!> @file diffusion_w.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 1997-2021 Leibniz Universitaet Hannover
!--------------------------------------------------------------------------------------------------!
!
! Description:
! ------------
!> Diffusion term of the w-component
!--------------------------------------------------------------------------------------------------!
MODULE diffusion_w_mod
PRIVATE
PUBLIC diffusion_w
INTERFACE diffusion_w
MODULE PROCEDURE diffusion_w
MODULE PROCEDURE diffusion_w_ij
END INTERFACE diffusion_w
CONTAINS
!--------------------------------------------------------------------------------------------------!
! Description:
! ------------
!> Call for all grid points
!--------------------------------------------------------------------------------------------------!
SUBROUTINE diffusion_w
USE arrays_3d, &
ONLY : ddzu, ddzw, drho_air_zw, km, rho_air, tend, u, v, w
USE grid_variables, &
ONLY : ddx, ddy
USE indices, &
ONLY : nxl, nxr, nyn, nys, nzb, nzt, topo_flags
USE kinds
USE surface_mod, &
ONLY : surf_def_v, surf_lsm_v, 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) :: kmxm !< diffusion coefficient on leftward side of the w-gridbox - interpolated onto xu-y grid
REAL(wp) :: kmxp ! 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_w(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_w(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_w(m) * ddy
ENDDO
ENDDO
!
!-- Add horizontal momentum flux u'w' at east- (l=2) and west-facing (l=3) surface.
!-- Default-type surfaces
DO l = 2, 3
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_w(m) * ddx
ENDDO
ENDDO
!
!-- Natural-type surfaces
DO l = 2, 3
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_w(m) * ddx
ENDDO
ENDDO
!
!-- Urban-type surfaces
DO l = 2, 3
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_w(m) * ddx
ENDDO
ENDDO
ENDDO
ENDDO
END SUBROUTINE diffusion_w
!--------------------------------------------------------------------------------------------------!
! Description:
! ------------
!> Call for grid point i,j
!--------------------------------------------------------------------------------------------------!
SUBROUTINE diffusion_w_ij( i, j )
USE arrays_3d, &
ONLY : ddzu, ddzw, drho_air_zw, km, rho_air, tend, u, v, w
USE grid_variables, &
ONLY : ddx, ddy
USE indices, &
ONLY : nzb, nzt, topo_flags
USE kinds
USE surface_mod, &
ONLY : surf_def_v, surf_lsm_v, 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) :: kmxm !< diffusion coefficient on leftward side of the w-gridbox - interpolated onto xu-y grid
REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the w-gridbox - interpolated onto xu-y grid
REAL(wp) :: kmym !< diffusion coefficient on southward side of the w-gridbox - interpolated onto x-yv grid
REAL(wp) :: kmyp !< diffusion coefficient on northward side of the w-gridbox - interpolated onto x-yv grid
REAL(wp) :: mask_east !< flag to mask vertical wall east of the grid point
REAL(wp) :: mask_north !< flag to mask vertical wall north of the grid point
REAL(wp) :: mask_south !< flag to mask vertical wall south of the grid point
REAL(wp) :: mask_west !< flag to mask vertical wall west of the grid point
DO k = nzb+1, nzt-1
!
!-- Predetermine flag to mask topography and wall-bounded grid points.
flag = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i), 3 ) )
mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i+1), 3 ) )
mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i-1), 3 ) )
mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j-1,i), 3 ) )
mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j+1,i), 3 ) )
!
!-- Interpolate eddy diffusivities on staggered gridpoints
kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k+1,j,i)+km(k+1,j,i+1) )
kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k+1,j,i)+km(k+1,j,i-1) )
kmyp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j+1,i)+km(k+1,j+1,i) )
kmym = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
tend(k,j,i) = tend(k,j,i) &
+ ( mask_east * kmxp * ( &
( w(k,j,i+1) - w(k,j,i) ) * ddx &
+ ( u(k+1,j,i+1) - u(k,j,i+1) ) * ddzu(k+1) &
) &
- mask_west * kmxm * ( &
( w(k,j,i) - w(k,j,i-1) ) * ddx &
+ ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
) &
) * ddx * flag &
+ ( mask_north * kmyp * ( &
( w(k,j+1,i) - w(k,j,i) ) * ddy &
+ ( v(k+1,j+1,i) - v(k,j+1,i) ) * ddzu(k+1) &
) &
- mask_south * kmym * ( &
( w(k,j,i) - w(k,j-1,i) ) * ddy &
+ ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
) &
) * ddy * flag &
+ 2.0_wp * ( &
km(k+1,j,i) * ( w(k+1,j,i) - w(k,j,i) ) * ddzw(k+1) &
* rho_air(k+1) &
- km(k,j,i) * ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) &
* rho_air(k) &
) * ddzu(k+1) * drho_air_zw(k) * flag
ENDDO
!
!-- Add horizontal momentum flux v'w' 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_w(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_w(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_w(m) * ddy
ENDDO
ENDDO
!
!-- Add horizontal momentum flux u'w' at east- (l=2) and west-facing (l=3) surfaces.
!-- Default-type surfaces
DO l = 2, 3
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_w(m) * ddx
ENDDO
ENDDO
!
!-- Natural-type surfaces
DO l = 2, 3
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_w(m) * ddx
ENDDO
ENDDO
!
!-- Urban-type surfaces
DO l = 2, 3
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_w(m) * ddx
ENDDO
ENDDO
END SUBROUTINE diffusion_w_ij
END MODULE diffusion_w_mod