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gyacomo/src/geometry_mod.F90
5e48668823b5shear_version

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geometry_mod.F90
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module geometry
! computes geometrical quantities
! Adapted from B.J.Frei MOLIX code (2021)
use prec_const
use model
use grid
use array
use fields
use basic
use calculus, ONLY: simpson_rule_z
implicit none
public
COMPLEX(dp), PROTECTED :: iInt_Jacobian
contains
subroutine eval_magnetic_geometry
! evalute metrix, elementwo_third_kpmaxts, jacobian and gradient
implicit none
REAL(dp) :: kx,ky
COMPLEX(dp), DIMENSION(izgs:izge) :: integrant
INTEGER :: fid
!
IF( (Ny .EQ. 1) .AND. (Nz .EQ. 1)) THEN !1D perp linear run
IF( my_id .eq. 0 ) WRITE(*,*) '1D perpendicular geometry'
call eval_1D_geometry
ELSE
IF( my_id .eq. 0 ) WRITE(*,*) 's-alpha-B geometry'
call eval_salphaB_geometry
ENDIF
!
! Evaluate perpendicular wavenumber
! k_\perp^2 = g^{xx} k_x^2 + 2 g^{xy}k_x k_y + k_y^2 g^{yy}
! normalized to rhos_
DO eo = 0,1
DO iky = ikys, ikye
ky = kyarray(iky)
DO ikx = ikxs, ikxe
kx = kxarray(ikx)
DO iz = izgs,izge
kparray(ikx, iky, iz, eo) = &
SQRT( gxx(iz,eo)*kx**2 + 2._dp*gxy(iz,eo)*kx*ky + gyy(iz,eo)*ky**2)/hatB(iz,eo)
! there is a factor 1/B from the normalization; important to match GENE
ENDDO
ENDDO
ENDDO
ENDDO
two_third_kpmax = 2._dp/3._dp * MAXVAL(kparray)
!
! Compute the inverse z integrated Jacobian (useful for flux averaging)
integrant = Jacobian(izgs:izge,0) ! Convert into complex array
CALL simpson_rule_z(integrant,iInt_Jacobian)
iInt_Jacobian = 1._dp/iInt_Jacobian ! reverse it
END SUBROUTINE eval_magnetic_geometry
!
!--------------------------------------------------------------------------------
!
subroutine eval_salphaB_geometry
! evaluate s-alpha geometry model
implicit none
REAL(dp) :: z, kx, ky, alpha_MHD
alpha_MHD = 0._dp
parity: DO eo = 0,1
zloop: DO iz = izgs,izge
z = zarray(iz,eo)
! metric
gxx(iz,eo) = 1._dp
gxy(iz,eo) = shear*z - alpha_MHD*SIN(z)
gxz(iz,eo) = 0._dp
gyy(iz,eo) = 1._dp + (shear*z - alpha_MHD*SIN(z))**2
gyz(iz,eo) = 1._dp/(eps + EPSILON(eps)) !avoid 1/0 in Zpinch config
gzz(iz,eo) = 0._dp
dxdR(iz,eo)= COS(z)
dxdZ(iz,eo)= SIN(z)
! Relative strengh of radius
hatR(iz,eo) = 1._dp + eps*COS(z)
hatZ(iz,eo) = 1._dp + eps*SIN(z)
! toroidal coordinates
Rc (iz,eo) = hatR(iz,eo)
phic(iz,eo) = z
Zc (iz,eo) = hatZ(iz,eo)
! Jacobian
Jacobian(iz,eo) = q0*hatR(iz,eo)
! Relative strengh of modulus of B
hatB(iz,eo) = 1._dp / hatR(iz,eo)
! Derivative of the magnetic field strenght
gradxB(iz,eo) = -COS(z) ! Gene put a factor hatB^2 or 1/hatR^2 in this
gradyB(iz,eo) = 0._dp
gradzB(iz,eo) = eps * SIN(z) / hatR(iz,eo) ! Gene put a factor hatB or 1/hatR in this
! Curvature operator
DO iky = ikys, ikye
ky = kyarray(iky)
DO ikx= ikxs, ikxe
kx = kxarray(ikx)
Ckxky(ikx, iky, iz,eo) = (-SIN(z)*kx - (COS(z) + (shear*z - alpha_MHD*SIN(z))* SIN(z))*ky) * hatB(iz,eo) ! .. multiply by hatB to cancel the 1/ hatB factor in moments_eqs_rhs.f90 routine
ENDDO
ENDDO
! coefficient in the front of parallel derivative
gradz_coeff(iz,eo) = 1._dp / Jacobian(iz,eo) / hatB(iz,eo)
ENDDO zloop
ENDDO parity
END SUBROUTINE eval_salphaB_geometry
!
!--------------------------------------------------------------------------------
!
subroutine eval_1D_geometry
! evaluate 1D perp geometry model
implicit none
REAL(dp) :: z, kx, ky
parity: DO eo = 0,1
zloop: DO iz = izs,ize
z = zarray(iz,eo)
! metric
gxx(iz,eo) = 1._dp
gxy(iz,eo) = 0._dp
gyy(iz,eo) = 1._dp
! Relative strengh of radius
hatR(iz,eo) = 1._dp
! Jacobian
Jacobian(iz,eo) = 1._dp
! Relative strengh of modulus of B
hatB(iz,eo) = 1._dp
! Curvature operator
DO iky = ikys, ikye
ky = kyarray(iky)
DO ikx= ikxs, ikxe
kx = kxarray(ikx)
Ckxky(ikx, iky, iz,eo) = -kx ! .. multiply by hatB to cancel the 1/ hatB factor in moments_eqs_rhs.f90 routine
ENDDO
ENDDO
! coefficient in the front of parallel derivative
gradz_coeff(iz,eo) = 1._dp
ENDDO zloop
ENDDO parity
END SUBROUTINE eval_1D_geometry
!
!--------------------------------------------------------------------------------
!
end module geometry
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