source: palm/trunk/SOURCE/diffusion_w.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: 15.4 KB
Line 
1 MODULE diffusion_w_mod
2
3!------------------------------------------------------------------------------!
4! Actual revisions:
5! -----------------
6!
7!
8! Former revisions:
9! -----------------
10! $Id: diffusion_w.f90 392 2009-09-24 10:39:14Z raasch $
11!
12! 366 2009-08-25 08:06:27Z raasch
13! bc_lr/bc_ns replaced by bc_lr_cyc/bc_ns_cyc
14!
15! 75 2007-03-22 09:54:05Z raasch
16! Wall functions now include diabatic conditions, call of routine wall_fluxes,
17! z0 removed from argument list
18!
19! 20 2007-02-26 00:12:32Z raasch
20! Bugfix: ddzw dimensioned 1:nzt"+1"
21!
22! RCS Log replace by Id keyword, revision history cleaned up
23!
24! Revision 1.12  2006/02/23 10:38:03  raasch
25! nzb_2d replaced by nzb_w_outer, wall functions added for all vertical walls,
26! +z0 in argument list
27! WARNING: loops containing the MAX function are still not properly vectorized!
28!
29! Revision 1.1  1997/09/12 06:24:11  raasch
30! Initial revision
31!
32!
33! Description:
34! ------------
35! Diffusion term of the w-component
36!------------------------------------------------------------------------------!
37
38    USE wall_fluxes_mod
39
40    PRIVATE
41    PUBLIC diffusion_w
42
43    INTERFACE diffusion_w
44       MODULE PROCEDURE diffusion_w
45       MODULE PROCEDURE diffusion_w_ij
46    END INTERFACE diffusion_w
47
48 CONTAINS
49
50
51!------------------------------------------------------------------------------!
52! Call for all grid points
53!------------------------------------------------------------------------------!
54    SUBROUTINE diffusion_w( ddzu, ddzw, km, km_damp_x, km_damp_y, tend, u, v, &
55                            w )
56
57       USE control_parameters
58       USE grid_variables
59       USE indices
60
61       IMPLICIT NONE
62
63       INTEGER ::  i, j, k
64       REAL    ::  kmxm_x, kmxm_z, kmxp_x, kmxp_z, kmym_y, kmym_z, kmyp_y, &
65                   kmyp_z
66       REAL    ::  ddzu(1:nzt+1), ddzw(1:nzt+1), km_damp_x(nxl-1:nxr+1), &
67                   km_damp_y(nys-1:nyn+1)
68       REAL    ::  tend(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1)
69       REAL, DIMENSION(:,:,:), POINTER ::  km, u, v, w
70       REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) ::  wsus, wsvs
71
72
73!
74!--    First calculate horizontal momentum flux w'u' and/or w'v' at vertical
75!--    walls, if neccessary
76       IF ( topography /= 'flat' )  THEN
77          CALL wall_fluxes( wsus, 0.0, 0.0, 0.0, 1.0, nzb_w_inner, &
78                            nzb_w_outer, wall_w_x )
79          CALL wall_fluxes( wsvs, 0.0, 0.0, 1.0, 0.0, nzb_w_inner, &
80                            nzb_w_outer, wall_w_y )
81       ENDIF
82
83       DO  i = nxl, nxr
84          DO  j = nys, nyn
85             DO  k = nzb_w_outer(j,i)+1, nzt-1
86!
87!--             Interpolate eddy diffusivities on staggered gridpoints
88                kmxp_x = 0.25 * &
89                         ( km(k,j,i)+km(k,j,i+1)+km(k+1,j,i)+km(k+1,j,i+1) )
90                kmxm_x = 0.25 * &
91                         ( km(k,j,i)+km(k,j,i-1)+km(k+1,j,i)+km(k+1,j,i-1) )
92                kmxp_z = kmxp_x
93                kmxm_z = kmxm_x
94                kmyp_y = 0.25 * &
95                         ( km(k,j,i)+km(k+1,j,i)+km(k,j+1,i)+km(k+1,j+1,i) )
96                kmym_y = 0.25 * &
97                         ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
98                kmyp_z = kmyp_y
99                kmym_z = kmym_y
100!
101!--             Increase diffusion at the outflow boundary in case of
102!--             non-cyclic lateral boundaries. Damping is only needed for
103!--             velocity components parallel to the outflow boundary in
104!--             the direction normal to the outflow boundary.
