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gyacomo/src/geometry_mod.F90
789906ab465ehalf_kx_plane

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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
PRIVATE
! Geometry parameters
CHARACTER(len=16), &
PUBLIC, PROTECTED :: geom
REAL(dp), PUBLIC, PROTECTED :: q0 = 1.4_dp ! safety factor
REAL(dp), PUBLIC, PROTECTED :: shear = 0._dp ! magnetic field shear
REAL(dp), PUBLIC, PROTECTED :: eps = 0.18_dp ! inverse aspect ratio
! Geometrical operators
! Curvature
REAL(dp), PUBLIC, DIMENSION(:,:,:,:), ALLOCATABLE :: Ckxky ! dimensions: kx, ky, z, odd/even p
! Jacobian
REAL(dp), PUBLIC, DIMENSION(:,:), ALLOCATABLE :: Jacobian ! dimensions: z, odd/even p
COMPLEX(dp), PUBLIC, PROTECTED :: iInt_Jacobian ! Inverse integrated Jacobian
! Metric
REAL(dp), PUBLIC, DIMENSION(:,:), ALLOCATABLE :: gxx, gxy, gxz, gyy, gyz, gzz ! dimensions: z, odd/even p
REAL(dp), PUBLIC, DIMENSION(:,:), ALLOCATABLE :: dxdr, dxdZ, Rc, phic, Zc
! derivatives of magnetic field strength
REAL(dp), PUBLIC, DIMENSION(:,:), ALLOCATABLE :: gradxB, gradyB, gradzB
! Relative magnetic field strength
REAL(dp), PUBLIC, DIMENSION(:,:), ALLOCATABLE :: hatB
! Relative strength of major radius
REAL(dp), PUBLIC, DIMENSION(:,:), ALLOCATABLE :: hatR, hatZ
! Some geometrical coefficients
REAL(dp), PUBLIC, DIMENSION(:,:) , ALLOCATABLE :: gradz_coeff ! 1 / [ J_{xyz} \hat{B} ]
! Functions
PUBLIC :: geometry_readinputs, geometry_outputinputs, eval_magnetic_geometry
CONTAINS
SUBROUTINE geometry_readinputs
! Read the input parameters
IMPLICIT NONE
NAMELIST /GEOMETRY/ geom, q0, shear, eps
READ(lu_in,geometry)
END SUBROUTINE geometry_readinputs
subroutine eval_magnetic_geometry
! evalute metrix, elementwo_third_kpmaxts, jacobian and gradient
implicit none
REAL(dp) :: kx,ky
COMPLEX(dp), DIMENSION(izs:ize) :: integrant
INTEGER :: fid
! Allocate arrays
CALL geometry_allocate_mem
!
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
SELECT CASE(geom)
CASE('s-alpha')
IF( my_id .eq. 0 ) WRITE(*,*) 's-alpha-B geometry'
call eval_salphaB_geometry
CASE('Z-pinch')
IF( my_id .eq. 0 ) WRITE(*,*) 'Z-pinch geometry'
call eval_zpinch_geometry
CASE DEFAULT
ERROR STOP 'Error stop: geometry not recognized!!'
END SELECT
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(izs:ize,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_zpinch_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) = 0._dp
gxz(iz,eo) = 0._dp
gyy(iz,eo) = 1._dp
gyz(iz,eo) = 0._dp
gzz(iz,eo) = 1._dp
dxdR(iz,eo)= COS(z)
dxdZ(iz,eo)= SIN(z)
! Relative strengh of radius
hatR(iz,eo) = 1._dp
hatZ(iz,eo) = 1._dp
! toroidal coordinates
Rc (iz,eo) = hatR(iz,eo)
phic(iz,eo) = z
Zc (iz,eo) = hatZ(iz,eo)
! Jacobian
Jacobian(iz,eo) = 1._dp
! Relative strengh of modulus of B
hatB(iz,eo) = 1._dp
! Derivative of the magnetic field strenght
gradxB(iz,eo) = 0._dp ! Gene put a factor hatB^2 or 1/hatR^2 in this
gradyB(iz,eo) = 0._dp
gradzB(iz,eo) = 0._dp ! 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) = - 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_zpinch_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
!
!--------------------------------------------------------------------------------
!
SUBROUTINE geometry_allocate_mem
! Curvature and geometry
CALL allocate_array( Ckxky, ikxs,ikxe, ikys,ikye,izgs,izge,0,1)
CALL allocate_array( Jacobian,izgs,izge, 0,1)
CALL allocate_array( gxx,izgs,izge, 0,1)
CALL allocate_array( gxy,izgs,izge, 0,1)
CALL allocate_array( gxz,izgs,izge, 0,1)
CALL allocate_array( gyy,izgs,izge, 0,1)
CALL allocate_array( gyz,izgs,izge, 0,1)
CALL allocate_array( gzz,izgs,izge, 0,1)
CALL allocate_array( gradxB,izgs,izge, 0,1)
CALL allocate_array( gradyB,izgs,izge, 0,1)
CALL allocate_array( gradzB,izgs,izge, 0,1)
CALL allocate_array( hatB,izgs,izge, 0,1)
CALL allocate_array( hatR,izgs,izge, 0,1)
CALL allocate_array( hatZ,izgs,izge, 0,1)
CALL allocate_array( Rc,izgs,izge, 0,1)
CALL allocate_array( phic,izgs,izge, 0,1)
CALL allocate_array( Zc,izgs,izge, 0,1)
CALL allocate_array( dxdR,izgs,izge, 0,1)
CALL allocate_array( dxdZ,izgs,izge, 0,1)
call allocate_array(gradz_coeff,izgs,izge, 0,1)
CALL allocate_array( kparray, ikxs,ikxe, ikys,ikye,izgs,izge,0,1)
END SUBROUTINE geometry_allocate_mem
SUBROUTINE geometry_outputinputs(fidres, str)
! Write the input parameters to the results_xx.h5 file
USE futils, ONLY: attach
USE prec_const
IMPLICIT NONE
INTEGER, INTENT(in) :: fidres
CHARACTER(len=256), INTENT(in) :: str
CALL attach(fidres, TRIM(str),"geometry", geom)
CALL attach(fidres, TRIM(str), "q0", q0)
CALL attach(fidres, TRIM(str), "shear", shear)
CALL attach(fidres, TRIM(str), "eps", eps)
END SUBROUTINE geometry_outputinputs
end module geometry
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