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/*@@
@file GRHydro_WENOReconstruct.F90
@date Fri Jan 3 2013
@author Ian Hawke, Christian Reisswig
@desc
Routines to set up the coefficient array and to perform one dimensional
ENO reconstruction of arbitrary order.
@enddesc
@@*/
#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_Arguments.h"
/*@@
@routine GRHydro_WENOSetup
@date Fri Jan 3 2013
@author Christian Reisswig
@desc
Sets up the coefficient array for WENO reconstruction.
Uses the notation of Shu, equation (2.21), in
''High Order ENO and WENO Schemes for CFD''
(see ThornGuide for full reference).
One exception: (Shu) r -> (Here) i: avoiding name clash.
@enddesc
@calls
@calledby
@history
@endhistory
@@*/
subroutine GRHydro_WENOSetup(CCTK_ARGUMENTS)
USE GRHydro_WENOScalars
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_PARAMETERS
CCTK_INT :: allocstat
if(.not.allocated(weno_coeffs)) then ! uses weno_coeffs as a sentinel
! Right now we hardcode to 5th order
allocate(weno_coeffs(3, 5), STAT=allocstat)
if (allocstat .ne. 0) call CCTK_WARN(0, "Failed to allocate WENO coefficient arrays!")
allocate(beta_shu(3, 6), STAT=allocstat)
if (allocstat .ne. 0) call CCTK_WARN(0, "Failed to allocate smoothness indicator stencil coefficient arrays!")
endif
! Set stencils
weno_coeffs(1,1) = 3.0d0/8.0d0
weno_coeffs(1,2) = -5.0d0/4.0d0
weno_coeffs(1,3) = 15.0d0/8.0d0
weno_coeffs(1,4) = 0.0d0
weno_coeffs(1,5) = 0.0d0
weno_coeffs(2,1) = 0.0d0
weno_coeffs(2,2) = -1.0d0/8.0d0
weno_coeffs(2,3) = 3.0d0/4.0d0
weno_coeffs(2,4) = 3.0d0/8.0d0
weno_coeffs(2,5) = 0.0d0
weno_coeffs(3,1) = 0.0d0
weno_coeffs(3,2) = 0.0d0
weno_coeffs(3,3) = 3.0d0/8.0d0
weno_coeffs(3,4) = 3.0d0/4.0d0
weno_coeffs(3,5) = -1.0d0/8.0d0
! Shu smoothness indicator stencil coefficients
beta_shu(1,1) = 4.0d0/3.0d0
beta_shu(1,2) = -19.0d0/3.0d0
beta_shu(1,3) = 25.0d0/3.0d0
beta_shu(1,4) = 11.0d0/3.0d0
beta_shu(1,5) = -31.0d0/3.0d0
beta_shu(1,6) = 10.0d0/3.0d0
beta_shu(2,1) = 4.0d0/3.0d0
beta_shu(2,2) = -13.0d0/3.0d0
beta_shu(2,3) = 13.0d0/3.0d0
beta_shu(2,4) = 5.0d0/3.0d0
beta_shu(2,5) = -13.0d0/3.0d0
beta_shu(2,6) = 4.0d0/3.0d0
beta_shu(3,1) = 10.0d0/3.0d0
beta_shu(3,2) = -31.0d0/3.0d0
beta_shu(3,3) = 25.0d0/3.0d0
beta_shu(3,4) = 11.0d0/3.0d0
beta_shu(3,5) = -19.0d0/3.0d0
beta_shu(3,6) = 4.0d0/3.0d0
end subroutine GRHydro_WENOSetup
/*@@
@routine GRHydro_ENOShutdown
@date Fri Jan 3 2013
@author Christian Reisswig
@desc
Deallocates the coefficient arrays
@enddesc
@calls
@calledby
@history
@endhistory
@@*/
subroutine GRHydro_WENOShutdown(CCTK_ARGUMENTS)
USE GRHydro_WENOScalars
implicit none
DECLARE_CCTK_ARGUMENTS
CCTK_INT :: deallocstat
if(allocated(weno_coeffs)) then
deallocate(weno_coeffs, STAT = deallocstat)
if (deallocstat .ne. 0) call CCTK_WARN(0, "Failed to deallocate WENO coefficients.")
deallocate(beta_shu, STAT = deallocstat)
if (deallocstat .ne. 0) call CCTK_WARN(0, "Failed to deallocate shu smoothness indicator coefficients.")
endif
end subroutine GRHydro_WENOShutdown
/*@@
@routine GRHydro_ENOReconstruct1d
@date Fri Jan 3 2013
@author Christian Reisswig
@desc
Perform a one dimensional reconstruction of a given array using WENO.
@enddesc
@calls
@calledby
@history
@endhistory
@@*/
#define SpaceMask_CheckStateBitsF90_1D(mask,i,type_bits,state_bits) \
(iand(mask((i)),(type_bits)).eq.(state_bits))
subroutine GRHydro_WENOReconstruct1d(order, nx, v, vminus, vplus, trivial_rp, &
hydro_excision_mask)
USE GRHydro_WENOScalars
implicit none
DECLARE_CCTK_PARAMETERS
CCTK_INT :: order, nx, i, j
CCTK_REAL, dimension(nx) :: v, vplus, vminus
CCTK_INT, dimension(nx) :: hydro_excision_mask
logical, dimension(nx) :: trivial_rp
logical, dimension(nx) :: excise
logical :: normal_weno
CCTK_REAL :: beta1, beta2, beta3, vnorm, betanorm
CCTK_REAL :: wplus1, wplus2, wplus3, wbarplus1, wbarplus2, wbarplus3
CCTK_REAL :: wminus1, wminus2, wminus3, wbarminus1, wbarminus2, wbarminus3
vminus = 0.d0
vplus = 0.d0
excise = .false.
trivial_rp = .false.