105                IF ( .NOT. bc_lr_cyc )  THEN
106                   kmxp_x = MAX( kmxp_x, km_damp_x(i) )
107                   kmxm_x = MAX( kmxm_x, km_damp_x(i) )
108                ENDIF
109                IF ( .NOT. bc_ns_cyc )  THEN
110                   kmyp_y = MAX( kmyp_y, km_damp_y(j) )
111                   kmym_y = MAX( kmym_y, km_damp_y(j) )
112                ENDIF
113
114                tend(k,j,i) = tend(k,j,i)                                      &
115                      & + ( kmxp_x * ( w(k,j,i+1)   - w(k,j,i)   ) * ddx       &
116                      &   + kmxp_z * ( u(k+1,j,i+1) - u(k,j,i+1) ) * ddzu(k+1) &
117                      &   - kmxm_x * ( w(k,j,i)   - w(k,j,i-1) ) * ddx         &
118                      &   - kmxm_z * ( u(k+1,j,i) - u(k,j,i)   ) * ddzu(k+1)   &
119                      &   ) * ddx                                              &
120                      & + ( kmyp_y * ( w(k,j+1,i)   - w(k,j,i)   ) * ddy       &
121                      &   + kmyp_z * ( v(k+1,j+1,i) - v(k,j+1,i) ) * ddzu(k+1) &
122                      &   - kmym_y * ( w(k,j,i)   - w(k,j-1,i) ) * ddy         &
123                      &   - kmym_z * ( v(k+1,j,i) - v(k,j,i)   ) * ddzu(k+1)   &
124                      &   ) * ddy                                              &
125                      & + 2.0 * (                                              &
126                      &   km(k+1,j,i) * ( w(k+1,j,i) - w(k,j,i) ) * ddzw(k+1)  &
127                      & - km(k,j,i)   * ( w(k,j,i)   - w(k-1,j,i) ) * ddzw(k)  &
128                      &         ) * ddzu(k+1)
129             ENDDO
130
131!
132!--          Wall functions at all vertical walls, where necessary
133             IF ( wall_w_x(j,i) /= 0.0  .OR.  wall_w_y(j,i) /= 0.0 )  THEN
134
135                DO  k = nzb_w_inner(j,i)+1, nzb_w_outer(j,i)
136!
137!--                Interpolate eddy diffusivities on staggered gridpoints
138                   kmxp_x = 0.25 * &
139                            ( km(k,j,i)+km(k,j,i+1)+km(k+1,j,i)+km(k+1,j,i+1) )
140                   kmxm_x = 0.25 * &
141                            ( km(k,j,i)+km(k,j,i-1)+km(k+1,j,i)+km(k+1,j,i-1) )
142                   kmxp_z = kmxp_x
143                   kmxm_z = kmxm_x
144                   kmyp_y = 0.25 * &
145                            ( km(k,j,i)+km(k+1,j,i)+km(k,j+1,i)+km(k+1,j+1,i) )
146                   kmym_y = 0.25 * &
147                            ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
148                   kmyp_z = kmyp_y
149                   kmym_z = kmym_y
150!
151!--                Increase diffusion at the outflow boundary in case of
152!--                non-cyclic lateral boundaries. Damping is only needed for
153!--                velocity components parallel to the outflow boundary in
154!--                the direction normal to the outflow boundary.
155                   IF ( .NOT. bc_lr_cyc )  THEN
156                      kmxp_x = MAX( kmxp_x, km_damp_x(i) )
157                      kmxm_x = MAX( kmxm_x, km_damp_x(i) )
158                   ENDIF
159                   IF ( .NOT. bc_ns_cyc )  THEN
160                      kmyp_y = MAX( kmyp_y, km_damp_y(j) )
161                      kmym_y = MAX( kmym_y, km_damp_y(j) )
162                   ENDIF
163
164                   tend(k,j,i) = tend(k,j,i)                                   &
165                                 + (   fwxp(j,i) * (                           &
166                            kmxp_x * ( w(k,j,i+1)   - w(k,j,i)   ) * ddx       &
167                          + kmxp_z * ( u(k+1,j,i+1) - u(k,j,i+1) ) * ddzu(k+1) &
168                                                   )                           &
169                                     - fwxm(j,i) * (                           &
170                            kmxm_x * ( w(k,j,i)     - w(k,j,i-1) ) * ddx       &
171                          + kmxm_z * ( u(k+1,j,i)   - u(k,j,i)   ) * ddzu(k+1) &
172                                                   )                           &
173                                     + wall_w_x(j,i) * wsus(k,j,i)             &
174                                   ) * ddx                                     &
175                                 + (   fwyp(j,i) * (                           &
176                            kmyp_y * ( w(k,j+1,i)   - w(k,j,i)   ) * ddy       &
177                          + kmyp_z * ( v(k+1,j+1,i) - v(k,j+1,i) ) * ddzu(k+1) &
178                                                   )                           &
179                                     - fwym(j,i) * (                           &
180                            kmym_y * ( w(k,j,i)     - w(k,j-1,i) ) * ddy       &
181                          + kmym_z * ( v(k+1,j,i)   - v(k,j,i)   ) * ddzu(k+1) &
182                                                   )                           &
183                                     + wall_w_y(j,i) * wsvs(k,j,i)             &
184                                   ) * ddy                                     &
185                                 + 2.0 * (                                     &
186                           km(k+1,j,i) * ( w(k+1,j,i) - w(k,j,i) ) * ddzw(k+1) &
187                         - km(k,j,i)   * ( w(k,j,i)   - w(k-1,j,i) ) * ddzw(k) &
188                                         ) * ddzu(k+1)
189                ENDDO
190             ENDIF
191
192          ENDDO
193       ENDDO
194
195    END SUBROUTINE diffusion_w
196
197
198!------------------------------------------------------------------------------!
