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gyacomo/src/numerics_mod.F90
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numerics_mod.F90
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!! MODULE NUMERICS
! The module numerics contains a set of routines that are called only once at
! the begining of a run. These routines do not need to be optimzed
MODULE numerics
USE basic
USE prec_const
USE grid
USE utility
implicit none
PUBLIC :: build_dnjs_table, evaluate_kernels, evaluate_EM_op
PUBLIC :: compute_lin_coeff
CONTAINS
!******************************************************************************!
!!!!!!! Build the Laguerre-Laguerre coupling coefficient table for nonlin
!******************************************************************************!
SUBROUTINE build_dnjs_table
USE array, Only : dnjs
USE coeff
IMPLICIT NONE
INTEGER :: in, ij, is, J
INTEGER :: n_, j_, s_
J = max(jmaxe,jmaxi)
DO in = 1,J+1 ! Nested dependent loops to make benefit from dnjs symmetry
n_ = in - 1
DO ij = in,J+1
j_ = ij - 1
DO is = ij,J+1
s_ = is - 1
dnjs(in,ij,is) = TO_DP(ALL2L(n_,j_,s_,0))
! By symmetry
dnjs(in,is,ij) = dnjs(in,ij,is)
dnjs(ij,in,is) = dnjs(in,ij,is)
dnjs(ij,is,in) = dnjs(in,ij,is)
dnjs(is,ij,in) = dnjs(in,ij,is)
dnjs(is,in,ij) = dnjs(in,ij,is)
ENDDO
ENDDO
ENDDO
END SUBROUTINE build_dnjs_table
!******************************************************************************!
!******************************************************************************!
!!!!!!! Evaluate the kernels once for all
!******************************************************************************!
SUBROUTINE evaluate_kernels
USE basic
USE array, Only : kernel_e, kernel_i, HF_phi_correction_operator
USE grid
USE model, ONLY : sigmae2_taue_o2, sigmai2_taui_o2, KIN_E
IMPLICIT NONE
INTEGER :: j_int
REAL(dp) :: j_dp, y_, factj
DO eo = 0,1
DO ikx = ikxs,ikxe
DO iky = ikys,ikye
DO iz = izgs,izge
!!!!! Electron kernels !!!!!
IF(KIN_E) THEN
DO ij = ijgs_e, ijge_e
j_int = jarray_e(ij)
j_dp = REAL(j_int,dp)
y_ = sigmae2_taue_o2 * kparray(iky,ikx,iz,eo)**2
IF(j_int .LE. 0) THEN
factj = 1._dp
kernel_e(ij,iky,ikx,iz,eo) = 0._dp
ELSE
factj = GAMMA(j_dp+1._dp)
kernel_e(ij,iky,ikx,iz,eo) = y_**j_int*EXP(-y_)/factj
ENDIF
ENDDO
IF (ijs_e .EQ. 1) &
kernel_e(ijgs_e,iky,ikx,iz,eo) = 0._dp
ENDIF
!!!!! Ion kernels !!!!!
DO ij = ijgs_i, ijge_i
j_int = jarray_i(ij)
j_dp = REAL(j_int,dp)
y_ = sigmai2_taui_o2 * kparray(iky,ikx,iz,eo)**2
IF(j_int .LT. 0) THEN
kernel_i(ij,iky,ikx,iz,eo) = 0._dp
ELSE
factj = GAMMA(j_dp+1._dp)
kernel_i(ij,iky,ikx,iz,eo) = y_**j_int*EXP(-y_)/factj
ENDIF
ENDDO
IF (ijs_i .EQ. 1) &
kernel_i(ijgs_i,iky,ikx,iz,eo) = 0._dp
ENDDO
ENDDO
ENDDO
ENDDO
!! Correction term for the evaluation of the heat flux
HF_phi_correction_operator(ikys:ikye,ikxs:ikxe,izs:ize) = &
2._dp * Kernel_i(1,ikys:ikye,ikxs:ikxe,izs:ize,0) &
-1._dp * Kernel_i(2,ikys:ikye,ikxs:ikxe,izs:ize,0)
DO ij = ijs_i, ije_i
j_int = jarray_i(ij)
j_dp = REAL(j_int,dp)
HF_phi_correction_operator(ikys:ikye,ikxs:ikxe,izs:ize) = HF_phi_correction_operator(ikys:ikye,ikxs:ikxe,izs:ize) &
- Kernel_i(ij,ikys:ikye,ikxs:ikxe,izs:ize,0) * (&
2._dp*(j_dp+1.5_dp) * Kernel_i(ij ,ikys:ikye,ikxs:ikxe,izs:ize,0) &
- (j_dp+1.0_dp) * Kernel_i(ij+1,ikys:ikye,ikxs:ikxe,izs:ize,0) &
- j_dp * Kernel_i(ij-1,ikys:ikye,ikxs:ikxe,izs:ize,0))
ENDDO
END SUBROUTINE evaluate_kernels
!******************************************************************************!