!!$ Initialize excision
do i = 1, nx
if (GRHydro_enable_internal_excision /= 0 .and. (hydro_excision_mask(i) .ne. 0)) then
trivial_rp(i) = .true.
excise(i) = .true.
if (i > 1) then
trivial_rp(i-1) = .true.
end if
end if
end do
do i = 3, nx-2
!!$ Handle excision
normal_weno = .true.
if (i < nx) then
if (excise(i+1)) then
vminus(i) = v(i)
vplus(i) = v(i)
normal_weno = .false.
end if
end if
if (i > 1) then
if (excise(i-1)) then
vminus(i) = v(i)
vplus(i) = v(i)
normal_weno = .false.
end if
end if
if (normal_weno) then
!!$ Compute smoothness indicators
!!$ This is from Tchekhovskoy et al 2007 (WHAM code paper).
beta1 = beta_shu(1,1)*v(i-2)**2 &
+ beta_shu(1,2)*v(i-2)*v(i-1) &
+ beta_shu(1,3)*v(i-1)**2 &
+ beta_shu(1,4)*v(i-2)*v(i) &
+ beta_shu(1,5)*v(i-1)*v(i) &
+ beta_shu(1,6)*v(i)**2
beta2 = beta_shu(2,1)*v(i-1)**2 &
+ beta_shu(2,2)*v(i-1)*v(i) &
+ beta_shu(2,3)*v(i)**2 &
+ beta_shu(2,4)*v(i-1)*v(i+1) &
+ beta_shu(2,5)*v(i)*v(i+1) &
+ beta_shu(2,6)*v(i+1)**2
beta3 = beta_shu(3,1)*v(i)**2 &
+ beta_shu(3,2)*v(i)*v(i+1) &
+ beta_shu(3,3)*v(i+1)**2 &
+ beta_shu(3,4)*v(i)*v(i+2) &
+ beta_shu(3,5)*v(i+1)*v(i+2) &
+ beta_shu(3,6)*v(i+2)**2
vnorm = (v(i-2)**2 + v(i-1)**2 + v(i)**2 + v(i+1)**2 + v(i+2)**2)
beta1 = beta1 + 100.0d0*weno_eps*(vnorm + 1.0d0)
beta2 = beta2 + 100.0d0*weno_eps*(vnorm + 1.0d0)
beta3 = beta3 + 100.0d0*weno_eps*(vnorm + 1.0d0)
betanorm = beta1 + beta2 + beta3
beta1 = beta1 / betanorm
beta2 = beta2 / betanorm
beta3 = beta3 / betanorm
wbarplus1 = 1.0d0/16.0d0 / (weno_eps + beta1)**2
wbarplus2 = 5.0d0/8.0d0 / (weno_eps + beta2)**2
wbarplus3 = 5.0d0/16.0d0 / (weno_eps + beta3)**2
wplus1 = wbarplus1 / (wbarplus1 + wbarplus2 + wbarplus3)
wplus2 = wbarplus2 / (wbarplus1 + wbarplus2 + wbarplus3)
wplus3 = wbarplus3 / (wbarplus1 + wbarplus2 + wbarplus3)
wbarminus1 = 5.0d0/16.0d0 / (weno_eps + beta1)**2
wbarminus2 = 5.0d0/8.0d0 / (weno_eps + beta2)**2
wbarminus3 = 1.0d0/16.0d0 / (weno_eps + beta3)**2
wminus1 = wbarminus1 / (wbarminus1 + wbarminus2 + wbarminus3)
wminus2 = wbarminus2 / (wbarminus1 + wbarminus2 + wbarminus3)
wminus3 = wbarminus3 / (wbarminus1 + wbarminus2 + wbarminus3)
!!$ Calculate the reconstruction
do j = 1, 5
vplus(i) = vplus(i) + wplus1 * weno_coeffs(1,j)*v(i-3+j) &
+ wplus2 * weno_coeffs(2,j)*v(i-3+j) &
+ wplus3 * weno_coeffs(3,j)*v(i-3+j)
vminus(i) = vminus(i) + wminus1 * weno_coeffs(3,6-j)*v(i-3+j) &
+ wminus2 * weno_coeffs(2,6-j)*v(i-3+j) &
+ wminus3 * weno_coeffs(1,6-j)*v(i-3+j)
end do
!vminus(i) = v(i)
!vplus(i) = v(i)
end if
end do
do i = 1, nx
if (excise(i)) then
if (i > 1) then
if (.not. excise(i-1)) then
vminus(i) = vplus(i-1)
end if
end if
vplus(i) = vminus(i)
end if
end do
do i = nx, 1, -1
if (excise(i)) then
if (i < nx) then
if (.not. excise(i+1)) then
vplus(i) = vminus(i+1)
end if
end if
vminus(i) = vplus(i)
end if
end do
end subroutine GRHydro_WENOReconstruct1d
|