199! Call for grid point i,j
200!------------------------------------------------------------------------------!
201    SUBROUTINE diffusion_w_ij( i, j, ddzu, ddzw, km, km_damp_x, km_damp_y, &
202                               tend, u, v, w )
203
204       USE control_parameters
205       USE grid_variables
206       USE indices
207
208       IMPLICIT NONE
209
210       INTEGER ::  i, j, k
211       REAL    ::  kmxm_x, kmxm_z, kmxp_x, kmxp_z, kmym_y, kmym_z, kmyp_y, &
212                   kmyp_z
213       REAL    ::  ddzu(1:nzt+1), ddzw(1:nzt+1), km_damp_x(nxl-1:nxr+1), &
214                   km_damp_y(nys-1:nyn+1)
215       REAL    ::  tend(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1)
216       REAL, DIMENSION(nzb:nzt+1)      ::  wsus, wsvs
217       REAL, DIMENSION(:,:,:), POINTER ::  km, u, v, w
218
219
220       DO  k = nzb_w_outer(j,i)+1, nzt-1
221!
222!--       Interpolate eddy diffusivities on staggered gridpoints
223          kmxp_x = 0.25 * ( km(k,j,i)+km(k,j,i+1)+km(k+1,j,i)+km(k+1,j,i+1) )
224          kmxm_x = 0.25 * ( km(k,j,i)+km(k,j,i-1)+km(k+1,j,i)+km(k+1,j,i-1) )
225          kmxp_z = kmxp_x
226          kmxm_z = kmxm_x
227          kmyp_y = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j+1,i)+km(k+1,j+1,i) )
228          kmym_y = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
229          kmyp_z = kmyp_y
230          kmym_z = kmym_y
231!
232!--       Increase diffusion at the outflow boundary in case of non-cyclic
233!--       lateral boundaries. Damping is only needed for velocity components
234!--       parallel to the outflow boundary in the direction normal to the
235!--       outflow boundary.
236          IF ( .NOT. bc_lr_cyc )  THEN
237             kmxp_x = MAX( kmxp_x, km_damp_x(i) )
238             kmxm_x = MAX( kmxm_x, km_damp_x(i) )
239          ENDIF
240          IF ( .NOT. bc_ns_cyc )  THEN
241             kmyp_y = MAX( kmyp_y, km_damp_y(j) )
242             kmym_y = MAX( kmym_y, km_damp_y(j) )
243          ENDIF
244
245          tend(k,j,i) = tend(k,j,i)                                            &
246                      & + ( kmxp_x * ( w(k,j,i+1)   - w(k,j,i)   ) * ddx       &
247                      &   + kmxp_z * ( u(k+1,j,i+1) - u(k,j,i+1) ) * ddzu(k+1) &
248                      &   - kmxm_x * ( w(k,j,i)   - w(k,j,i-1) ) * ddx         &
249                      &   - kmxm_z * ( u(k+1,j,i) - u(k,j,i)   ) * ddzu(k+1)   &
250                      &   ) * ddx                                              &
251                      & + ( kmyp_y * ( w(k,j+1,i)   - w(k,j,i)   ) * ddy       &
252                      &   + kmyp_z * ( v(k+1,j+1,i) - v(k,j+1,i) ) * ddzu(k+1) &
253                      &   - kmym_y * ( w(k,j,i)   - w(k,j-1,i) ) * ddy         &
254                      &   - kmym_z * ( v(k+1,j,i) - v(k,j,i)   ) * ddzu(k+1)   &
255                      &   ) * ddy                                              &
256                      & + 2.0 * (                                              &
257                      &   km(k+1,j,i) * ( w(k+1,j,i) - w(k,j,i) ) * ddzw(k+1)  &
258                      & - km(k,j,i)   * ( w(k,j,i)   - w(k-1,j,i) ) * ddzw(k)  &
259                      &         ) * ddzu(k+1)
260       ENDDO
261
262!
