433 lines
15 KiB
Fortran
433 lines
15 KiB
Fortran
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#include "macrodef.fh"
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! we need only distinguish different finite difference order
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! Vertex or Cell is distinguished in routine symmetry_bd which locates in
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! file "fmisc.f90"
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#if (ghost_width == 2)
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! second order code
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!------------------------------------------------------------------------------------------------------------------------------
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!usual type Kreiss-Oliger type numerical dissipation
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!We support cell center only
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! (D_+D_-)^2 =
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! f(i-2) - 4 f(i-1) + 6 f(i) - 4 f(i+1) + f(i+2)
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! ------------------------------------------------------
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! dx^4
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!------------------------------------------------------------------------------------------------------------------------------
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! do not add dissipation near boundary
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subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
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implicit none
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! argument variables
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integer,intent(in) :: Symmetry
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integer,dimension(3),intent(in)::ex
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real*8, dimension(1:3), intent(in) :: SoA
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double precision,intent(in),dimension(ex(1))::X
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double precision,intent(in),dimension(ex(2))::Y
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double precision,intent(in),dimension(ex(3))::Z
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double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
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double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
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real*8,intent(in) :: eps
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!~~~~~~ other variables
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real*8 :: dX,dY,dZ
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real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh
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integer :: imin,jmin,kmin,imax,jmax,kmax
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integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
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real*8,parameter :: cof = 1.6d1 ! 2^4
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real*8, parameter :: F4=4.d0,F6=6.d0
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integer::i,j,k
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dX = X(2)-X(1)
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dY = Y(2)-Y(1)
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dZ = Z(2)-Z(1)
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imax = ex(1)
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jmax = ex(2)
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kmax = ex(3)
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imin = 1
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jmin = 1
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kmin = 1
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if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
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if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
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if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
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call symmetry_bd(2,ex,f,fh,SoA)
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! f(i-2) - 4 f(i-1) + 6 f(i) - 4 f(i+1) + f(i+2)
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! ------------------------------------------------------
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! dx^4
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! note the sign (-1)^r-1, now r=2
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do k=1,ex(3)
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do j=1,ex(2)
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do i=1,ex(1)
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if(i-2 >= imin .and. i+2 <= imax .and. &
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j-2 >= jmin .and. j+2 <= jmax .and. &
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k-2 >= kmin .and. k+2 <= kmax) then
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! x direction
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f_rhs(i,j,k) = f_rhs(i,j,k) - eps/dX/cof * ( &
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(fh(i-2,j,k)+fh(i+2,j,k)) &
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- F4 * (fh(i-1,j,k)+fh(i+1,j,k)) &
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+ F6 * fh(i,j,k) )
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! y direction
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f_rhs(i,j,k) = f_rhs(i,j,k) - eps/dY/cof * ( &
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(fh(i,j-2,k)+fh(i,j+2,k)) &
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- F4 * (fh(i,j-1,k)+fh(i,j+1,k)) &
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+ F6 * fh(i,j,k) )
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! z direction
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f_rhs(i,j,k) = f_rhs(i,j,k) - eps/dZ/cof * ( &
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(fh(i,j,k-2)+fh(i,j,k+2)) &
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- F4 * (fh(i,j,k-1)+fh(i,j,k+1)) &
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+ F6 * fh(i,j,k) )
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endif
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enddo
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enddo
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enddo
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return
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end subroutine kodis
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#elif (ghost_width == 3)
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! fourth order code
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!---------------------------------------------------------------------------------------------
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!usual type Kreiss-Oliger type numerical dissipation
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!We support cell center only
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! Note the notation D_+ and D_- [P240 of B. Gustafsson, H.-O. Kreiss, and J. Oliger, Time
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! Dependent Problems and Difference Methods (Wiley, New York, 1995).]