!******************************************************************************!
SUBROUTINE evaluate_EM_op
IMPLICIT NONE
CALL evaluate_poisson_op
CALL evaluate_ampere_op
END SUBROUTINE evaluate_EM_op
!!!!!!! Evaluate inverse polarisation operator for Poisson equation
!******************************************************************************!
SUBROUTINE evaluate_poisson_op
USE basic
USE array, Only : kernel_e, kernel_i, inv_poisson_op, inv_pol_ion
USE grid
USE model, ONLY : qe2_taue, qi2_taui, KIN_E
IMPLICIT NONE
REAL(dp) :: pol_i, pol_e ! (Z_a^2/tau_a (1-sum_n kernel_na^2))
INTEGER :: ini,ine
! This term has no staggered grid dependence. It is evalued for the
! even z grid since poisson uses p=0 moments and phi only.
kxloop: DO ikx = ikxs,ikxe
kyloop: DO iky = ikys,ikye
zloop: DO iz = izs,ize
IF( (kxarray(ikx).EQ.0._dp) .AND. (kyarray(iky).EQ.0._dp) ) THEN
inv_poisson_op(iky, ikx, iz) = 0._dp
ELSE
!!!!!!!!!!!!!!!!! Ion contribution
! loop over n only if the max polynomial degree
pol_i = 0._dp
DO ini=1,jmaxi+1
pol_i = pol_i + qi2_taui*kernel_i(ini,iky,ikx,iz,0)**2 ! ... sum recursively ...
END DO
!!!!!!!!!!!!! Electron contribution
pol_e = 0._dp
IF (KIN_E) THEN ! Kinetic model
! loop over n only if the max polynomial degree
DO ine=1,jmaxe+1 ! ine = n+1
pol_e = pol_e + qe2_taue*kernel_e(ine,iky,ikx,iz,0)**2 ! ... sum recursively ...
END DO
ELSE ! Adiabatic model
pol_e = qe2_taue - 1._dp
ENDIF
inv_poisson_op(iky, ikx, iz) = 1._dp/(qe2_taue + qi2_taui - pol_i - pol_e)
inv_pol_ion (iky, ikx, iz) = 1._dp/(qi2_taui - pol_i)
ENDIF
END DO zloop
END DO kyloop
END DO kxloop
END SUBROUTINE evaluate_poisson_op
!******************************************************************************!
!******************************************************************************!
!!!!!!! Evaluate inverse polarisation operator for Poisson equation
!******************************************************************************!
SUBROUTINE evaluate_ampere_op
USE basic
USE array, Only : kernel_e, kernel_i, inv_ampere_op
USE grid
USE model, ONLY : q_e, q_i, beta, sigma_e, sigma_i
USE geometry, ONLY : hatB
IMPLICIT NONE
REAL(dp) :: pol_i, pol_e, kperp2 ! (Z_a^2/tau_a (1-sum_n kernel_na^2))
INTEGER :: ini,ine
! We do not solve Ampere if beta = 0 to spare waste of ressources
IF(SOLVE_AMPERE) THEN
! This term has no staggered grid dependence. It is evalued for the
! even z grid since poisson uses p=0 moments and phi only.
kxloop: DO ikx = ikxs,ikxe
kyloop: DO iky = ikys,ikye
zloop: DO iz = izs,ize
kperp2 = kparray(iky,ikx,iz,0)**2
IF( (kxarray(ikx).EQ.0._dp) .AND. (kyarray(iky).EQ.0._dp) ) THEN
inv_ampere_op(iky, ikx, iz) = 0._dp
ELSE
!!!!!!!!!!!!!!!!! Ion contribution
pol_i = 0._dp
! loop over n only up to the max polynomial degree
DO ini=1,jmaxi+1
pol_i = pol_i + kernel_i(ini,iky,ikx,iz,0)**2 ! ... sum recursively ...
