source: palm/trunk/SOURCE/diffusion_w.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: 15.4 KB
Line 
1 MODULE diffusion_w_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_w.f90 667 2010-12-23 12:06:00Z suehring $
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(nxlg:nxrg),        & 
67                   km_damp_y(nysg:nyng)
68       REAL    ::  tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg)
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(nxlg:nxrg),        & 
214                   km_damp_y(nysg:nyng)
215       REAL    ::  tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg)
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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