INTERPOLATIONS: Implement 7th order MP reconstruction.
Signed-off-by: Grzegorz Kowal <grzegorz@amuncode.org>
This commit is contained in:
parent
b43dbe50ee
commit
97b10008f0
@ -264,6 +264,13 @@ module interpolations
|
||||
if (verbose .and. ng < 4) &
|
||||
call print_warning("interpolations:initialize_interpolation" &
|
||||
, "Increase the number of ghost cells (at least 4).")
|
||||
case ("mp7", "MP7")
|
||||
name_rec = "7th order Monotonicity Preserving"
|
||||
interfaces => interfaces_dir
|
||||
reconstruct_states => reconstruct_mp7
|
||||
if (verbose .and. ng < 4) &
|
||||
call print_warning("interpolations:initialize_interpolation" &
|
||||
, "Increase the number of ghost cells (at least 4).")
|
||||
case ("crmp5", "CRMP5")
|
||||
name_rec = "5th order Compact Monotonicity Preserving"
|
||||
interfaces => interfaces_dir
|
||||
@ -3496,6 +3503,137 @@ module interpolations
|
||||
!
|
||||
!===============================================================================
|
||||
!
|
||||
! subroutine RECONSTRUCT_MP7:
|
||||
! --------------------------
|
||||
!
|
||||
! Subroutine reconstructs the interface states using the seventh order
|
||||
! Monotonicity Preserving (MP) method.
|
||||
!
|
||||
! Arguments are described in subroutine reconstruct().
|
||||
!
|
||||
! References:
|
||||
!
|
||||
! [1] Suresh, A. & Huynh, H. T.,
|
||||
! "Accurate Monotonicity-Preserving Schemes with Runge-Kutta
|
||||
! Time Stepping"
|
||||
! Journal on Computational Physics,
|
||||
! 1997, vol. 136, pp. 83-99,
|
||||
! http://dx.doi.org/10.1006/jcph.1997.5745
|
||||
! [2] He, ZhiWei, Li, XinLiang, Fu, DeXun, & Ma, YanWen,
|
||||
! "A 5th order monotonicity-preserving upwind compact difference
|
||||
! scheme",
|
||||
! Science China Physics, Mechanics and Astronomy,
|
||||
! Volume 54, Issue 3, pp. 511-522,
|
||||
! http://dx.doi.org/10.1007/s11433-010-4220-x
|
||||
!
|
||||
!===============================================================================
|
||||
!
|
||||
subroutine reconstruct_mp7(n, h, fc, fl, fr)
|
||||
|
||||
! local variables are not implicit by default
|
||||
!
|
||||
implicit none
|
||||
|
||||
! subroutine arguments
|
||||
!
|
||||
integer , intent(in) :: n
|
||||
real(kind=8) , intent(in) :: h
|
||||
real(kind=8), dimension(n), intent(in) :: fc
|
||||
real(kind=8), dimension(n), intent(out) :: fl, fr
|
||||
|
||||
! local variables
|
||||
!
|
||||
integer :: i
|
||||
|
||||
! local arrays for derivatives
|
||||
!
|
||||
real(kind=8), dimension(n) :: fi
|
||||
real(kind=8), dimension(n) :: u
|
||||
|
||||
! local parameters
|
||||
!
|
||||
real(kind=8), dimension(7), parameter :: &
|
||||
ce7 = (/-3.0d+00, 2.5d+01,-1.01d+02, 3.19d+02 &
|
||||
, 2.14d+02,-3.8d+01, 4.0d+00 /) / 4.2d+02
|
||||
real(kind=8), dimension(5), parameter :: &
|
||||
ce5 = (/ 2.0d+00,-1.3d+01, 4.7d+01 &
|
||||
, 2.7d+01,-3.0d+00 /) / 6.0d+01
|
||||
real(kind=8), dimension(3), parameter :: &
|
||||
ce3 = (/-1.0d+00, 5.0d+00, 2.0d+00 /) / 6.0d+00
|
||||
real(kind=8), dimension(2), parameter :: ce2 = (/ 5.0d-01, 5.0d-01 /)
|
||||
!
|
||||
!-------------------------------------------------------------------------------
|
||||
!
|
||||
!! === left-side interpolation ===
|
||||
!!
|
||||
! reconstruct the interface state using the 5th order interpolation
|
||||
!
|
||||
do i = 4, n - 3
|
||||
u(i) = sum(ce7(:) * fc(i-3:i+3))
|
||||
end do
|
||||
|
||||
! interpolate the interface state of the ghost zones using the interpolations
|
||||
! of lower orders
|
||||
!
|
||||
u( 1) = sum(ce2(:) * fc( 1: 2))
|
||||
u( 2) = sum(ce3(:) * fc( 1: 3))
|
||||
u( 3) = sum(ce5(:) * fc( 1: 5))
|
||||
u(n-2) = sum(ce5(:) * fc(n-4: n))
|
||||
u(n-1) = sum(ce3(:) * fc(n-2: n))
|
||||
u(n ) = fc(n )
|
||||
|
||||
! apply the monotonicity preserving limiting
|
||||
!
|
||||
call mp_limiting(n, fc(1:n), u(1:n))
|
||||
|
||||
! copy the interpolation to the respective vector
|
||||
!
|
||||
fl(1:n) = u(1:n)
|
||||
|
||||
!! === right-side interpolation ===
|
||||
!!
|
||||
! invert the cell-centered value vector
|
||||
!
|
||||
fi(1:n) = fc(n:1:-1)
|
||||
|
||||
! reconstruct the interface state using the 5th order interpolation
|
||||
!
|
||||
do i = 4, n - 3
|
||||
u(i) = sum(ce7(:) * fi(i-3:i+3))
|
||||
end do
|
||||
|
||||
! interpolate the interface state of the ghost zones using the interpolations
|
||||
! of lower orders
|
||||
!
|
||||
u( 1) = sum(ce2(:) * fi( 1: 2))
|
||||
u( 2) = sum(ce3(:) * fi( 1: 3))
|
||||
u( 3) = sum(ce5(:) * fi( 1: 5))
|
||||
u(n-2) = sum(ce5(:) * fi(n-4: n))
|
||||
u(n-1) = sum(ce3(:) * fi(n-2: n))
|
||||
u(n ) = fi(n )
|
||||
|
||||
! apply the monotonicity preserving limiting
|
||||
!
|
||||
call mp_limiting(n, fi(1:n), u(1:n))
|
||||
|
||||
! copy the interpolation to the respective vector
|
||||
!
|
||||
fr(1:n-1) = u(n-1:1:-1)
|
||||
|
||||
! update the interpolation of the first and last points
|
||||
!
|
||||
i = n - 1
|
||||
fl(1) = 0.5d+00 * (fc(1) + fc(2))
|
||||
fr(i) = 0.5d+00 * (fc(i) + fc(n))
|
||||
fl(n) = fc(n)
|
||||
fr(n) = fc(n)
|
||||
|
||||
!-------------------------------------------------------------------------------
|
||||
!
|
||||
end subroutine reconstruct_mp7
|
||||
!
|
||||
!===============================================================================
|
||||
!
|
||||
! subroutine RECONSTRUCT_CRMP5:
|
||||
! ----------------------------
|
||||
!
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user