INTERPOLATIONS: Implement explicit 5th order WENO reconstruction.
Signed-off-by: Grzegorz Kowal <grzegorz@amuncode.org>
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@ -150,6 +150,9 @@ module interpolations
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case ("limo3", "LIMO3", "LimO3")
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name_rec = "3rd order logarithmic limited"
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reconstruct_states => reconstruct_limo3
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case ("weno5", "WENO5")
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name_rec = "5th order WENO"
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reconstruct_states => reconstruct_weno5
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case ("crweno5", "CRWENO5")
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name_rec = "5th order Compact WENO"
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reconstruct_states => reconstruct_crweno5
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@ -225,7 +228,7 @@ module interpolations
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write (*,"(4x,a15,8x,'=',1x,a)") "reconstruction ", trim(name_rec)
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select case(trim(sreconstruction))
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case ("crweno5", "CRWENO5")
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case ("weno5", "WENO5", "crweno5", "CRWENO5")
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write (*,"(4x,a15,8x,'=',1x,a)") "stencil weights", trim(name_wei)
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case default
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end select
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@ -680,6 +683,79 @@ module interpolations
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!
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!===============================================================================
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!
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! subroutine RECONSTRUCT_WENO5:
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! ----------------------------
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!
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! Subroutine reconstructs the interface states using the fifth order
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! Explicit Reconstruction Weighted Essentially Non-Oscillatory (WENO5)
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! method.
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!
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! Arguments are described in subroutine reconstruct().
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!
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! References:
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!
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! [1] Jiang, G.-S., Shu, C.-W.,
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! "Efficient Implementation of Weighted ENO Schemes"
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! Journal of Computational Physics,
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! 1996, vol. 126, pp. 202-228,
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! http://dx.doi.org/10.1006/jcph.1996.0130
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!
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!===============================================================================
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!
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subroutine reconstruct_weno5(n, h, f, fl, fr)
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! local variables are not implicit by default
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!
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implicit none
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! subroutine arguments
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!
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integer , intent(in) :: n
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real(kind=8) , intent(in) :: h
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real(kind=8), dimension(n), intent(in) :: f
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real(kind=8), dimension(n), intent(out) :: fl, fr
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! local arrays
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!
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real(kind=8), dimension(1:n) :: bl, bc, br
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real(kind=8), dimension(1:n) :: wl, wc, wr
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real(kind=8), dimension(1:n) :: u
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!
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!-------------------------------------------------------------------------------
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!
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! calculate smoothness indicators
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!
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call smoothness_indicators(n, f(1:n), bl(1:n), bc(1:n), br(1:n))
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! calculate stencil weights
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!
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call stencil_weights(n, f(1:n), bl(1:n), bc(1:n), br(1:n) &
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, wl(1:n), wc(1:n), wr(1:n))
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! find the left state interpolation implicitelly
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!
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call weno5_explicit(n, f(1:n), wl(1:n), wc(1:n), wr(1:n), u(1:n))
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! substitute the left state
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!
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fl(1:n) = u(1:n)
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! find the right state interpolation implicitelly
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!
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call weno5_explicit(n, f(n:1:-1), wr(n:1:-1), wc(n:1:-1), wl(n:1:-1) &
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, u(n:1:-1))
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! substitute the right state
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!
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fr(1:n-1) = u (2:n)
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fr( n ) = fl( n)
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!-------------------------------------------------------------------------------
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!
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end subroutine reconstruct_weno5
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!
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!===============================================================================
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!
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! subroutine RECONSTRUCT_CRWENO5:
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! ------------------------------
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!
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@ -761,6 +837,103 @@ module interpolations
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!
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!===============================================================================
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!
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! subroutine WENO5_EXPLICIT:
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! -------------------------
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!
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! Subroutine reconstructs the interface states using the fifth order
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! Explicit Reconstruction Weighted Essentially Non-Oscillatory (WENO)
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! method.
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!
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! Arguments are described in subroutine reconstruct().
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!
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! References:
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!
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! [1] Jiang, G.-S., Shu, C.-W.,
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! "Efficient Implementation of Weighted ENO Schemes"
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! Journal of Computational Physics,
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! 1996, vol. 126, pp. 202-228,
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! http://dx.doi.org/10.1006/jcph.1996.0130
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!
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!===============================================================================
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!
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subroutine weno5_explicit(n, f, wl, wc, wr, u)
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! local variables are not implicit by default
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!
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implicit none
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! subroutine arguments
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!
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integer , intent(in) :: n
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real(kind=8), dimension(n), intent(in) :: f
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real(kind=8), dimension(n), intent(in) :: wl, wc, wr
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real(kind=8), dimension(n), intent(out) :: u
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! local variables
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!
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integer :: im2, im1, i , ip1, ip2
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integer :: nm1, nm2
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real(kind=8) :: xl, xc, xr, xx
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real(kind=8) :: bl, bc, br, bt
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! local constants
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!
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real(kind=8), parameter :: al = 1.0d-01, ac = 6.0d-01, ar = 3.0d-01
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real(kind=8), parameter :: dh = 5.0d-01, ds = 1.0d+00 / 6.0d+00
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!
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!-------------------------------------------------------------------------------
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!
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! calculate indices
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!
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nm1 = n - 1
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nm2 = n - 2
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! prepare coefficients
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!
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do i = 3, nm2
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! prepare indices
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!
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im2 = i - 2
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im1 = i - 1
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ip1 = i + 1
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ip2 = i + 2
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! normalize weigths
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!
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xc = ac * wc(i)
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xl = al * wl(i)
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xr = ar * wr(i)
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xx = xc + (xl + xr)
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bl = xl / xx
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br = xr / xx
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bc = 1.0d+00 - (bl + br)
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! prepare right hand side of tridiagonal equation
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!
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u(i) = (bl * (2.0d+00 * f(im2) - 7.0d+00 * f(im1) + 1.1d+01 * f(i )) &
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+ bc * ( - f(im1) + 5.0d+00 * f(i ) + 2.0d+00 * f(ip1)) &
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+ br * (2.0d+00 * f(i ) + 5.0d+00 * f(ip1) - f(ip2))) * ds
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end do
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! at the left boundaries, we apply 5th order explicit WENO interpolation with
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! different weights
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!
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u(1) = dh * (f(1) + f(2 ))
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u(2) = f(2) + limiter(dh, f(2) - f(1), f(3) - f(2))
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! at the right boundaries, we do the similar thing
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!
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u(nm1) = f(nm1) + limiter(dh, f(nm1) - f(nm2), f(n) - f(nm1))
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u(n ) = f(n ) + dh * (f(n) - f(nm1))
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!-------------------------------------------------------------------------------
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!
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end subroutine weno5_explicit
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!
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!===============================================================================
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!
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! subroutine CRWENO5_IMPLICIT:
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! ---------------------------
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!
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