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! D_+ = (f(i+1) - f(i))/h
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! D_- = (f(i) - f(i-1))/h
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! then we have D_+D_- = D_-D_+
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! D_+^3D_-^3 = (D_+D_-)^3 =
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! f(i-3) - 6 f(i-2) + 15 f(i-1) - 20 f(i) + 15 f(i+1) - 6 f(i+2) + f(i+3)
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! -----------------------------------------------------------------------------
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! dx^6
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! this is for 4th order accurate finite difference scheme
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!---------------------------------------------------------------------------------------------
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subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
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implicit none
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! argument variables
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integer,intent(in) :: Symmetry
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integer,dimension(3),intent(in)::ex
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real*8, dimension(1:3), intent(in) :: SoA
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double precision,intent(in),dimension(ex(1))::X
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double precision,intent(in),dimension(ex(2))::Y
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double precision,intent(in),dimension(ex(3))::Z
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double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
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double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
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real*8,intent(in) :: eps
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! local variables
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real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3)) :: fh
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integer :: imin,jmin,kmin,imax,jmax,kmax
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integer :: i,j,k
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real*8 :: dX,dY,dZ
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real*8, parameter :: ONE=1.d0,SIX=6.d0,FIT=1.5d1,TWT=2.d1
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real*8,parameter::cof=6.4d1 ! 2^6
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integer, parameter :: NO_SYMM=0, OCTANT=2
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!rhs_i = rhs_i + eps/dx/cof*(f_i-3 - 6*f_i-2 + 15*f_i-1 - 20*f_i + 15*f_i+1 - 6*f_i+2 + f_i+3)
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dX = X(2)-X(1)
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dY = Y(2)-Y(1)
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dZ = Z(2)-Z(1)
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imax = ex(1)
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jmax = ex(2)
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kmax = ex(3)
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imin = 1
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jmin = 1
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kmin = 1
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if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
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if(Symmetry == OCTANT .and. dabs(X(1)) < dX) imin = -2
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if(Symmetry == OCTANT .and. dabs(Y(1)) < dY) jmin = -2
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call symmetry_bd(3,ex,f,fh,SoA)
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do k=1,ex(3)
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do j=1,ex(2)
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do i=1,ex(1)
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if(i-3 >= imin .and. i+3 <= imax .and. &
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j-3 >= jmin .and. j+3 <= jmax .and. &
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k-3 >= kmin .and. k+3 <= kmax) then
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#if 0
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! x direction
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f_rhs(i,j,k) = f_rhs(i,j,k) + eps/dX/cof * ( &
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(fh(i-3,j,k)+fh(i+3,j,k)) - &
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SIX*(fh(i-2,j,k)+fh(i+2,j,k)) + &
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FIT*(fh(i-1,j,k)+fh(i+1,j,k)) - &
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TWT* fh(i,j,k) )
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! y direction
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f_rhs(i,j,k) = f_rhs(i,j,k) + eps/dY/cof * ( &
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(fh(i,j-3,k)+fh(i,j+3,k)) - &
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SIX*(fh(i,j-2,k)+fh(i,j+2,k)) + &
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FIT*(fh(i,j-1,k)+fh(i,j+1,k)) - &
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TWT* fh(i,j,k) )
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! z direction
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f_rhs(i,j,k) = f_rhs(i,j,k) + eps/dZ/cof * ( &
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(fh(i,j,k-3)+fh(i,j,k+3)) - &
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SIX*(fh(i,j,k-2)+fh(i,j,k+2)) + &
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FIT*(fh(i,j,k-1)+fh(i,j,k+1)) - &
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TWT* fh(i,j,k) )
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#else
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! calculation order if important ?
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f_rhs(i,j,k) = f_rhs(i,j,k) + eps/cof *( ( &
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(fh(i-3,j,k)+fh(i+3,j,k)) - &
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SIX*(fh(i-2,j,k)+fh(i+2,j,k)) + &
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FIT*(fh(i-1,j,k)+fh(i+1,j,k)) - &
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TWT* fh(i,j,k) )/dX + &
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( &
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(fh(i,j-3,k)+fh(i,j+3,k)) - &
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SIX*(fh(i,j-2,k)+fh(i,j+2,k)) + &
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FIT*(fh(i,j-1,k)+fh(i,j+1,k)) - &
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TWT* fh(i,j,k) )/dY + &
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( &
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(fh(i,j,k-3)+fh(i,j,k+3)) - &
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SIX*(fh(i,j,k-2)+fh(i,j,k+2)) + &
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FIT*(fh(i,j,k-1)+fh(i,j,k+1)) - &
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TWT* fh(i,j,k) )/dZ )
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#endif
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endif
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enddo
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enddo
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enddo
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return
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end subroutine kodis
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#elif (ghost_width == 4)
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! sixth order code
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!------------------------------------------------------------------------------------------------------------------------------
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!usual type Kreiss-Oliger type numerical dissipation
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!We support cell center only