263!--    Wall functions at all vertical walls, where necessary
264       IF ( wall_w_x(j,i) /= 0.0  .OR.  wall_w_y(j,i) /= 0.0 )  THEN
265
266!
267!--       Calculate the horizontal momentum fluxes w'u' and/or w'v'
268          IF ( wall_w_x(j,i) /= 0.0 )  THEN
269             CALL wall_fluxes( i, j, nzb_w_inner(j,i)+1, nzb_w_outer(j,i), &
270                               wsus, 0.0, 0.0, 0.0, 1.0 )
271          ELSE
272             wsus = 0.0
273          ENDIF
274
275          IF ( wall_w_y(j,i) /= 0.0 )  THEN
276             CALL wall_fluxes( i, j, nzb_w_inner(j,i)+1, nzb_w_outer(j,i),  &
277                               wsvs, 0.0, 0.0, 1.0, 0.0 )
278          ELSE
279             wsvs = 0.0
280          ENDIF
281
282          DO  k = nzb_w_inner(j,i)+1, nzb_w_outer(j,i)
283!
284!--          Interpolate eddy diffusivities on staggered gridpoints
285             kmxp_x = 0.25 * ( km(k,j,i)+km(k,j,i+1)+km(k+1,j,i)+km(k+1,j,i+1) )
286             kmxm_x = 0.25 * ( km(k,j,i)+km(k,j,i-1)+km(k+1,j,i)+km(k+1,j,i-1) )
287             kmxp_z = kmxp_x
288             kmxm_z = kmxm_x
289             kmyp_y = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j+1,i)+km(k+1,j+1,i) )
290             kmym_y = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
291             kmyp_z = kmyp_y
292             kmym_z = kmym_y
293!
294!--          Increase diffusion at the outflow boundary in case of
295!--          non-cyclic lateral boundaries. Damping is only needed for
296!--          velocity components parallel to the outflow boundary in
297!--          the direction normal to the outflow boundary.
298             IF ( .NOT. bc_lr_cyc )  THEN
299                kmxp_x = MAX( kmxp_x, km_damp_x(i) )
300                kmxm_x = MAX( kmxm_x, km_damp_x(i) )
301             ENDIF
302             IF ( .NOT. bc_ns_cyc )  THEN
303                kmyp_y = MAX( kmyp_y, km_damp_y(j) )
304                kmym_y = MAX( kmym_y, km_damp_y(j) )
305             ENDIF
306
307             tend(k,j,i) = tend(k,j,i)                                         &
308                                 + (   fwxp(j,i) * (                           &
309                            kmxp_x * ( w(k,j,i+1)   - w(k,j,i)   ) * ddx       &
310                          + kmxp_z * ( u(k+1,j,i+1) - u(k,j,i+1) ) * ddzu(k+1) &
311                                                   )                           &
312                                     - fwxm(j,i) * (                           &
313                            kmxm_x * ( w(k,j,i)     - w(k,j,i-1) ) * ddx       &
314                          + kmxm_z * ( u(k+1,j,i)   - u(k,j,i)   ) * ddzu(k+1) &
315                                                   )                           &
316                                     + wall_w_x(j,i) * wsus(k)                 &
317                                   ) * ddx                                     &
318                                 + (   fwyp(j,i) * (                           &
319                            kmyp_y * ( w(k,j+1,i)   - w(k,j,i)   ) * ddy       &
320                          + kmyp_z * ( v(k+1,j+1,i) - v(k,j+1,i) ) * ddzu(k+1) &
321                                                   )                           &
322                                     - fwym(j,i) * (                           &
323                            kmym_y * ( w(k,j,i)     - w(k,j-1,i) ) * ddy       &
324                          + kmym_z * ( v(k+1,j,i)   - v(k,j,i)   ) * ddzu(k+1) &
325                                                   )                           &
326                                     + wall_w_y(j,i) * wsvs(k)                 &
327                                   ) * ddy                                     &
328                                 + 2.0 * (                                     &
329                           km(k+1,j,i) * ( w(k+1,j,i) - w(k,j,i) ) * ddzw(k+1) &
330                         - km(k,j,i)   * ( w(k,j,i)   - w(k-1,j,i) ) * ddzw(k) &
331                                         ) * ddzu(k+1)
332          ENDDO
333       ENDIF
334
335    END SUBROUTINE diffusion_w_ij
336
337 END MODULE diffusion_w_mod
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