BoundaryFlux_DGModel1D_t Subroutine

  subroutine BoundaryFlux_DGModel1D_t(this)
    ! this method uses an linear upwind solver for the
    ! advective flux and the bassi-rebay method for the
    ! diffusive fluxes
    implicit none
    class(DGModel1D_t),intent(inout) :: this
    ! Local
    integer :: iel
    integer :: iside
    real(prec) :: fin(1:this%solution%nvar)
    real(prec) :: fout(1:this%solution%nvar)
    real(prec) :: dfdx(1:this%solution%nvar),nhat

    do iel = 1,this%mesh%nelem
      do iside = 1,2

        ! set the normal velocity
        if(iside == 1) then
          nhat = -1.0_prec
        else
          nhat = 1.0_prec
        endif

        fin = this%solution%boundary(iside,iel,1:this%solution%nvar) ! interior solution
        fout = this%solution%extboundary(iside,iel,1:this%solution%nvar) ! exterior solution
        dfdx = this%solutionGradient%avgboundary(iside,iel,1:this%solution%nvar) ! average solution gradient (with direction taken into account)
        this%flux%boundarynormal(iside,iel,1:this%solution%nvar) = &
          this%riemannflux1d(fin,fout,dfdx,nhat)

      enddo
    enddo

  endsubroutine BoundaryFlux_DGModel1D_t