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! (D_+D_-)^4 =
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! f(i-4) - 8 f(i-3) + 28 f(i-2) - 56 f(i-1) + 70 f(i) - 56 f(i+1) + 28 f(i+2) - 8 f(i+3) + f(i+4)
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! ----------------------------------------------------------------------------------------------------------
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! dx^8
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!------------------------------------------------------------------------------------------------------------------------------
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! do not add dissipation near boundary
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subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
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implicit none
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! argument variables
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integer,intent(in) :: Symmetry
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integer,dimension(3),intent(in)::ex
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real*8, dimension(1:3), intent(in) :: SoA
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double precision,intent(in),dimension(ex(1))::X
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double precision,intent(in),dimension(ex(2))::Y
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double precision,intent(in),dimension(ex(3))::Z
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double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
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double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
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real*8,intent(in) :: eps
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!~~~~~~ other variables
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real*8 :: dX,dY,dZ
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real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3)) :: fh
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integer :: imin,jmin,kmin,imax,jmax,kmax
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integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
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real*8,parameter :: cof = 2.56d2 ! 2^8
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real*8, parameter :: F8=8.d0,F28=2.8d1,F56=5.6d1,F70=7.d1
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integer::i,j,k
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dX = X(2)-X(1)
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dY = Y(2)-Y(1)
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dZ = Z(2)-Z(1)
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imax = ex(1)
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jmax = ex(2)
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kmax = ex(3)
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imin = 1
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jmin = 1
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kmin = 1
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if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
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if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
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if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
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call symmetry_bd(4,ex,f,fh,SoA)
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! f(i-4) - 8 f(i-3) + 28 f(i-2) - 56 f(i-1) + 70 f(i) - 56 f(i+1) + 28 f(i+2) - 8 f(i+3) + f(i+4)
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! ----------------------------------------------------------------------------------------------------------
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! dx^8
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! note the sign (-1)^r-1, now r=4
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do k=1,ex(3)
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do j=1,ex(2)
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do i=1,ex(1)
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if(i>imin+3 .and. i < imax-3 .and. &
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j>jmin+3 .and. j < jmax-3 .and. &
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k>kmin+3 .and. k < kmax-3) then
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! x direction
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f_rhs(i,j,k) = f_rhs(i,j,k) - eps/dX/cof * ( &
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(fh(i-4,j,k)+fh(i+4,j,k)) &
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- F8 * (fh(i-3,j,k)+fh(i+3,j,k)) &
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+F28 * (fh(i-2,j,k)+fh(i+2,j,k)) &
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-F56 * (fh(i-1,j,k)+fh(i+1,j,k)) &
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+F70 * fh(i,j,k) )
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! y direction
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f_rhs(i,j,k) = f_rhs(i,j,k) - eps/dY/cof * ( &
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(fh(i,j-4,k)+fh(i,j+4,k)) &
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- F8 * (fh(i,j-3,k)+fh(i,j+3,k)) &
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+F28 * (fh(i,j-2,k)+fh(i,j+2,k)) &
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-F56 * (fh(i,j-1,k)+fh(i,j+1,k)) &
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+F70 * fh(i,j,k) )
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! z direction
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f_rhs(i,j,k) = f_rhs(i,j,k) - eps/dZ/cof * ( &
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(fh(i,j,k-4)+fh(i,j,k+4)) &
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- F8 * (fh(i,j,k-3)+fh(i,j,k+3)) &
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+F28 * (fh(i,j,k-2)+fh(i,j,k+2)) &
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-F56 * (fh(i,j,k-1)+fh(i,j,k+1)) &
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+F70 * fh(i,j,k) )
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endif
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enddo
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enddo
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enddo
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return
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end subroutine kodis
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#elif (ghost_width == 5)
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! eighth order code
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!------------------------------------------------------------------------------------------------------------------------------
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!usual type Kreiss-Oliger type numerical dissipation
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!We support cell center only
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! Note the notation D_+ and D_- [P240 of B. Gustafsson, H.-O. Kreiss, and J. Oliger, Time
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! Dependent Problems and Difference Methods (Wiley, New York, 1995).]
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! D_+ = (f(i+1) - f(i))/h
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! D_- = (f(i) - f(i-1))/h
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! then we have D_+D_- = D_-D_+ = (f(i+1) - 2f(i) + f(i-1))/h^2
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! for nth order accurate finite difference code, we need r =n/2+1
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! D_+^rD_-^r = (D_+D_-)^r
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! following the tradiation of PRD 77, 024027 (BB's calibration paper, Eq.(64),
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! correct some typo according to above book) :
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! + eps*(-1)^(r-1)*h^(2r-1)/2^(2r)*(D_+D_-)^r
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!
