upwind2.f90 Source File

!> @file upwind2.f90
!> @brief Second-order upwind reconstruction scheme.

module upwind2
  use precision, only: wp
  implicit none
  private

  public :: upwind2_reconstruct

contains

  ! ---------------------------------------------------------------------------
  !> Second-order upwind reconstruction.
  !!
  !! Uses a 3-point stencil (half_stencil = 2, stencil_width = 3).
  !! For the positive (left-biased) stencil:
  !!   stencil(:,1) = F^+_{i-1},  stencil(:,2) = F^+_i  (centre)
  !!   F_hat^+ = 1.5 * F^+_i - 0.5 * F^+_{i-1}
  !!
  !! For the negative (right-biased, reversed) stencil:
  !!   stencil(:,1) = F^-_{i+2},  stencil(:,2) = F^-_{i+1} (centre)
  !!   F_hat^- = 1.5 * F^-_{i+1} - 0.5 * F^-_{i+2}   [same formula]
  !!
  !! @param[in]  f_stencil  Stencil (neq x 3)
  !! @param[out] f_hat      Reconstructed flux at the interface
  ! ---------------------------------------------------------------------------
  pure subroutine upwind2_reconstruct(f_stencil, f_hat)
    real(wp), intent(in) :: f_stencil(:, :)
    real(wp), intent(out) :: f_hat(:)

    ! 2nd-order upwind: (3/2)*f_centre - (1/2)*f_{centre-1}
    ! Centre is index 2 for the 3-point stencil.
    f_hat = 1.5_wp * f_stencil(:, 2) - 0.5_wp * f_stencil(:, 1)
  end subroutine upwind2_reconstruct

end module upwind2