w_split_adv - 1D z-advection

INTERFACE:

    subroutine w_split_adv(dt,f,ww,az,splitfac,method)

DESCRIPTION:

Here, the $z$-directional split 1D advection step is executed with a number of options for the numerical scheme. The basic advection equation is accompanied by an fractional step for the continuity equation and both equations look as follows:

$$h^n_{i,j,k} c^n_{i,j,k} = h^o_{i,j,k} c^o_{i,j,k} - \Delta t \left(w_{i,j,k}\tilde c^w_{i,j,k}-w_{i,j,k-1}\tilde c^w_{i,j,k-1}\right),$$ (157)

with the 1D continuity equation

$$h^n_{i,j,k} = h^o_{i,j,k} - \Delta t \left(w_{i,j,k}\tilde -w_{i,j,k-1}\right).$$ (158)

Here, $n$ and $o$ denote values before and after this operation, respectively, $n$ denote intermediate values when other 1D advection steps come after this and $o$ denotes intermediate values when other 1D advection steps came before this.

The interfacial fluxes $\tilde c^w_{i,j,k}$ are calculated by means of monotone and non-monotone schemes which are described in detail in u_split_adv, see section 8.29.5 on page .

USES:

    use domain, only: imin,imax,jmin,jmax,kmax
    use advection_3d, only: hi,hio,cu
    use advection_3d, only: UPSTREAM_SPLIT,P2,SUPERBEE,MUSCL,P2_PDM
    use advection_3d, only: ONE6TH
  $ use omp_lib
    IMPLICIT NONE

INPUT PARAMETERS:

    REALTYPE , intent(in)               :: ww(I3DFIELD),dt
    integer , intent(in)                :: az(E2DFIELD)
    REALTYPE, intent(in)                :: splitfac
    integer, intent(in)                 :: method

INPUT/OUTPUT PARAMETERS:

    REALTYPE, intent(inout)             :: f(I3DFIELD)

REVISION HISTORY:

    Original author(s): Hans Burchard & Karsten Bolding

LOCAL VARIABLES:

    integer         :: i,j,k
    REALTYPE        :: c,x,r,Phi,limit,fu,fc,fd