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gyacomo/src/grad_we4.h
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grad_we4.h
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! see "Efficient Implementation of Weighted ENO Schemes", GUANG-SHAN JIANG et all, 1996
SUBROUTINE gradz_we4( f , f_z ) ! implemented for periodic boundary conditions
use prec_const
use space_grid
implicit none
real(dp), dimension(izs:ize),intent(in) :: f
real(dp), dimension(izs:ize),intent(out) :: f_z
real(dp) :: tmp
integer :: i
call compute_f_hat_plus_one_half_we4( f, f_z )
! f_z contains f_hat_plus_one_half
tmp = f_z(ize)
do i=1,ize-izs
f_z(ize+1-i) = ( f_z(ize+1-i) - f_z(ize-i) )*deltazi
enddo
f_z(izs) = ( f_z(izs)- tmp )*deltazi
!! write(*,*) "gradz_we4"
END SUBROUTINE gradz_we4
SUBROUTINE compute_IS_we4( f, IS )
use prec_const
use space_grid
use array
implicit none
real(dp), dimension(izs:ize),intent(in) :: f
real(dp), dimension(izs:ize,0:2),intent(out) :: IS
integer :: iz
! SI_0
tmp1(izs) = f(ize-1) - 2.0_dp*f(ize) + f(izs)
tmp1(izs+1) = f(ize) - 2.0_dp*f(izs) + f(izs+1)
do iz=izs+2,ize
tmp1(iz) = f(iz-2) - 2.0_dp*f(iz-1) + f(iz)
enddo
tmp2(izs) = f(ize-1) - 4.0_dp*f(ize) + 3.0_dp*f(izs)
tmp2(izs+1) = f(ize) - 4.0_dp*f(izs) + 3.0_dp*f(izs+1)
do iz=izs+2,ize
tmp2(iz) = f(iz-2) - 4.0_dp*f(iz-1) + 3.0_dp*f(iz)
enddo
do iz=izs,ize
IS(iz,0) = thirteentwelfths*tmp1(iz)*tmp1(iz) + 0.25_dp*tmp2(iz)*tmp2(iz)
enddo
! SI_1
tmp1(izs) = f(ize) - 2.0_dp*f(izs) + f(izs+1)
do iz=izs+1,ize-1
tmp1(iz) = f(iz-1) - 2.0_dp*f(iz) + f(iz+1)
enddo
tmp1(ize) = f(ize-1) - 2.0_dp*f(ize) + f(izs)
tmp2(izs) = f(ize) - f(izs+1)
do iz=izs+1,ize-1
tmp2(iz) = f(iz-1) - f(iz+1)
enddo
tmp2(ize) = f(ize-1)- f(izs)
do iz=izs,ize
IS(iz,1) = thirteentwelfths*tmp1(iz)*tmp1(iz) + 0.25_dp*tmp2(iz)*tmp2(iz)
enddo
! SI_2
do iz=izs,ize-2
tmp1(iz) = f(iz) - 2.0_dp*f(iz+1) + f(iz+2)
enddo
tmp1(ize-1) = f(ize-1) - 2.0_dp*f(ize) + f(izs)
tmp1(ize) = f(ize) - 2.0_dp*f(izs) + f(izs+1)
do iz=izs,ize-2
tmp2(iz) = 3.0_dp*f(iz) - 4.0_dp*f(iz+1) + f(iz+2)
enddo
tmp2(ize-1) = 3.0_dp*f(ize-1) - 4.0_dp*f(ize) + f(izs)
tmp2(ize) = 3.0_dp*f(ize) - 4.0_dp*f(izs) + f(izs+1)
do iz=izs,ize
IS(iz,2) = thirteentwelfths*tmp1(iz)*tmp1(iz) + 0.25_dp*tmp2(iz)*tmp2(iz)
enddo
END SUBROUTINE compute_IS_we4
SUBROUTINE compute_omegas_we4( f, omegas )
use prec_const
use space_grid
implicit none
real(dp), dimension(izs:ize),intent(in) :: f
real(dp), dimension(izs:ize,0:2),intent(out) :: omegas
real(dp) :: epsi = 0.000001_dp ! 1e-6
