source: palm/trunk/SOURCE/diffusion_u.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: 17.8 KB
Line 
1 MODULE diffusion_u_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_u.f90 667 2010-12-23 12:06:00Z suehring $
11!
12! 366 2009-08-25 08:06:27Z raasch
13! bc_ns replaced by bc_ns_cyc
14!
15! 106 2007-08-16 14:30:26Z raasch
16! Momentumflux at top (uswst) included as boundary condition,
17! i loop is starting from nxlu (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, uxrp 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 10:35:35  raasch
29! nzb_2d replaced by nzb_u_outer in horizontal diffusion and by nzb_u_inner
30! or nzb_diff_u, 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 06:23:51  raasch
37! Initial revision
38!
39!
40! Description:
41! ------------
42! Diffusion term of the u-component
43! To do: additional damping (needed for non-cyclic bc) causes bad vectorization
44!        and slows down the speed on NEC about 5-10%
45!------------------------------------------------------------------------------!
46
47    USE wall_fluxes_mod
48
49    PRIVATE
50    PUBLIC diffusion_u
51
52    INTERFACE diffusion_u
53       MODULE PROCEDURE diffusion_u
54       MODULE PROCEDURE diffusion_u_ij
55    END INTERFACE diffusion_u
56
57 CONTAINS
58
59
60!------------------------------------------------------------------------------!
61! Call for all grid points
62!------------------------------------------------------------------------------!
63    SUBROUTINE diffusion_u( ddzu, ddzw, km, km_damp_y, tend, u, usws, uswst, &
64                            v, w )
65
66       USE control_parameters
67       USE grid_variables
68       USE indices
69
70       IMPLICIT NONE
71
72       INTEGER ::  i, j, k
73       REAL    ::  kmym_x, kmym_y, kmyp_x, kmyp_y, kmzm, kmzp
74       REAL    ::  ddzu(1:nzt+1), ddzw(1:nzt+1), km_damp_y(nysg:nyng)
75       REAL    ::  tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg)
76       REAL, DIMENSION(:,:),   POINTER ::  usws, uswst
77       REAL, DIMENSION(:,:,:), POINTER ::  km, u, v, w
78       REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) ::  usvs
79
80!
81!--    First calculate horizontal momentum flux u'v' at vertical walls,
82!--    if neccessary
83       IF ( topography /= 'flat' )  THEN
84          CALL wall_fluxes( usvs, 1.0, 0.0, 0.0, 0.0, nzb_u_inner, &
85                            nzb_u_outer, wall_u )
86       ENDIF
87
88       DO  i = nxlu, nxr
89          DO  j = nys,nyn
90!
91!--          Compute horizontal diffusion
92             DO  k = nzb_u_outer(j,i)+1, nzt
93!
94!--             Interpolate eddy diffusivities on staggered gridpoints
95                kmyp_x = 0.25 * &
96                         ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
97                kmym_x = 0.25 * &
98                         ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
99                kmyp_y = kmyp_x
100                kmym_y = kmym_x
101!
102!--             Increase diffusion at the outflow boundary in case of
103!--             non-cyclic lateral boundaries. Damping is only needed for
104!--             velocity components parallel to the outflow boundary in
105!--             the direction normal to the outflow boundary.
106                IF ( .NOT. bc_ns_cyc )  THEN
107                   kmyp_y = MAX( kmyp_y, km_damp_y(j) )
108                   kmym_y = MAX( kmym_y, km_damp_y(j) )
109                ENDIF
110
111                tend(k,j,i) = tend(k,j,i)                                    &
112                      & + 2.0 * (                                            &
113                      &           km(k,j,i)   * ( u(k,j,i+1) - u(k,j,i)   )  &
114                      &         - km(k,j,i-1) * ( u(k,j,i)   - u(k,j,i-1) )  &
115                      &         ) * ddx2                                     &
116                      & + ( kmyp_y * ( u(k,j+1,i) - u(k,j,i)     ) * ddy     &
117                      &   + kmyp_x * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx     &
118                      &   - kmym_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy         &
119                      &   - kmym_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx         &
120                      &   ) * ddy
121             ENDDO
122
123!
