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Commit 4516e5c7 authored by Antoine Cyril David Hoffmann's avatar Antoine Cyril David Hoffmann
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Dougherty collision operator

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src/moments_eq_rhs.F90
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SUBROUTINE moments_eq_rhs SUBROUTINE moments_eq_rhs
USE basic USE basic
USE time_integration USE time_integration
...@@ -12,18 +12,19 @@ SUBROUTINE moments_eq_rhs ...@@ -12,18 +12,19 @@ SUBROUTINE moments_eq_rhs
INTEGER :: ip,ij, ikr,ikz ! loops indices INTEGER :: ip,ij, ikr,ikz ! loops indices
REAL(dp) :: ip_dp, ij_dp REAL(dp) :: ip_dp, ij_dp
REAL(dp) :: kr, kz, kperp2 REAL(dp) :: kr, kz, kperp2
REAL(dp) :: taue_qe_etaB, taui_qi_etaB REAL(dp) :: taue_qe_etaB, taui_qi_etaB
REAL(dp) :: kernelj, kerneljp1, kerneljm1, b_e2, b_i2 ! Kernel functions and variable REAL(dp) :: kernelj, kerneljp1, kerneljm1, b_e2, b_i2 ! Kernel functions and variable
REAL(dp) :: factj, xb_e2, xb_i2 ! Auxiliary variables REAL(dp) :: factj, xb_e2, xb_i2 ! Auxiliary variables
REAL(dp) :: xNapj, xNapp2j, xNapm2j, xNapjp1, xNapjm1 ! factors depending on the pj loop REAL(dp) :: xNapj, xNapp2j, xNapm2j, xNapjp1, xNapjm1 ! factors depending on the pj loop
REAL(dp) :: xphij, xphijp1, xphijm1, xColl REAL(dp) :: xphij, xphijp1, xphijm1, xColl
COMPLEX(dp) :: TNapj, TNapp2j, TNapm2j, TNapjp1, TNapjm1, Tphi, TColl ! terms of the rhs COMPLEX(dp) :: TNapj, TNapp2j, TNapm2j, TNapjp1, TNapjm1, Tphi
COMPLEX(dp) :: TColl, TColl20, TColl01, TColl10 ! terms of the rhs
!Precompute species dependant factors !Precompute species dependant factors
taue_qe_etaB = tau_e/q_e * eta_B taue_qe_etaB = tau_e/q_e * eta_B
xb_e2 = sigma_e**2 * tau_e!/2.0 ! species dependant factor of the Kernel, squared xb_e2 = sigma_e**2 * tau_e!/2.0 ! species dependant factor of the Kernel, squared
taui_qi_etaB = tau_i/q_i * eta_B taui_qi_etaB = tau_i/q_i * eta_B
xb_i2 = sigma_i**2 * tau_i!/2.0 ! species dependant factor of the Kernel, squared xb_i2 = sigma_i**2 * tau_i!/2.0 ! species dependant factor of the Kernel, squared
!!!!!!!!! Electrons moments RHS !!!!!!!!! !!!!!!!!! Electrons moments RHS !!!!!!!!!
...@@ -65,8 +66,23 @@ SUBROUTINE moments_eq_rhs ...@@ -65,8 +66,23 @@ SUBROUTINE moments_eq_rhs
! N_e^{pj} multiplicator ! N_e^{pj} multiplicator
xNapj = -taue_qe_etaB * 2.*(ip_dp + ij_dp + 1.) xNapj = -taue_qe_etaB * 2.*(ip_dp + ij_dp + 1.)