END DO
pol_i = q_i**2/(sigma_i**2) * pol_i
!!!!!!!!!!!!! Electron contribution
pol_e = 0._dp
! loop over n only up to the max polynomial degree
DO ine=1,jmaxe+1 ! ine = n+1
pol_e = pol_e + kernel_e(ine,iky,ikx,iz,0)**2 ! ... sum recursively ...
END DO
pol_e = q_e**2/(sigma_e**2) * pol_e
inv_ampere_op(iky, ikx, iz) = 1._dp/(2._dp*kperp2*hatB(iz,0)**2 + beta*(pol_i + pol_e))
ENDIF
END DO zloop
END DO kyloop
END DO kxloop
ENDIF
END SUBROUTINE evaluate_ampere_op
!******************************************************************************!
SUBROUTINE compute_lin_coeff
USE array
USE model, ONLY: taue_qe, taui_qi, &
k_Te, k_Ti, k_Ne, k_Ni, CurvB, GradB, KIN_E,&
tau_e, tau_i, sigma_e, sigma_i
USE prec_const
USE grid, ONLY: parray_e, parray_i, jarray_e, jarray_i, &
ip,ij, ips_e,ipe_e, ips_i,ipe_i, ijs_e,ije_e, ijs_i,ije_i
IMPLICIT NONE
INTEGER :: p_int, j_int ! polynom. degrees
REAL(dp) :: p_dp, j_dp
!! Electrons linear coefficients for moment RHS !!!!!!!!!!
IF(KIN_E)THEN
DO ip = ips_e, ipe_e
p_int= parray_e(ip) ! Hermite degree
p_dp = REAL(p_int,dp) ! REAL of Hermite degree
DO ij = ijs_e, ije_e
j_int= jarray_e(ij) ! Laguerre degree
j_dp = REAL(j_int,dp) ! REAL of Laguerre degree
! All Napj terms
xnepj(ip,ij) = taue_qe*(CurvB*(2._dp*p_dp + 1._dp) &
+GradB*(2._dp*j_dp + 1._dp))
! Mirror force terms
ynepp1j (ip,ij) = -SQRT(tau_e)/sigma_e * (j_dp+1)*SQRT(p_dp+1._dp)
ynepm1j (ip,ij) = -SQRT(tau_e)/sigma_e * (j_dp+1)*SQRT(p_dp)
ynepp1jm1(ip,ij) = +SQRT(tau_e)/sigma_e * j_dp*SQRT(p_dp+1._dp)
ynepm1jm1(ip,ij) = +SQRT(tau_e)/sigma_e * j_dp*SQRT(p_dp)
zNepm1j (ip,ij) = +SQRT(tau_e)/sigma_e * (2._dp*j_dp+1_dp)*SQRT(p_dp)
zNepm1jp1(ip,ij) = -SQRT(tau_e)/sigma_e * (j_dp+1_dp)*SQRT(p_dp)
zNepm1jm1(ip,ij) = -SQRT(tau_e)/sigma_e * j_dp*SQRT(p_dp)
ENDDO
ENDDO
DO ip = ips_e, ipe_e
p_int= parray_e(ip) ! Hermite degree
p_dp = REAL(p_int,dp) ! REAL of Hermite degree
! Landau damping coefficients (ddz napj term)
xnepp1j(ip) = SQRT(tau_e)/sigma_e * SQRT(p_dp + 1_dp)
xnepm1j(ip) = SQRT(tau_e)/sigma_e * SQRT(p_dp)
! Magnetic curvature term
xnepp2j(ip) = taue_qe * CurvB * SQRT((p_dp + 1._dp) * (p_dp + 2._dp))
xnepm2j(ip) = taue_qe * CurvB * SQRT(p_dp * (p_dp - 1._dp))
ENDDO
DO ij = ijs_e, ije_e
j_int= jarray_e(ij) ! Laguerre degree
j_dp = REAL(j_int,dp) ! REAL of Laguerre degree
! Magnetic gradient term
xnepjp1(ij) = -taue_qe * GradB * (j_dp + 1._dp)
xnepjm1(ij) = -taue_qe * GradB * j_dp
ENDDO
ENDIF
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!! Ions linear coefficients for moment RHS !!!!!!!!!!
