!> @file diffusion_u.f90
!------------------------------------------------------------------------------!
! This file is part of the PALM model system.
!
! PALM is free software: you can redistribute it and/or modify it under the
! terms of the GNU General Public License as published by the Free Software
! Foundation, either version 3 of the License, or (at your option) any later
! version.
!
! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License along with
! PALM. If not, see .
!
! Copyright 1997-2018 Leibniz Universitaet Hannover
!------------------------------------------------------------------------------!
!
! Current revisions:
! -----------------
!
!
! Former revisions:
! -----------------
! $Id: diffusion_u.f90 3547 2018-11-21 13:21:24Z eckhard $
! variables documented
!
! 3241 2018-09-12 15:02:00Z raasch
! unused variables removed
!
! 2718 2018-01-02 08:49:38Z maronga
! Corrected "Former revisions" section
!
! 2696 2017-12-14 17:12:51Z kanani
! Change in file header (GPL part)
!
! 2638 2017-11-23 12:44:23Z raasch
! bugfix for constant top momentumflux
!
! 2233 2017-05-30 18:08:54Z suehring
!
! 2232 2017-05-30 17:47:52Z suehring
! Adjustments to new topography and surface concept
!
! 2118 2017-01-17 16:38:49Z raasch
! OpenACC version of subroutine removed
!
! 2037 2016-10-26 11:15:40Z knoop
! Anelastic approximation implemented
!
! 2000 2016-08-20 18:09:15Z knoop
! Forced header and separation lines into 80 columns
!
! 1873 2016-04-18 14:50:06Z maronga
! Module renamed (removed _mod)
!
! 1850 2016-04-08 13:29:27Z maronga
! Module renamed
!
! 1740 2016-01-13 08:19:40Z raasch
! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
!
! 1691 2015-10-26 16:17:44Z maronga
! Formatting corrections.
!
! 1682 2015-10-07 23:56:08Z knoop
! Code annotations made doxygen readable
!
! 1340 2014-03-25 19:45:13Z kanani
! REAL constants defined as wp-kind
!
! 1320 2014-03-20 08:40:49Z raasch
! ONLY-attribute added to USE-statements,
! kind-parameters added to all INTEGER and REAL declaration statements,
! kinds are defined in new module kinds,
! revision history before 2012 removed,
! comment fields (!:) to be used for variable explanations added to
! all variable declaration statements
!
! 1257 2013-11-08 15:18:40Z raasch
! openacc loop and loop vector clauses removed, declare create moved after
! the FORTRAN declaration statement
!
! 1128 2013-04-12 06:19:32Z raasch
! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
! j_north
!
! 1036 2012-10-22 13:43:42Z raasch
! code put under GPL (PALM 3.9)
!
! 1015 2012-09-27 09:23:24Z raasch
! accelerator version (*_acc) added
!
! 1001 2012-09-13 14:08:46Z raasch
! arrays comunicated by module instead of parameter list
!
! 978 2012-08-09 08:28:32Z fricke
! outflow damping layer removed
! kmym_x/_y and kmyp_x/_y change to kmym and kmyp
!
! Revision 1.1 1997/09/12 06:23:51 raasch
! Initial revision
!
!
! Description:
! ------------
!> Diffusion term of the u-component
!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
!> and slows down the speed on NEC about 5-10%
!------------------------------------------------------------------------------!
MODULE diffusion_u_mod
PRIVATE
PUBLIC diffusion_u
INTERFACE diffusion_u
MODULE PROCEDURE diffusion_u
MODULE PROCEDURE diffusion_u_ij
END INTERFACE diffusion_u
CONTAINS
!------------------------------------------------------------------------------!
! Description:
! ------------
!> Call for all grid points
!------------------------------------------------------------------------------!
