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diffusion_v.f90 @ 667

Last change on this file since 667 was 667, checked in by suehring, 13 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: 17.7 KB

Rev	Line
[1]	1	MODULE diffusion_v_mod
	2
	3	!------------------------------------------------------------------------------!
[484]	4	! Current revisions:
[1]	5	! -----------------
[667]	6	! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng
[1]	7	!
	8	! Former revisions:
	9	! -----------------
[3]	10	! $Id: diffusion_v.f90 667 2010-12-23 12:06:00Z suehring $
[39]	11	!
[392]	12	! 366 2009-08-25 08:06:27Z raasch
	13	! bc_lr replaced by bc_lr_cyc
	14	!
[110]	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	!
[77]	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	!
[39]	23	! 20 2007-02-26 00:12:32Z raasch
	24	! Bugfix: ddzw dimensioned 1:nzt"+1"
	25	!
[3]	26	! RCS Log replace by Id keyword, revision history cleaned up
	27	!
[1]	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
[56]	45	USE wall_fluxes_mod
	46
[1]	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	!------------------------------------------------------------------------------!
[102]	61	SUBROUTINE diffusion_v( ddzu, ddzw, km, km_damp_x, tend, u, v, vsws, &
	62	vswst, w )
[1]	63
	64	USE control_parameters
	65	USE grid_variables
	66	USE indices
	67
	68	IMPLICIT NONE
	69
	70	INTEGER :: i, j, k
[51]	71	REAL :: kmxm_x, kmxm_y, kmxp_x, kmxp_y, kmzm, kmzp
[667]	72	REAL :: ddzu(1:nzt+1), ddzw(1:nzt+1), km_damp_x(nxlg:nxrg)
	73	REAL :: tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg)
[102]	74	REAL, DIMENSION(:,:), POINTER :: vsws, vswst
[1]	75	REAL, DIMENSION(:,:,:), POINTER :: km, u, v, w
[75]	76	REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus
[1]	77
[56]	78	!
	79	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	80	!-- if neccessary
	81	IF ( topography /= 'flat' ) THEN
[75]	82	CALL wall_fluxes( vsus, 0.0, 1.0, 0.0, 0.0, nzb_v_inner, &
[56]	83	nzb_v_outer, wall_v )
	84	ENDIF
	85
[1]	86	DO i = nxl, nxr
[106]	87	DO j = nysv, nyn
[1]	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.
[366]	104	IF ( .NOT. bc_lr_cyc ) THEN
[1]	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
[51]	124
[1]	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.
[366]	137	IF ( .NOT. bc_lr_cyc ) THEN
[1]	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	) &
[56]	155	+ wall_v(j,i) * vsus(k,j,i) &
[1]	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.
[102]	163	DO k = nzb_diff_v(j,i), nzt_diff
[1]	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) &
[102]	203	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
[1]	204	& + vsws(j,i) &
	205	& ) * ddzw(k)
	206	ENDIF
	207
[102]	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
[103]	211	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	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
[1]	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, &
[102]	238	vsws, vswst, w )
[1]	239
	240	USE control_parameters
	241	USE grid_variables
	242	USE indices
	243
	244	IMPLICIT NONE
	245
	246	INTEGER :: i, j, k
[51]	247	REAL :: kmxm_x, kmxm_y, kmxp_x, kmxp_y, kmzm, kmzp
[667]	248	REAL :: ddzu(1:nzt+1), ddzw(1:nzt+1), km_damp_x(nxlg:nxrg)
	249	REAL :: tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg)
[51]	250	REAL, DIMENSION(nzb:nzt+1) :: vsus
[102]	251	REAL, DIMENSION(:,:), POINTER :: vsws, vswst
[1]	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.
[366]	268	IF ( .NOT. bc_lr_cyc ) THEN
[1]	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
[51]	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
[1]	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.
[366]	306	IF ( .NOT. bc_lr_cyc ) THEN
[1]	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	) &
[51]	324	+ wall_v(j,i) * vsus(k) &
[1]	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.
[102]	332	DO k = nzb_diff_v(j,i), nzt_diff
[1]	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) &
[102]	368	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
[1]	369	& + vsws(j,i) &
	370	& ) * ddzw(k)
	371	ENDIF
	372
[102]	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
[103]	376	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	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
[1]	393	END SUBROUTINE diffusion_v_ij
	394
	395	END MODULE diffusion_v_mod

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