! first part of collision operator (Lenard-Bernstein) ! Collision operator (DK Lenard-Bernstein basis)
xColl = -(ip_dp + 2.*ij_dp) xColl = ip_dp + 2.*ij_dp
! ... adding Dougherty terms
IF ( (ip .EQ. 1) .AND. (ij .EQ. 2) ) THEN ! kronecker p0 * j1
TColl01 = 2.0/3.0*(SQRT2*moments_e(3,1,ikr,ikz,updatetlevel)&
- 2.0*moments_e(1,2,ikr,ikz,updatetlevel))
TColl20 = 0.0; TColl10 = 0.0;
ELSEIF ( (ip .EQ. 3) .AND. (ij .EQ. 1) ) THEN ! kronecker p2 * j0
TColl20 = -SQRT2/3.0*(SQRT2*moments_e(3,1,ikr,ikz,updatetlevel)&
- 2.0*moments_e(1,2,ikr,ikz,updatetlevel))
TColl10 = 0.0; TColl01 = 0.0;
ELSEIF ( (ip .EQ. 2) .AND. (ij .EQ. 1) ) THEN ! kronecker p1 * j0
TColl10 = moments_e(2,1,ikr,ikz,updatetlevel)
TColl20 = 0.0; TColl01 = 0.0;
ELSE
TColl10 = 0.0; TColl20 = 0.0; TColl01 = 0.0;
ENDIF
! phi multiplicator for different kernel numbers ! phi multiplicator for different kernel numbers
IF (ip .EQ. 1) THEN !(kronecker delta_p^0) IF (ip .EQ. 1) THEN !(kronecker delta_p^0)
...@@ -76,16 +92,16 @@ SUBROUTINE moments_eq_rhs ...@@ -76,16 +92,16 @@ SUBROUTINE moments_eq_rhs
factj = REAL(Factorial(ij-1),dp) factj = REAL(Factorial(ij-1),dp)
ELSE IF (ip .EQ. 3) THEN !(kronecker delta_p^2) ELSE IF (ip .EQ. 3) THEN !(kronecker delta_p^2)
xphij = (eta_T/SQRT2 - SQRT2*eta_B) xphij = (eta_T/SQRT2 - SQRT2*eta_B)
factj = REAL(Factorial(ij-1),dp) factj = REAL(Factorial(ij-1),dp)
ELSE ELSE
xphij = 0.; xphijp1 = 0.; xphijm1 = 0. xphij = 0.; xphijp1 = 0.; xphijm1 = 0.
factj = 1 factj = 1
ENDIF ENDIF
!write(*,*) '(ip,ij) = (', ip,',', ij,')' !write(*,*) '(ip,ij) = (', ip,',', ij,')'
! Loop on kspace ! Loop on kspace
krloope : DO ikr = ikrs,ikre krloope : DO ikr = ikrs,ikre
kzloope : DO ikz = ikzs,ikze kzloope : DO ikz = ikzs,ikze
kr = krarray(ikr) ! Poloidal wavevector kr = krarray(ikr) ! Poloidal wavevector
kz = kzarray(ikz) ! Toroidal wavevector kz = kzarray(ikz) ! Toroidal wavevector
...@@ -94,25 +110,25 @@ SUBROUTINE moments_eq_rhs ...@@ -94,25 +110,25 @@ SUBROUTINE moments_eq_rhs
!! Compute moments and mixing terms !! Compute moments and mixing terms
! term propto N_e^{p,j} ! term propto N_e^{p,j}
TNapj = moments_e(ip,ij,ikr,ikz,updatetlevel) * xNapj TNapj = moments_e(ip,ij,ikr,ikz,updatetlevel) * xNapj
! term propto N_e^{p+2,j} ! term propto N_e^{p+2,j}
IF (ip+2 .LE. ipe_e) THEN IF (ip+2 .LE. ipe_e) THEN
TNapp2j = moments_e(ip+2,ij,ikr,ikz,updatetlevel) * xNapp2j TNapp2j = moments_e(ip+2,ij,ikr,ikz,updatetlevel) * xNapp2j
ELSE ELSE
TNapp2j = 0. TNapp2j = 0.
ENDIF ENDIF
! term propto N_e^{p-2,j} ! term propto N_e^{p-2,j}
IF (ip-2 .GE. ips_e) THEN IF (ip-2 .GE. ips_e) THEN
TNapm2j = moments_e(ip-2,ij,ikr,ikz,updatetlevel) * xNapm2j TNapm2j = moments_e(ip-2,ij,ikr,ikz,updatetlevel) * xNapm2j
ELSE ELSE
TNapm2j = 0. TNapm2j = 0.
