                                  )                            &
155                                     + wall_v(j,i) * vsus(k,j,i)               &
156                                   ) * ddx
157                ENDDO
158             ENDIF
159
160!
161!--          Compute vertical diffusion. In case of simulating a Prandtl
162!--          layer, index k starts at nzb_v_inner+2.
163             DO  k = nzb_diff_v(j,i), nzt_diff
164!
165!--             Interpolate eddy diffusivities on staggered gridpoints
166                kmzp = 0.25 * &
167                       ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
168                kmzm = 0.25 * &
169                       ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
170
171                tend(k,j,i) = tend(k,j,i)                                    &
172                      & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1)   &
173                      &            + ( w(k,j,i) - w(k,j-1,i) ) * ddy         &
174                      &            )                                         &
175                      &   - kmzm * ( ( v(k,j,i)   - v(k-1,j,i)   ) * ddzu(k) &
176                      &            + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy     &
177                      &            )                                         &
178                      &   ) * ddzw(k)
179             ENDDO
180
181!
182!--          Vertical diffusion at the first grid point above the surface,
183!--          if the momentum flux at the bottom is given by the Prandtl law
184!--          or if it is prescribed by the user.
185!--          Difference quotient of the momentum flux is not formed over
186!--          half of the grid spacing (2.0*ddzw(k)) any more, since the
187!--          comparison with other (LES) modell showed that the values of
188!--          the momentum flux becomes too large in this case.
189!--          The term containing w(k-1,..) (see above equation) is removed here
190!--          because the vertical velocity is assumed to be zero at the surface.
191             IF ( use_surface_fluxes )  THEN
192                k = nzb_v_inner(j,i)+1
193!
194!--             Interpolate eddy diffusivities on staggered gridpoints
195                kmzp = 0.25 * &
196                       ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
197                kmzm = 0.25 * &
198                       ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
199
200                tend(k,j,i) = tend(k,j,i)                                    &
201                      & + ( kmzp * ( w(k,j,i) - w(k,j-1,i)     ) * ddy       &
202                      &   ) * ddzw(k)                                        &
203                      & + ( kmzp * ( v(k+1,j,i) - v(k,j,i)     ) * ddzu(k+1) &
204                      &   + vsws(j,i)                                        &
205                      &   ) * ddzw(k)
206             ENDIF
207
208!
209!--          Vertical diffusion at the first gridpoint below the top boundary,
210!--          if the momentum flux at the top is prescribed by the user
211             IF ( use_top_fluxes  .AND.  constant_top_momentumflux )  THEN
212                k = nzt
213!
214!--             Interpolate eddy diffusivities on staggered gridpoints
215                kmzp = 0.25 * &
216                       ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
217                kmzm = 0.25 * &
218                       ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
219
220                tend(k,j,i) = tend(k,j,i)                                    &
221                      & - ( kmzm *  ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy      &
222                      &   ) * ddzw(k)                                        &
223                      & + ( -vswst(j,i)                                      &
224                      &   - kmzm * ( v(k,j,i)   - v(k-1,j,i)    ) * ddzu(k)  &
225                      &   ) * ddzw(k)
226             ENDIF
227
228          ENDDO
229       ENDDO
230
231    END SUBROUTINE diffusion_v
232
233
234!------------------------------------------------------------------------------!
235! Call for grid point i,j
236!------------------------------------------------------------------------------!
237    SUBROUTINE diffusion_v_ij( i, j, ddzu, ddzw, km, km_damp_x, tend, u, v, &
238                               vsws, vswst, w )
239
240       USE control_parameters
241       USE grid_variables
242       USE indices
243
244       IMPLICIT NONE
245
246       INTEGER ::  i, j, k
247       REAL    ::  kmxm_x, kmxm_y, kmxp_x, kmxp_y, kmzm, kmzp
248       REAL    ::  ddzu(1:nzt+1), ddzw(1:nzt+1), km_damp_x(nxl-1:nxr+1)
249       REAL    ::  tend(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1)
250       REAL, DIMENSION(nzb:nzt+1)      ::  vsus
251       REAL, DIMENSION(:,:),   POINTER ::  vsws, vswst
252       REAL, DIMENSION(:,:,:), POINTER ::  km, u, v, w
253
254!
255!--    Compute horizontal diffusion
256       DO  k = nzb_v_outer(j,i)+1, nzt
257!
258!--       Interpolate eddy diffusivities on staggered gridpoints
259          kmxp_x = 0.25 * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
260          kmxm_x = 0.25 * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
261          kmxp_y = kmxp_x
262          kmxm_y = kmxm_x
263!
264!--       Increase diffusion at the outflow boundary in case of non-cyclic
265!--       lateral boundaries. Damping is only needed for velocity components
266!--       parallel to the outflow boundary in the direction normal to the
267!--       outflow boundary.