DO ip = ips_i, ipe_i
p_int= parray_i(ip) ! Hermite degree
p_dp = REAL(p_int,dp) ! REAL of Hermite degree
DO ij = ijs_i, ije_i
j_int= jarray_i(ij) ! Laguerre degree
j_dp = REAL(j_int,dp) ! REAL of Laguerre degree
! All Napj terms
xnipj(ip,ij) = taui_qi*(CurvB*(2._dp*p_dp + 1._dp) &
+GradB*(2._dp*j_dp + 1._dp))
! Mirror force terms
ynipp1j (ip,ij) = -SQRT(tau_i)/sigma_i* (j_dp+1)*SQRT(p_dp+1._dp)
ynipm1j (ip,ij) = -SQRT(tau_i)/sigma_i* (j_dp+1)*SQRT(p_dp)
ynipp1jm1(ip,ij) = +SQRT(tau_i)/sigma_i* j_dp*SQRT(p_dp+1._dp)
ynipm1jm1(ip,ij) = +SQRT(tau_i)/sigma_i* j_dp*SQRT(p_dp)
! Trapping terms
zNipm1j (ip,ij) = +SQRT(tau_i)/sigma_i* (2._dp*j_dp+1_dp)*SQRT(p_dp)
zNipm1jp1(ip,ij) = -SQRT(tau_i)/sigma_i* (j_dp+1_dp)*SQRT(p_dp)
zNipm1jm1(ip,ij) = -SQRT(tau_i)/sigma_i* j_dp*SQRT(p_dp)
ENDDO
ENDDO
DO ip = ips_i, ipe_i
p_int= parray_i(ip) ! Hermite degree
p_dp = REAL(p_int,dp) ! REAL of Hermite degree
! Landau damping coefficients (ddz napj term)
xnipp1j(ip) = SQRT(tau_i)/sigma_i * SQRT(p_dp + 1._dp)
xnipm1j(ip) = SQRT(tau_i)/sigma_i * SQRT(p_dp)
! Magnetic curvature term
xnipp2j(ip) = taui_qi * CurvB * SQRT((p_dp + 1._dp) * (p_dp + 2._dp))
xnipm2j(ip) = taui_qi * CurvB * SQRT(p_dp * (p_dp - 1._dp))
ENDDO
DO ij = ijs_i, ije_i
j_int= jarray_i(ij) ! Laguerre degree
j_dp = REAL(j_int,dp) ! REAL of Laguerre degree
! Magnetic gradient term
xnipjp1(ij) = -taui_qi * GradB * (j_dp + 1._dp)
xnipjm1(ij) = -taui_qi * GradB * j_dp
ENDDO
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!! ES linear coefficients for moment RHS !!!!!!!!!!
