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diffusion_u.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: 17.8 KB

Rev	Line
[1]	1	MODULE diffusion_u_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
[106]	7	!
[1]	8	! Former revisions:
	9	! -----------------
[3]	10	! $Id: diffusion_u.f90 667 2010-12-23 12:06:00Z suehring $
[39]	11	!
[392]	12	! 366 2009-08-25 08:06:27Z raasch
	13	! bc_ns replaced by bc_ns_cyc
	14	!
[110]	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	!
[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, uxrp 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 10:35:35 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
[51]	43	! To do: additional damping (needed for non-cyclic bc) causes bad vectorization
	44	! and slows down the speed on NEC about 5-10%
[1]	45	!------------------------------------------------------------------------------!
	46
[56]	47	USE wall_fluxes_mod
	48
[1]	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	!------------------------------------------------------------------------------!
[102]	63	SUBROUTINE diffusion_u( ddzu, ddzw, km, km_damp_y, tend, u, usws, uswst, &
	64	v, w )
[1]	65
	66	USE control_parameters
	67	USE grid_variables
	68	USE indices
	69
	70	IMPLICIT NONE
	71
	72	INTEGER :: i, j, k
[51]	73	REAL :: kmym_x, kmym_y, kmyp_x, kmyp_y, kmzm, kmzp
[667]	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)
[102]	76	REAL, DIMENSION(:,:), POINTER :: usws, uswst
[1]	77	REAL, DIMENSION(:,:,:), POINTER :: km, u, v, w
[75]	78	REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs
[1]	79
[56]	80	!
	81	!-- First calculate horizontal momentum flux u'v' at vertical walls,
	82	!-- if neccessary
	83	IF ( topography /= 'flat' ) THEN
[75]	84	CALL wall_fluxes( usvs, 1.0, 0.0, 0.0, 0.0, nzb_u_inner, &
[56]	85	nzb_u_outer, wall_u )
	86	ENDIF
	87
[106]	88	DO i = nxlu, nxr
[1]	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.
[366]	106	IF ( .NOT. bc_ns_cyc ) THEN
[1]	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
[51]	126
[1]	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.
[366]	139	IF ( .NOT. bc_ns_cyc ) THEN
[1]	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	) &
[56]	157	+ wall_u(j,i) * usvs(k,j,i) &
[1]	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.
[102]	165	DO k = nzb_diff_u(j,i), nzt_diff
[1]	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 &
[667]	179	& ) &
[1]	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) &
[102]	205	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
[1]	206	& + usws(j,i) &
	207	& ) * ddzw(k)
	208	ENDIF
	209
[102]	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
[103]	213	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	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
[1]	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, &
[102]	240	uswst, v, w )
[1]	241
	242	USE control_parameters
	243	USE grid_variables
	244	USE indices
	245
	246	IMPLICIT NONE
	247
	248	INTEGER :: i, j, k
[51]	249	REAL :: kmym_x, kmym_y, kmyp_x, kmyp_y, kmzm, kmzp
[667]	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)
[51]	252	REAL, DIMENSION(nzb:nzt+1) :: usvs
[102]	253	REAL, DIMENSION(:,:), POINTER :: usws, uswst
[1]	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.
[366]	271	IF ( .NOT. bc_ns_cyc ) THEN
[1]	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
[51]	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
[1]	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.
[366]	307	IF ( .NOT. bc_ns_cyc ) THEN
[1]	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	) &
[51]	325	+ wall_u(j,i) * usvs(k) &
[1]	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.
[102]	333	DO k = nzb_diff_u(j,i), nzt_diff
[1]	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) &
[102]	369	& + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
[1]	370	& + usws(j,i) &
	371	& ) * ddzw(k)
	372	ENDIF
	373
[102]	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
[103]	377	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	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
[1]	394	END SUBROUTINE diffusion_u_ij
	395
	396	END MODULE diffusion_u_mod

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