!> @file advec_w_pw.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
! <http://www.gnu.org/licenses/>.
!
! Copyright 1997-2021 Leibniz Universitaet Hannover
!--------------------------------------------------------------------------------------------------!
!
! Description:
! ------------
!> Advection term for w velocity-component using Piacsek and Williams.
!> Vertical advection at the first grid point above the surface is done with normal centred
!> differences, because otherwise no information from the surface would be communicated upwards due
!> to w=0 at k=nzb.
!--------------------------------------------------------------------------------------------------!
 MODULE advec_w_pw_mod
 

    PRIVATE
    PUBLIC advec_w_pw

    INTERFACE advec_w_pw
       MODULE PROCEDURE advec_w_pw
       MODULE PROCEDURE advec_w_pw_ij
    END INTERFACE advec_w_pw
 
 CONTAINS


!--------------------------------------------------------------------------------------------------!
! Description:
! ------------
!> Call for all grid points
!--------------------------------------------------------------------------------------------------!
 SUBROUTINE advec_w_pw

    USE arrays_3d,                                                                                 &
        ONLY:  ddzu, tend, u, v, w

    USE control_parameters,                                                                        &
        ONLY:  u_gtrans, v_gtrans

    USE grid_variables,                                                                            &
        ONLY:  ddx, ddy

    USE indices,                                                                                   &
        ONLY:  nxl, nxr, nyn, nys, nzb, nzt

    USE kinds


    IMPLICIT NONE

    INTEGER(iwp) ::  i !< grid index along x-direction
    INTEGER(iwp) ::  j !< grid index along y-direction
    INTEGER(iwp) ::  k !< grid index along z-direction
    
    REAL(wp)     ::  gu !< Galilei-transformation velocity along x
    REAL(wp)     ::  gv !< Galilei-transformation velocity along y


    gu = 2.0_wp * u_gtrans
    gv = 2.0_wp * v_gtrans
    DO  i = nxl, nxr
       DO  j = nys, nyn
          DO  k = nzb+1, nzt
             tend(k,j,i) = tend(k,j,i) - 0.25_wp * (                                               &
                           ( w(k,j,i+1)   * ( u(k+1,j,i+1) + u(k,j,i+1) - gu )                     &
                           - w(k,j,i-1)   * ( u(k+1,j,i)   + u(k,j,i) - gu ) ) * ddx               &
                           + ( w(k,j+1,i) * ( v(k+1,j+1,i) + v(k,j+1,i) - gv )                     &
                           - w(k,j-1,i)   * ( v(k+1,j,i)   + v(k,j,i) - gv ) ) * ddy               &
                           + ( w(k+1,j,i) * ( w(k+1,j,i)   + w(k,j,i) )                            &
                           - w(k-1,j,i)   * ( w(k,j,i)     + w(k-1,j,i) ) )    * ddzu(k+1)         &
                                                   )
          ENDDO
       ENDDO
    ENDDO

 END SUBROUTINE advec_w_pw


!--------------------------------------------------------------------------------------------------!
! Description:
! ------------
!> Call for grid point i,j
!--------------------------------------------------------------------------------------------------!
 SUBROUTINE advec_w_pw_ij( i, j )

    USE arrays_3d,                                                                                 &
        ONLY:  ddzu, tend, u, v, w

    USE control_parameters,                                                                        &
        ONLY:  u_gtrans, v_gtrans

    USE grid_variables,                                                                            &
        ONLY:  ddx, ddy

    USE indices,                                                                                   &
        ONLY:  nzb, nzt

    USE kinds


    IMPLICIT NONE

    INTEGER(iwp) ::  i !< grid index along x-direction
    INTEGER(iwp) ::  j !< grid index along y-direction
    INTEGER(iwp) ::  k !< grid index along z-direction
    
    REAL(wp)     ::  gu !< Galilei-transformation velocity along x
    REAL(wp)     ::  gv !< Galilei-transformation velocity along y

    gu = 2.0_wp * u_gtrans
    gv = 2.0_wp * v_gtrans
    DO  k = nzb+1, nzt
       tend(k,j,i) = tend(k,j,i) - 0.25_wp * (                                                     &
                      ( w(k,j,i+1)   * ( u(k+1,j,i+1) + u(k,j,i+1) - gu )                          &
                      - w(k,j,i-1)   * ( u(k+1,j,i)   + u(k,j,i) - gu ) ) * ddx                    &
                      + ( w(k,j+1,i) * ( v(k+1,j+1,i) + v(k,j+1,i) - gv )                          &
                      - w(k,j-1,i)   * ( v(k+1,j,i)   + v(k,j,i) - gv ) ) * ddy                    &
                      + ( w(k+1,j,i) * ( w(k+1,j,i)   + w(k,j,i) )                                 &
                      - w(k-1,j,i)   * ( w(k,j,i)     + w(k-1,j,i) ) )    * ddzu(k+1)              &
                                             )
    ENDDO
 END SUBROUTINE advec_w_pw_ij

 END MODULE advec_w_pw_mod