IF (KIN_E) THEN
DO ip = ips_e, ipe_e
p_int= parray_e(ip) ! Hermite degree
DO ij = ijs_e, ije_e
j_int= jarray_e(ij) ! REALof Laguerre degree
j_dp = REAL(j_int,dp) ! REALof Laguerre degree
!! Electrostatic potential pj terms
IF (p_int .EQ. 0) THEN ! kronecker p0
xphij_e(ip,ij) = +k_Ne+ 2.*j_dp*k_Te
xphijp1_e(ip,ij) = -k_Te*(j_dp+1._dp)
xphijm1_e(ip,ij) = -k_Te* j_dp
ELSE IF (p_int .EQ. 2) THEN ! kronecker p2
xphij_e(ip,ij) = +k_Te/SQRT2
xphijp1_e(ip,ij) = 0._dp; xphijm1_e(ip,ij) = 0._dp;
ELSE
xphij_e(ip,ij) = 0._dp; xphijp1_e(ip,ij) = 0._dp
xphijm1_e(ip,ij) = 0._dp;
ENDIF
ENDDO
ENDDO
ENDIF
DO ip = ips_i, ipe_i
p_int= parray_i(ip) ! Hermite degree
DO ij = ijs_i, ije_i
j_int= jarray_i(ij) ! REALof Laguerre degree
j_dp = REAL(j_int,dp) ! REALof Laguerre degree
!! Electrostatic potential pj terms
IF (p_int .EQ. 0) THEN ! kronecker p0
xphij_i(ip,ij) = +k_Ni + 2._dp*j_dp*k_Ti
xphijp1_i(ip,ij) = -k_Ti*(j_dp+1._dp)
xphijm1_i(ip,ij) = -k_Ti* j_dp
ELSE IF (p_int .EQ. 2) THEN ! kronecker p2
xphij_i(ip,ij) = +k_Ti/SQRT2
xphijp1_i(ip,ij) = 0._dp; xphijm1_i(ip,ij) = 0._dp;
ELSE
xphij_i(ip,ij) = 0._dp; xphijp1_i(ip,ij) = 0._dp
xphijm1_i(ip,ij) = 0._dp;
ENDIF
ENDDO
ENDDO
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!! EM linear coefficients for moment RHS !!!!!!!!!!
IF (KIN_E) THEN
DO ip = ips_e, ipe_e
p_int= parray_e(ip) ! Hermite degree
DO ij = ijs_e, ije_e
j_int= jarray_e(ij) ! REALof Laguerre degree
j_dp = REAL(j_int,dp) ! REALof Laguerre degree
!! Electrostatic potential pj terms
IF (p_int .EQ. 1) THEN ! kronecker p1
xpsij_e (ip,ij) = +(k_Ne + (2._dp*j_dp+1._dp)*k_Te)* SQRT(tau_e)/sigma_e
xpsijp1_e(ip,ij) = - k_Te*(j_dp+1._dp) * SQRT(tau_e)/sigma_e
xpsijm1_e(ip,ij) = - k_Te* j_dp * SQRT(tau_e)/sigma_e
ELSE IF (p_int .EQ. 3) THEN ! kronecker p3
xpsij_e (ip,ij) = + k_Te*SQRT3/SQRT2 * SQRT(tau_e)/sigma_e
xpsijp1_e(ip,ij) = 0._dp; xpsijm1_e(ip,ij) = 0._dp;
ELSE
xpsij_e (ip,ij) = 0._dp; xpsijp1_e(ip,ij) = 0._dp
xpsijm1_e(ip,ij) = 0._dp;
ENDIF
ENDDO
ENDDO
ENDIF
DO ip = ips_i, ipe_i
p_int= parray_i(ip) ! Hermite degree
DO ij = ijs_i, ije_i
j_int= jarray_i(ij) ! REALof Laguerre degree
j_dp = REAL(j_int,dp) ! REALof Laguerre degree
!! Electrostatic potential pj terms
IF (p_int .EQ. 1) THEN ! kronecker p1
xpsij_i (ip,ij) = +(k_Ni + (2._dp*j_dp+1._dp)*k_Ti)* SQRT(tau_i)/sigma_i
xpsijp1_i(ip,ij) = - k_Ti*(j_dp+1._dp) * SQRT(tau_i)/sigma_i
xpsijm1_i(ip,ij) = - k_Ti* j_dp * SQRT(tau_i)/sigma_i
ELSE IF (p_int .EQ. 3) THEN ! kronecker p3
xpsij_i (ip,ij) = + k_Ti*SQRT3/SQRT2 * SQRT(tau_i)/sigma_i
xpsijp1_i(ip,ij) = 0._dp; xpsijm1_i(ip,ij) = 0._dp;
ELSE
xpsij_i (ip,ij) = 0._dp; xpsijp1_i(ip,ij) = 0._dp
xpsijm1_i(ip,ij) = 0._dp;
ENDIF
ENDDO
ENDDO
END SUBROUTINE compute_lin_coeff
END MODULE numerics
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