124!--          Wall functions at the north and south walls, respectively
125             IF ( wall_u(j,i) /= 0.0 )  THEN
126
127                DO  k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i)
128                   kmyp_x = 0.25 * &
129                            ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
130                   kmym_x = 0.25 * &
131                            ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
132                   kmyp_y = kmyp_x
133                   kmym_y = kmym_x
134!
135!--                Increase diffusion at the outflow boundary in case of
136!--                non-cyclic lateral boundaries. Damping is only needed for
137!--                velocity components parallel to the outflow boundary in
138!--                the direction normal to the outflow boundary.
139                   IF ( .NOT. bc_ns_cyc )  THEN
140                      kmyp_y = MAX( kmyp_y, km_damp_y(j) )
141                      kmym_y = MAX( kmym_y, km_damp_y(j) )
142                   ENDIF
143
144                   tend(k,j,i) = tend(k,j,i)                                   &
145                                 + 2.0 * (                                     &
146                                       km(k,j,i)   * ( u(k,j,i+1) - u(k,j,i) ) &
147                                     - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
148                                         ) * ddx2                              &
149                                 + (   fyp(j,i) * (                            &
150                                  kmyp_y * ( u(k,j+1,i) - u(k,j,i)     ) * ddy &
151                                + kmyp_x * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
152                                                  )                            &
153                                     - fym(j,i) * (                            &
154                                  kmym_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy     &
155                                + kmym_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx     &
156                                                  )                            &
157                                     + wall_u(j,i) * usvs(k,j,i)               &
158                                   ) * ddy
159                ENDDO
160             ENDIF
161
162!
163!--          Compute vertical diffusion. In case of simulating a Prandtl layer,
164!--          index k starts at nzb_u_inner+2.
165             DO  k = nzb_diff_u(j,i), nzt_diff
166!
167!--             Interpolate eddy diffusivities on staggered gridpoints
168                kmzp = 0.25 * &
169                       ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
170                kmzm = 0.25 * &
171                       ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
172
173                tend(k,j,i) = tend(k,j,i)                                    &
174                      & + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i)   ) * ddzu(k+1) &
175                      &            + ( w(k,j,i)   - w(k,j,i-1) ) * ddx       &
176                      &            )                                         &
177                      &   - kmzm * ( ( u(k,j,i)   - u(k-1,j,i)   ) * ddzu(k) &
178                      &            + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx     &
179                      &            )                                          &
180                      &   ) * ddzw(k)
181             ENDDO
182
183!
184!--          Vertical diffusion at the first grid point above the surface,
185!--          if the momentum flux at the bottom is given by the Prandtl law or
186!--          if it is prescribed by the user.
187!--          Difference quotient of the momentum flux is not formed over half
188!--          of the grid spacing (2.0*ddzw(k)) any more, since the comparison
189!--          with other (LES) modell showed that the values of the momentum
190!--          flux becomes too large in this case.
191!--          The term containing w(k-1,..) (see above equation) is removed here
192!--          because the vertical velocity is assumed to be zero at the surface.
193             IF ( use_surface_fluxes )  THEN
194                k = nzb_u_inner(j,i)+1
195!
196!--             Interpolate eddy diffusivities on staggered gridpoints
197                kmzp = 0.25 * &
198                      ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
199                kmzm = 0.25 * &
200                      ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
201
202                tend(k,j,i) = tend(k,j,i)                                    &
203                      & + ( kmzp * ( w(k,j,i)   - w(k,j,i-1)   ) * ddx       &
204                      &   ) * ddzw(k)                                        &
205                      & + ( kmzp * ( u(k+1,j,i) - u(k,j,i)     ) * ddzu(k+1) &
206                      &   + usws(j,i)                                        &
207                      &   ) * ddzw(k)
208             ENDIF
209
210!