SUBROUTINE diffusion_u
USE arrays_3d, &
ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
USE control_parameters, &
ONLY: constant_top_momentumflux, use_surface_fluxes, &
use_top_fluxes
USE grid_variables, &
ONLY: ddx, ddx2, ddy
USE indices, &
ONLY: nxlu, nxr, nyn, nys, nzb, nzt, wall_flags_0
USE kinds
USE surface_mod, &
ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
surf_usm_v
IMPLICIT NONE
INTEGER(iwp) :: i !< running index x direction
INTEGER(iwp) :: j !< running index y direction
INTEGER(iwp) :: k !< running index z direction
INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
INTEGER(iwp) :: m !< running index surface elements
INTEGER(iwp) :: surf_e !< end index of surface elements at (j,i)-gridpoint
INTEGER(iwp) :: surf_s !< start index of surface elements at (j,i)-gridpoint
REAL(wp) :: flag !< flag to mask topography grid points
REAL(wp) :: kmym !< diffusion coefficient on southward side of the u-gridbox - interpolated onto xu-yv grid
REAL(wp) :: kmyp !< diffusion coefficient on northward side of the u-gridbox - interpolated onto xu-yv grid
REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
DO i = nxlu, nxr
DO j = nys, nyn
!
!-- Compute horizontal diffusion
DO k = nzb+1, nzt
!
!-- Predetermine flag to mask topography and wall-bounded grid points.
!-- It is sufficient to masked only north- and south-facing surfaces, which
!-- need special treatment for the u-component.
flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
!
!-- Interpolate eddy diffusivities on staggered gridpoints
kmyp = 0.25_wp * &
( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
kmym = 0.25_wp * &
( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
tend(k,j,i) = tend(k,j,i) &
+ 2.0_wp * ( &
km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
) * ddx2 * flag &
+ ( mask_north * ( &
kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
) &
- mask_south * ( &
kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
) &
) * ddy * flag
ENDDO
!
!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
!-- surfaces. Note, in the the flat case, loops won't be entered as
!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
!-- so far.
!-- Default-type surfaces
DO l = 0, 1
surf_s = surf_def_v(l)%start_index(j,i)
surf_e = surf_def_v(l)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_def_v(l)%k(m)
tend(k,j,i) = tend(k,j,i) + &
surf_def_v(l)%mom_flux_uv(m) * ddy
ENDDO
ENDDO
!
!-- Natural-type surfaces
DO l = 0, 1
surf_s = surf_lsm_v(l)%start_index(j,i)
surf_e = surf_lsm_v(l)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_lsm_v(l)%k(m)
tend(k,j,i) = tend(k,j,i) + &
surf_lsm_v(l)%mom_flux_uv(m) * ddy
ENDDO
ENDDO
!
!-- Urban-type surfaces
DO l = 0, 1
surf_s = surf_usm_v(l)%start_index(j,i)
surf_e = surf_usm_v(l)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_usm_v(l)%k(m)
tend(k,j,i) = tend(k,j,i) + &
surf_usm_v(l)%mom_flux_uv(m) * ddy
ENDDO
ENDDO
!
!-- Compute vertical diffusion. In case of simulating a surface layer,
!-- respective grid diffusive fluxes are masked (flag 8) within this
!-- loop, and added further below, else, simple gradient approach is
!-- applied. Model top is also mask if top-momentum flux is given.
DO k = nzb+1, nzt
!
!-- Determine flags to mask topography below and above. Flag 1 is
!-- used to mask topography in general, and flag 8 implies
!-- information about use_surface_fluxes. Flag 9 is used to control
!-- momentum flux at model top.
mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
BTEST( wall_flags_0(k-1,j,i), 8 ) )
mask_top = MERGE( 1.0_wp, 0.0_wp, &
BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
MERGE( 1.0_wp, 0.0_wp, &
BTEST( wall_flags_0(k+1,j,i), 9 ) )
flag = MERGE( 1.0_wp, 0.0_wp, &
BTEST( wall_flags_0(k,j,i), 1 ) )
!
!-- Interpolate eddy diffusivities on staggered gridpoints
kmzp = 0.25_wp * &
( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
kmzm = 0.25_wp * &
( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
tend(k,j,i) = tend(k,j,i) &
+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
) * rho_air_zw(k) * mask_top &
- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
) * rho_air_zw(k-1) * mask_bottom &
) * ddzw(k) * drho_air(k) * flag
ENDDO
!
