!> @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 1997-2021 Leibniz Universitaet Hannover
!--------------------------------------------------------------------------------------------------!
!
! 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, drho_air, km, rho_air_zw, tend, u, v, w
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, topo_flags
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
!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k, l, m) &
!$ACC PRIVATE(surf_e, surf_s, flag, kmym, kmyp, kmzm, kmzp) &
!$ACC PRIVATE(mask_bottom, mask_north, mask_south, mask_top) &
!$ACC PRESENT(topo_flags, km) &
!$ACC PRESENT(u, v, w) &
!$ACC PRESENT(ddzu, ddzw, drho_air, rho_air_zw) &
!$ACC PRESENT(surf_def_h(0:2), surf_def_v(0:1)) &
!$ACC PRESENT(surf_lsm_h(0:1), surf_lsm_v(0:1)) &
!$ACC PRESENT(surf_usm_h(0:1), surf_usm_v(0:1)) &
!$ACC PRESENT(tend)
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( topo_flags(k,j,i), 1 ) )
mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j-1,i), 1 ) )
mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(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( topo_flags(k-1,j,i), 8 ) )
mask_top = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k+1,j,i), 8 ) ) * &
MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k+1,j,i), 9 ) )
flag = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(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(0)%start_index(j,i)
surf_e = surf_lsm_h(0)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_lsm_h(0)%k(m)
tend(k,j,i) = tend(k,j,i) &
+ ( - ( - surf_lsm_h(0)%usws(m) ) ) * ddzw(k) * drho_air(k)
ENDDO
!
!-- Natural-type surfaces, downward-facing
surf_s = surf_lsm_h(1)%start_index(j,i)
surf_e = surf_lsm_h(1)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_lsm_h(1)%k(m)
tend(k,j,i) = tend(k,j,i) &
+ ( - surf_lsm_h(1)%usws(m) ) * ddzw(k) * drho_air(k)
ENDDO
!
!-- Urban-type surfaces, upward-facing
surf_s = surf_usm_h(0)%start_index(j,i)
surf_e = surf_usm_h(0)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_usm_h(0)%k(m)
tend(k,j,i) = tend(k,j,i) &
+ ( - ( - surf_usm_h(0)%usws(m) ) ) * ddzw(k) * drho_air(k)
ENDDO
!
!-- Urban-type surfaces, downward-facing
surf_s = surf_usm_h(1)%start_index(j,i)
surf_e = surf_usm_h(1)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_usm_h(1)%k(m)
tend(k,j,i) = tend(k,j,i) &
+ ( - surf_usm_h(1)%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, drho_air, km, tend, u, v, w, 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, topo_flags
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( topo_flags(k-1,j,i), 8 ) )
mask_top = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k+1,j,i), 8 ) ) * &
MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k+1,j,i), 9 ) )
flag = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(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(0)%start_index(j,i)
surf_e = surf_lsm_h(0)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_lsm_h(0)%k(m)
tend(k,j,i) = tend(k,j,i) + ( - ( - surf_lsm_h(0)%usws(m) ) ) * ddzw(k) * drho_air(k)
ENDDO
!
!-- Natural-type surfaces, downward-facing
surf_s = surf_lsm_h(1)%start_index(j,i)
surf_e = surf_lsm_h(1)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_lsm_h(1)%k(m)
tend(k,j,i) = tend(k,j,i) + ( - surf_lsm_h(1)%usws(m) ) * ddzw(k) * drho_air(k)
ENDDO
!
!-- Urban-type surfaces, upward-facing
surf_s = surf_usm_h(0)%start_index(j,i)
surf_e = surf_usm_h(0)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_usm_h(0)%k(m)
tend(k,j,i) = tend(k,j,i) + ( - ( - surf_usm_h(0)%usws(m) ) ) * ddzw(k) * drho_air(k)
ENDDO
!
!-- Urban-type surfaces, downward-facing
surf_s = surf_usm_h(1)%start_index(j,i)
surf_e = surf_usm_h(1)%end_index(j,i)
DO m = surf_s, surf_e
k = surf_usm_h(1)%k(m)
tend(k,j,i) = tend(k,j,i) + ( - surf_usm_h(1)%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