211!--          Vertical diffusion at the first gridpoint below the top boundary,
212!--          if the momentum flux at the top is prescribed by the user
213             IF ( use_top_fluxes  .AND.  constant_top_momentumflux )  THEN
214                k = nzt
215!
216!--             Interpolate eddy diffusivities on staggered gridpoints
217                kmzp = 0.25 * &
218                       ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
219                kmzm = 0.25 * &
220                       ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
221
222                tend(k,j,i) = tend(k,j,i)                                    &
223                      & - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx       &
224                      &   ) * ddzw(k)                                        &
225                      & + ( -uswst(j,i)                                      &
226                      &   - kmzm * ( u(k,j,i)   - u(k-1,j,i)   ) * ddzu(k)   &
227                      &   ) * ddzw(k)
228             ENDIF
229
230          ENDDO
231       ENDDO
232
233    END SUBROUTINE diffusion_u
234
235
236!------------------------------------------------------------------------------!
237! Call for grid point i,j
238!------------------------------------------------------------------------------!
239    SUBROUTINE diffusion_u_ij( i, j, ddzu, ddzw, km, km_damp_y, tend, u, usws, &
240                               uswst, v, w )
241
242       USE control_parameters
243       USE grid_variables
244       USE indices
245
246       IMPLICIT NONE
247
248       INTEGER ::  i, j, k
249       REAL    ::  kmym_x, kmym_y, kmyp_x, kmyp_y, kmzm, kmzp
250       REAL    ::  ddzu(1:nzt+1), ddzw(1:nzt+1), km_damp_y(nysg:nyng)
251       REAL    ::  tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg)
252       REAL, DIMENSION(nzb:nzt+1)      ::  usvs
253       REAL, DIMENSION(:,:),   POINTER ::  usws, uswst
254       REAL, DIMENSION(:,:,:), POINTER ::  km, u, v, w
255
256!
257!--    Compute horizontal diffusion
258       DO  k = nzb_u_outer(j,i)+1, nzt
259!
260!--       Interpolate eddy diffusivities on staggered gridpoints
261          kmyp_x = 0.25 * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
262          kmym_x = 0.25 * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
263          kmyp_y = kmyp_x
264          kmym_y = kmym_x
265
266!
267!--       Increase diffusion at the outflow boundary in case of non-cyclic
268!--       lateral boundaries. Damping is only needed for velocity components
269!--       parallel to the outflow boundary in the direction normal to the
270!--       outflow boundary.
271          IF ( .NOT. bc_ns_cyc )  THEN
272             kmyp_y = MAX( kmyp_y, km_damp_y(j) )
273             kmym_y = MAX( kmym_y, km_damp_y(j) )
274          ENDIF
275
276          tend(k,j,i) = tend(k,j,i)                                          &
277                      & + 2.0 * (                                            &
278                      &           km(k,j,i)   * ( u(k,j,i+1) - u(k,j,i)   )  &
279                      &         - km(k,j,i-1) * ( u(k,j,i)   - u(k,j,i-1) )  &
280                      &         ) * ddx2                                     &
281                      & + ( kmyp_y * ( u(k,j+1,i) - u(k,j,i)     ) * ddy     &
282                      &   + kmyp_x * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx     &
283                      &   - kmym_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy         &
284                      &   - kmym_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx         &
285                      &   ) * ddy
286       ENDDO
287
288!
289!--    Wall functions at the north and south walls, respectively
290       IF ( wall_u(j,i) .NE. 0.0 )  THEN
291
292!
293!--       Calculate the horizontal momentum flux u'v'
294          CALL wall_fluxes( i, j, nzb_u_inner(j,i)+1, nzb_u_outer(j,i),  &
295                            usvs, 1.0, 0.0, 0.0, 0.0 )
296
297          DO  k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i)
298             kmyp_x = 0.25 * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
299             kmym_x = 0.25 * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
300             kmyp_y = kmyp_x
301             kmym_y = kmym_x
302!
303!--          Increase diffusion at the outflow boundary in case of
304!--          non-cyclic lateral boundaries. Damping is only needed for
305!--          velocity components parallel to the outflow boundary in
306!--          the direction normal to the outflow boundary.