!-- Vertical diffusion at the first grid point above the surface,
!-- if the momentum flux at the bottom is given by the Prandtl law or
!-- if it is prescribed by the user.
!-- Difference quotient of the momentum flux is not formed over half
!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
!-- with other (LES) models showed that the values of the momentum
!-- flux becomes too large in this case.
!-- The term containing w(k-1,..) (see above equation) is removed here
!-- because the vertical velocity is assumed to be zero at the surface.
IF ( use_surface_fluxes ) THEN
!
!-- Default-type surfaces, upward-facing
surf_s = surf_def_h(0)%start_index(j,i)
surf_e = surf_def_h(0)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_def_h(0)%k(m)
tend(k,j,i) = tend(k,j,i) &
+ ( - ( - surf_def_h(0)%usws(m) ) &
) * ddzw(k) * drho_air(k)
ENDDO
!
!-- Default-type surfaces, dowward-facing
surf_s = surf_def_h(1)%start_index(j,i)
surf_e = surf_def_h(1)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_def_h(1)%k(m)
tend(k,j,i) = tend(k,j,i) &
+ ( - surf_def_h(1)%usws(m) &
) * ddzw(k) * drho_air(k)
ENDDO
!
!-- Natural-type surfaces, upward-facing
surf_s = surf_lsm_h%start_index(j,i)
surf_e = surf_lsm_h%end_index(j,i)
DO m = surf_s, surf_e
k = surf_lsm_h%k(m)
tend(k,j,i) = tend(k,j,i) &
+ ( - ( - surf_lsm_h%usws(m) ) &
) * ddzw(k) * drho_air(k)
ENDDO
!
!-- Urban-type surfaces, upward-facing
surf_s = surf_usm_h%start_index(j,i)
surf_e = surf_usm_h%end_index(j,i)
DO m = surf_s, surf_e
k = surf_usm_h%k(m)
tend(k,j,i) = tend(k,j,i) &
+ ( - ( - surf_usm_h%usws(m) ) &
) * ddzw(k) * drho_air(k)
ENDDO
ENDIF
!
!-- Add momentum flux at model top
IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
surf_s = surf_def_h(2)%start_index(j,i)
surf_e = surf_def_h(2)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_def_h(2)%k(m)
tend(k,j,i) = tend(k,j,i) &
+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
ENDDO
ENDIF
ENDDO
ENDDO
END SUBROUTINE diffusion_u
!------------------------------------------------------------------------------!
! Description:
! ------------
!> Call for grid point i,j
!------------------------------------------------------------------------------!
SUBROUTINE diffusion_u_ij( i, j )
USE arrays_3d, &
ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
USE control_parameters, &
ONLY: constant_top_momentumflux, use_surface_fluxes, &
use_top_fluxes
USE grid_variables, &
ONLY: ddx, ddx2, ddy
USE indices, &
ONLY: nzb, nzt, wall_flags_0
USE kinds
USE surface_mod, &
ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
surf_usm_v
IMPLICIT NONE
INTEGER(iwp) :: i !< running index x direction
INTEGER(iwp) :: j !< running index y direction
INTEGER(iwp) :: k !< running index z direction
INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
INTEGER(iwp) :: m !< running index surface elements
INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
REAL(wp) :: flag !< flag to mask topography grid points
REAL(wp) :: kmym !< diffusion coefficient on southward side of the u-gridbox - interpolated onto xu-yv grid
REAL(wp) :: kmyp ! end_index. Furtermore, note, no vertical natural surfaces
!-- so far.
!-- Default-type surfaces
DO l = 0, 1
surf_s = surf_def_v(l)%start_index(j,i)
surf_e = surf_def_v(l)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_def_v(l)%k(m)
tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy
ENDDO
ENDDO
!