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!
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! this is for 8th order accurate finite difference scheme
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! (D_+D_-)^5 =
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! f(i-5) - 10 f(i-4) + 45 f(i-3) - 120 f(i-2) + 210 f(i-1) - 252 f(i) + 210 f(i+1) - 120 f(i+2) + 45 f(i+3) - 10 f(i+4) + f(i+5)
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! -------------------------------------------------------------------------------------------------------------------------------
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! dx^10
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!---------------------------------------------------------------------------------------------------------------------------------
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! do not add dissipation near boundary
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subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
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implicit none
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! argument variables
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integer,intent(in) :: Symmetry
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integer,dimension(3),intent(in)::ex
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real*8, dimension(1:3), intent(in) :: SoA
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double precision,intent(in),dimension(ex(1))::X
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double precision,intent(in),dimension(ex(2))::Y
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double precision,intent(in),dimension(ex(3))::Z
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double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
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double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
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real*8,intent(in) :: eps
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!~~~~~~ other variables
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real*8 :: dX,dY,dZ
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real*8,dimension(-4:ex(1),-4:ex(2),-4:ex(3)) :: fh
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integer :: imin,jmin,kmin,imax,jmax,kmax
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integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
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real*8,parameter :: cof = 1.024d3 ! 2^2r = 2^10
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real*8, parameter :: F10=1.d1,F45=4.5d1,F120=1.2d2,F210=2.1d2,F252=2.52d2
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integer::i,j,k
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dX = X(2)-X(1)
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dY = Y(2)-Y(1)
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dZ = Z(2)-Z(1)
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imax = ex(1)
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jmax = ex(2)
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kmax = ex(3)
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imin = 1
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jmin = 1
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kmin = 1
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if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -4
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if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -4
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if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -4
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call symmetry_bd(5,ex,f,fh,SoA)
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! f(i-5) - 10 f(i-4) + 45 f(i-3) - 120 f(i-2) + 210 f(i-1) - 252 f(i) + 210 f(i+1) - 120 f(i+2) + 45 f(i+3) - 10 f(i+4) + f(i+5)
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! -------------------------------------------------------------------------------------------------------------------------------
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! dx^10
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! note the sign (-1)^r-1, now r=5
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do k=1,ex(3)
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do j=1,ex(2)
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do i=1,ex(1)
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if(i>imin+4 .and. i < imax-4 .and. &
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j>jmin+4 .and. j < jmax-4 .and. &
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k>kmin+4 .and. k < kmax-4) then
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! x direction
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f_rhs(i,j,k) = f_rhs(i,j,k) + eps/dX/cof * ( &
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(fh(i-5,j,k)+fh(i+5,j,k)) &
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- F10 * (fh(i-4,j,k)+fh(i+4,j,k)) &
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+ F45 * (fh(i-3,j,k)+fh(i+3,j,k)) &
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- F120* (fh(i-2,j,k)+fh(i+2,j,k)) &
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+ F210* (fh(i-1,j,k)+fh(i+1,j,k)) &
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- F252 * fh(i,j,k) )
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! y direction
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f_rhs(i,j,k) = f_rhs(i,j,k) + eps/dY/cof * ( &
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(fh(i,j-5,k)+fh(i,j+5,k)) &
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- F10 * (fh(i,j-4,k)+fh(i,j+4,k)) &
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+ F45 * (fh(i,j-3,k)+fh(i,j+3,k)) &
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- F120* (fh(i,j-2,k)+fh(i,j+2,k)) &
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+ F210* (fh(i,j-1,k)+fh(i,j+1,k)) &
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- F252 * fh(i,j,k) )
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! z direction
|
|
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f_rhs(i,j,k) = f_rhs(i,j,k) + eps/dZ/cof * ( &
|
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(fh(i,j,k-5)+fh(i,j,k+5)) &
|
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- F10 * (fh(i,j,k-4)+fh(i,j,k+4)) &
|
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+ F45 * (fh(i,j,k-3)+fh(i,j,k+3)) &
|
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- F120* (fh(i,j,k-2)+fh(i,j,k+2)) &
|
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+ F210* (fh(i,j,k-1)+fh(i,j,k+1)) &
|
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- F252 * fh(i,j,k) )
|
|
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endif
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enddo
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enddo
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enddo
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return
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end subroutine kodis
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#endif
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