! real(dp) :: p = 2.0_dp ! this is hardcoded to go faster
real(dp), dimension(0:2) :: C3k = (/ 0.1, 0.6, 0.3 /)
integer :: iz
integer :: k
real(dp) :: sumalphas ! tmp variable
call compute_IS_we4( f, omegas )
! omegas now contains IS
do k=0,2
do iz=izs,ize
omegas(iz,k) = C3k(k) / ( (epsi + omegas(iz,k))*(epsi + omegas(iz,k)) )
! omegas(iz,k) = C3k(k) / power( epsi + IS, p)
enddo
enddo
! omegas now contains alphas
do iz=izs,ize
sumalphas = omegas(iz,0)+omegas(iz,1)+omegas(iz,2)
do k=0,2
omegas(iz,k) = omegas(iz,k) / sumalphas
enddo
enddo
! omegas now contains omegas
END SUBROUTINE compute_omegas_we4
SUBROUTINE compute_f_hat_plus_one_half_we4( f, f_hat )
use prec_const
use space_grid
use array
implicit none
real(dp), dimension(izs:ize),intent(in) :: f
real(dp), dimension(izs:ize),intent(out) :: f_hat
real(dp) :: epsi = 0.000001_dp ! 1e-6
! real(dp) :: p = 2.0_dp ! this is hardcoded to go faster
real(dp), dimension(0:2,0:2) :: a3kl = reshape((/ onethird, -sevensixths, elevensixths, &
-onesixth, fivesixths, onethird, &
onethird, fivesixths, -onesixth /) &
, shape(a3kl), order=(/2,1/) )
integer :: iz
call compute_omegas_we4( f, omegak_times_q3k )
! omegak_times_q3k contains omegas
! k=0
omegak_times_q3k(izs,0) = omegak_times_q3k(izs,0) *( a3kl(0,0)*f(ize-1)+ a3kl(0,1)*f(ize) + a3kl(0,2)*f(izs) )
omegak_times_q3k(izs+1,0)= omegak_times_q3k(izs+1,0)*( a3kl(0,0)*f(ize) + a3kl(0,1)*f(izs) + a3kl(0,2)*f(izs+1) )
do iz=izs+2,ize
omegak_times_q3k(iz,0) = omegak_times_q3k(iz,0) *( a3kl(0,0)*f(iz-2) + a3kl(0,1)*f(iz-1) + a3kl(0,2)*f(iz) )
enddo
! k=1
omegak_times_q3k(izs,1) = omegak_times_q3k(izs,1) *( a3kl(1,0)*f(ize) + a3kl(1,1)*f(izs) + a3kl(1,2)*f(izs+1) )
do iz=izs+1,ize-1
omegak_times_q3k(iz,1) = omegak_times_q3k(iz,1) *( a3kl(1,0)*f(iz-1) + a3kl(1,1)*f(iz) + a3kl(1,2)*f(iz+1) )
enddo
omegak_times_q3k(ize,1) = omegak_times_q3k(ize,1) *( a3kl(1,0)*f(ize-1)+ a3kl(1,1)*f(ize) + a3kl(1,2)*f(izs) )
! k=2
do iz=izs,ize-2
omegak_times_q3k(iz,2) = omegak_times_q3k(iz,2) *( a3kl(2,0)*f(iz) + a3kl(2,1)*f(iz+1) + a3kl(2,2)*f(iz+2) )
enddo
omegak_times_q3k(ize-1,2)= omegak_times_q3k(ize-1,2)*( a3kl(2,0)*f(ize-1)+ a3kl(2,1)*f(ize) + a3kl(2,2)*f(izs) )
omegak_times_q3k(ize,2) = omegak_times_q3k(ize,2) *( a3kl(2,0)*f(ize) + a3kl(2,1)*f(izs) + a3kl(2,2)*f(izs+1) )
do iz=izs,ize
f_hat(iz) = omegak_times_q3k(iz,0) + omegak_times_q3k(iz,1) + omegak_times_q3k(iz,2)
enddo
END SUBROUTINE compute_f_hat_plus_one_half_we4
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