!-- Natural-type surfaces
DO l = 0, 1
surf_s = surf_lsm_v(l)%start_index(j,i)
surf_e = surf_lsm_v(l)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_lsm_v(l)%k(m)
tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy
ENDDO
ENDDO
!
!-- Urban-type surfaces
DO l = 0, 1
surf_s = surf_usm_v(l)%start_index(j,i)
surf_e = surf_usm_v(l)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_usm_v(l)%k(m)
tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy
ENDDO
ENDDO
!
!-- Compute vertical diffusion. In case of simulating a surface layer,
!-- respective grid diffusive fluxes are masked (flag 8) within this
!-- loop, and added further below, else, simple gradient approach is
!-- applied. Model top is also mask if top-momentum flux is given.
DO k = nzb+1, nzt
!
!-- Determine flags to mask topography below and above. Flag 1 is
!-- used to mask topography in general, and flag 8 implies
!-- information about use_surface_fluxes. Flag 9 is used to control
!-- momentum flux at model top.
mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
BTEST( wall_flags_0(k-1,j,i), 8 ) )
mask_top = MERGE( 1.0_wp, 0.0_wp, &
BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
MERGE( 1.0_wp, 0.0_wp, &
BTEST( wall_flags_0(k+1,j,i), 9 ) )
flag = MERGE( 1.0_wp, 0.0_wp, &
BTEST( wall_flags_0(k,j,i), 1 ) )
!
!-- Interpolate eddy diffusivities on staggered gridpoints
kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
tend(k,j,i) = tend(k,j,i) &
+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
) * rho_air_zw(k) * mask_top &
- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
) * rho_air_zw(k-1) * mask_bottom &
) * ddzw(k) * drho_air(k) * flag
ENDDO
!
!-- Vertical diffusion at the first surface grid points, if the
!-- momentum flux at the bottom is given by the Prandtl law or if it is
!-- prescribed by the user.
!-- Difference quotient of the momentum flux is not formed over half of
!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
!-- other (LES) models showed that the values of the momentum flux becomes
!-- too large in this case.
IF ( use_surface_fluxes ) THEN
!
!-- Default-type surfaces, upward-facing
surf_s = surf_def_h(0)%start_index(j,i)
surf_e = surf_def_h(0)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_def_h(0)%k(m)
tend(k,j,i) = tend(k,j,i) &
+ ( - ( - surf_def_h(0)%usws(m) ) &
) * ddzw(k) * drho_air(k)
ENDDO
!
!-- Default-type surfaces, dowward-facing (except for model-top fluxes)
surf_s = surf_def_h(1)%start_index(j,i)
surf_e = surf_def_h(1)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_def_h(1)%k(m)
tend(k,j,i) = tend(k,j,i) &
+ ( - surf_def_h(1)%usws(m) &
) * ddzw(k) * drho_air(k)
ENDDO
!
!-- Natural-type surfaces, upward-facing
surf_s = surf_lsm_h%start_index(j,i)
surf_e = surf_lsm_h%end_index(j,i)
DO m = surf_s, surf_e
k = surf_lsm_h%k(m)
tend(k,j,i) = tend(k,j,i) &
+ ( - ( - surf_lsm_h%usws(m) ) &
) * ddzw(k) * drho_air(k)
ENDDO
!
!-- Urban-type surfaces, upward-facing
surf_s = surf_usm_h%start_index(j,i)
surf_e = surf_usm_h%end_index(j,i)
DO m = surf_s, surf_e
k = surf_usm_h%k(m)
tend(k,j,i) = tend(k,j,i) &
+ ( - ( - surf_usm_h%usws(m) ) &
) * ddzw(k) * drho_air(k)
ENDDO
ENDIF
!
!-- Add momentum flux at model top
IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
surf_s = surf_def_h(2)%start_index(j,i)
surf_e = surf_def_h(2)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_def_h(2)%k(m)
tend(k,j,i) = tend(k,j,i) &
+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
ENDDO
ENDIF
END SUBROUTINE diffusion_u_ij
END MODULE diffusion_u_mod