268          IF ( .NOT. bc_lr_cyc )  THEN
269             kmxp_x = MAX( kmxp_x, km_damp_x(i) )
270             kmxm_x = MAX( kmxm_x, km_damp_x(i) )
271          ENDIF
272
273          tend(k,j,i) = tend(k,j,i)                                          &
274                      & + ( kmxp_x * ( v(k,j,i+1) - v(k,j,i)     ) * ddx     &
275                      &   + kmxp_y * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy     &
276                      &   - kmxm_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx         &
277                      &   - kmxm_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy         &
278                      &   ) * ddx                                            &
279                      & + 2.0 * (                                            &
280                      &           km(k,j,i)   * ( v(k,j+1,i) - v(k,j,i) )    &
281                      &         - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) )    &
282                      &         ) * ddy2
283       ENDDO
284
285!
286!--    Wall functions at the left and right walls, respectively
287       IF ( wall_v(j,i) /= 0.0 )  THEN
288
289!
290!--       Calculate the horizontal momentum flux v'u'
291          CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), &
292                            vsus, 0.0, 1.0, 0.0, 0.0 )
293
294          DO  k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
295             kmxp_x = 0.25 * &
296                      ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
297             kmxm_x = 0.25 * &
298                      ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
299             kmxp_y = kmxp_x
300             kmxm_y = kmxm_x
301!
302!--          Increase diffusion at the outflow boundary in case of
303!--          non-cyclic lateral boundaries. Damping is only needed for
304!--          velocity components parallel to the outflow boundary in
305!--          the direction normal to the outflow boundary.
306             IF ( .NOT. bc_lr_cyc )  THEN
307                kmxp_x = MAX( kmxp_x, km_damp_x(i) )
308                kmxm_x = MAX( kmxm_x, km_damp_x(i) )
309             ENDIF
310
311             tend(k,j,i) = tend(k,j,i)                                         &
312                                 + 2.0 * (                                     &
313                                       km(k,j,i)   * ( v(k,j+1,i) - v(k,j,i) ) &
314                                     - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
315                                         ) * ddy2                              &
316                                 + (   fxp(j,i) * (                            &
317                                  kmxp_x * ( v(k,j,i+1) - v(k,j,i)     ) * ddx &
318                                + kmxp_y * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
319                                                  )                            &
320                                     - fxm(j,i) * (                            &
321                                  kmxm_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx     &
322                                + kmxm_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy     &
323                                                  )                            &
324                                     + wall_v(j,i) * vsus(k)                   &
325                                   ) * ddx
326          ENDDO
327       ENDIF
328
329!
330!--    Compute vertical diffusion. In case of simulating a Prandtl layer,
331!--    index k starts at nzb_v_inner+2.
332       DO  k = nzb_diff_v(j,i), nzt_diff
333!
334!--       Interpolate eddy diffusivities on staggered gridpoints
335          kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
336          kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
337
338          tend(k,j,i) = tend(k,j,i)                                          &
339                      & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1)   &
340                      &            + ( w(k,j,i) - w(k,j-1,i) ) * ddy         &
341                      &            )                                         &
342                      &   - kmzm * ( ( v(k,j,i)   - v(k-1,j,i)   ) * ddzu(k) &
343                      &            + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy     &
344                      &            )                                         &
345                      &   ) * ddzw(k)
346       ENDDO
347
348!
349!--    Vertical diffusion at the first grid point above the surface, if the
350!--    momentum flux at the bottom is given by the Prandtl law or if it is
351!--    prescribed by the user.
352!--    Difference quotient of the momentum flux is not formed over half of
353!--    the grid spacing (2.0*ddzw(k)) any more, since the comparison with
354!--    other (LES) modell showed that the values of the momentum flux becomes
355!--    too large in this case.
356!--    The term containing w(k-1,..) (see above equation) is removed here
357!--    because the vertical velocity is assumed to be zero at the surface.
358       IF ( use_surface_fluxes )  THEN
359          k = nzb_v_inner(j,i)+1
360!
361!--       Interpolate eddy diffusivities on staggered gridpoints
362          kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
363          kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
364
365          tend(k,j,i) = tend(k,j,i)                                          &
366                      & + ( kmzp * ( w(k,j,i) - w(k,j-1,i)     ) * ddy       &
367                      &   ) * ddzw(k)                                        &
368                      & + ( kmzp * ( v(k+1,j,i) - v(k,j,i)     ) * ddzu(k+1) &
369                      &   + vsws(j,i)                                        &
370                      &   ) * ddzw(k)
371       ENDIF
372
373!
374!--    Vertical diffusion at the first gridpoint below the top boundary,
375!--    if the momentum flux at the top is prescribed by the user
376       IF ( use_top_fluxes  .AND.  constant_top_momentumflux )  THEN
377          k = nzt
378!
379!--       Interpolate eddy diffusivities on staggered gridpoints
380          kmzp = 0.25 * &
381                 ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
382          kmzm = 0.25 * &
383                 ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
384
385          tend(k,j,i) = tend(k,j,i)                                          &
386                      & - ( kmzm *  ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy      &
387                      &   ) * ddzw(k)                                        &
388                      & + ( -vswst(j,i)                                      &
389                      &   - kmzm * ( v(k,j,i)   - v(k-1,j,i)    ) * ddzu(k)  &
390                      &   ) * ddzw(k)
391       ENDIF
392
393    END SUBROUTINE diffusion_v_ij
394
395 END MODULE diffusion_v_mod
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