weno5_js.f90 Source File

!> @file weno5_js.f90
!> @brief WENO5-JS (Jiang & Shu 1996) reconstruction scheme.
!!
!! 5th-order weighted essentially non-oscillatory reconstruction using the
!! Jiang-Shu nonlinear weight formula.  Substencil reconstructions and
!! smoothness indicators are provided by the weno_family module.
!!
!! References:
!!   [1] G.-S. Jiang and C.-W. Shu, "Efficient Implementation of Weighted ENO
!!       Schemes," J. Comput. Phys., 126:202-228, 1996.

module weno5_js
  use precision, only: wp
  use solver_state, only: neq
  use weno_family, only: eps_weno, d0, d1, d2, weno5_substencils, weno5_smoothness
  implicit none
  private

  public :: weno5_js_reconstruct

contains

  ! ---------------------------------------------------------------------------
  !> Perform WENO5-JS reconstruction on the supplied stencil.
  !!
  !! Applies WENO5-JS reconstruction component-wise to a 5-point stencil.
  !! The stencil may be in physical or characteristic space depending on
  !! whether spatial_discretization applied characteristic projection first.
  !!
  !! Nonlinear weight formula (Jiang & Shu 1996, Eq. 22):
  !!   omega_tilde_k = d_k / (eps + beta_k)^2
  !!   omega_k       = omega_tilde_k / sum(omega_tilde)
  !!
  !! @param[in]  f_stencil  Stencil at 5 points (neq x 5)
  !! @param[out] f_hat      Reconstructed value at the interface
  ! ---------------------------------------------------------------------------
  pure subroutine weno5_js_reconstruct(f_stencil, f_hat)
    real(wp), intent(in) :: f_stencil(:, :)
    real(wp), intent(out) :: f_hat(:)

    real(wp) :: vp0(neq), vp1(neq), vp2(neq)
    real(wp) :: beta0(neq), beta1(neq), beta2(neq)
    real(wp) :: w0(neq), w1(neq), w2(neq), w_sum(neq)
    integer :: i

    call weno5_substencils(f_stencil, vp0, vp1, vp2)
    call weno5_smoothness(f_stencil, beta0, beta1, beta2)

    do i = 1, neq
      w0(i) = d0 / (eps_weno + beta0(i))**2
      w1(i) = d1 / (eps_weno + beta1(i))**2
      w2(i) = d2 / (eps_weno + beta2(i))**2
    end do

    w_sum = w0 + w1 + w2

    do i = 1, neq
      f_hat(i) = (vp0(i) * w0(i) + vp1(i) * w1(i) + vp2(i) * w2(i)) / w_sum(i)
    end do
  end subroutine weno5_js_reconstruct

end module weno5_js