307             IF ( .NOT. bc_ns_cyc )  THEN
308                kmyp_y = MAX( kmyp_y, km_damp_y(j) )
309                kmym_y = MAX( kmym_y, km_damp_y(j) )
310             ENDIF
311
312             tend(k,j,i) = tend(k,j,i)                                         &
313                                 + 2.0 * (                                     &
314                                       km(k,j,i)   * ( u(k,j,i+1) - u(k,j,i) ) &
315                                     - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
316                                         ) * ddx2                              &
317                                 + (   fyp(j,i) * (                            &
318                                  kmyp_y * ( u(k,j+1,i) - u(k,j,i)     ) * ddy &
319                                + kmyp_x * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
320                                                  )                            &
321                                     - fym(j,i) * (                            &
322                                  kmym_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy     &
323                                + kmym_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx     &
324                                                  )                            &
325                                     + wall_u(j,i) * usvs(k)                   &
326                                   ) * ddy
327          ENDDO
328       ENDIF
329
330!
331!--    Compute vertical diffusion. In case of simulating a Prandtl layer,
332!--    index k starts at nzb_u_inner+2.
333       DO  k = nzb_diff_u(j,i), nzt_diff
334!
335!--       Interpolate eddy diffusivities on staggered gridpoints
336          kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
337          kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
338
339          tend(k,j,i) = tend(k,j,i)                                          &
340                      & + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i)   ) * ddzu(k+1) &
341                      &            + ( w(k,j,i)   - w(k,j,i-1) ) * ddx       &
342                      &            )                                         &
343                      &   - kmzm * ( ( u(k,j,i)   - u(k-1,j,i)   ) * ddzu(k) &
344                      &            + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx     &
345                      &            )                                         &
346                      &   ) * ddzw(k)
347       ENDDO
348
349!
350!--    Vertical diffusion at the first grid point above the surface, if the
351!--    momentum flux at the bottom is given by the Prandtl law or if it is
352!--    prescribed by the user.
353!--    Difference quotient of the momentum flux is not formed over half of
354!--    the grid spacing (2.0*ddzw(k)) any more, since the comparison with
355!--    other (LES) modell showed that the values of the momentum flux becomes
356!--    too large in this case.
357!--    The term containing w(k-1,..) (see above equation) is removed here
358!--    because the vertical velocity is assumed to be zero at the surface.
359       IF ( use_surface_fluxes )  THEN
360          k = nzb_u_inner(j,i)+1
361!
362!--       Interpolate eddy diffusivities on staggered gridpoints
363          kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
364          kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
365
366          tend(k,j,i) = tend(k,j,i)                                          &
367                      & + ( kmzp * ( w(k,j,i)   - w(k,j,i-1)   ) * ddx       &
368                      &   ) * ddzw(k)                                        &
369                      & + ( kmzp * ( u(k+1,j,i) - u(k,j,i)     ) * ddzu(k+1) &
370                      &   + usws(j,i)                                        &
371                      &   ) * ddzw(k)
372       ENDIF
373
374!
375!--    Vertical diffusion at the first gridpoint below the top boundary,
376!--    if the momentum flux at the top is prescribed by the user
377       IF ( use_top_fluxes  .AND.  constant_top_momentumflux )  THEN
378          k = nzt
379!
380!--       Interpolate eddy diffusivities on staggered gridpoints
381          kmzp = 0.25 * &
382                 ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
383          kmzm = 0.25 * &
384                 ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
385
386          tend(k,j,i) = tend(k,j,i)                                          &
387                      & - ( kmzm * ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx       &
388                      &   ) * ddzw(k)                                        &
389                      & + ( -uswst(j,i)                                      &
390                      &   - kmzm * ( u(k,j,i)   - u(k-1,j,i)   ) * ddzu(k)   &
391                      &   ) * ddzw(k)
392       ENDIF
393
394    END SUBROUTINE diffusion_u_ij
395
396 END MODULE diffusion_u_mod
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