ENDIF ENDIF
! xterm propto N_e^{p,j+1} ! xterm propto N_e^{p,j+1}
IF (ij+1 .LE. ije_e) THEN IF (ij+1 .LE. ije_e) THEN
TNapjp1 = moments_e(ip,ij+1,ikr,ikz,updatetlevel) * xNapjp1 TNapjp1 = moments_e(ip,ij+1,ikr,ikz,updatetlevel) * xNapjp1
ELSE ELSE
TNapjp1 = 0. TNapjp1 = 0.
ENDIF ENDIF
! term propto N_e^{p,j-1} ! term propto N_e^{p,j-1}
IF (ij-1 .GE. ijs_e) THEN IF (ij-1 .GE. ijs_e) THEN
TNapjm1 = moments_e(ip,ij-1,ikr,ikz,updatetlevel) * xNapjm1 TNapjm1 = moments_e(ip,ij-1,ikr,ikz,updatetlevel) * xNapjm1
...@@ -120,12 +136,9 @@ SUBROUTINE moments_eq_rhs ...@@ -120,12 +136,9 @@ SUBROUTINE moments_eq_rhs
TNapjm1 = 0. TNapjm1 = 0.
ENDIF ENDIF
! Collision term completed (Lenard-Bernstein) ! Collision term completed (DK Dougherty)
IF (ip+2 .LE. ipe_e) THEN TColl = -nu * (xColl * moments_e(ip,ij,ikr,ikz,updatetlevel) &
TColl = nu*(xColl - b_e2) * moments_e(ip+2,ij,ikr,ikz,updatetlevel) + TColl01 + TColl10 + TColl20)
ELSE
TColl = 0.
ENDIF
!! Electrical potential term !! Electrical potential term
Tphi = 0 Tphi = 0
...@@ -150,7 +163,7 @@ SUBROUTINE moments_eq_rhs ...@@ -150,7 +163,7 @@ SUBROUTINE moments_eq_rhs
Tphi = 0 ! electrostatic potential term Tphi = 0 ! electrostatic potential term
ploopi : DO ip = ips_i, ipe_i ploopi : DO ip = ips_i, ipe_i
ip_dp = REAL(ip-1.,dp) ip_dp = REAL(ip-1.,dp)
! x N_i^{p+2,j} ! x N_i^{p+2,j}
IF (ip+2 .LE. ipe_i) THEN IF (ip+2 .LE. ipe_i) THEN
...@@ -167,7 +180,7 @@ SUBROUTINE moments_eq_rhs ...@@ -167,7 +180,7 @@ SUBROUTINE moments_eq_rhs
ENDIF ENDIF
jloopi : DO ij = ijs_i, ije_i jloopi : DO ij = ijs_i, ije_i
ij_dp = REAL(ij-1.,dp) ij_dp = REAL(ij-1.,dp)
! x N_i^{p,j+1} ! x N_i^{p,j+1}
IF (ij+1 .LE. ije_i) THEN IF (ij+1 .LE. ije_i) THEN
...@@ -186,8 +199,25 @@ SUBROUTINE moments_eq_rhs ...@@ -186,8 +199,25 @@ SUBROUTINE moments_eq_rhs
! x N_i^{pj} ! x N_i^{pj}
xNapj = -taui_qi_etaB * 2.*(ip_dp + ij_dp + 1.) xNapj = -taui_qi_etaB * 2.*(ip_dp + ij_dp + 1.)
! first part of collision operator (Lenard-Bernstein) ! Collision term completed (DK Dougherty)
xColl = -(ip_dp + 2.0*ij_dp) TColl = -nu * (xColl * moments_i(ip,ij,ikr,ikz,updatetlevel) &
+ TColl01 + TColl10 + TColl20)
! ... adding Dougherty terms
IF ( (ip .EQ. 1) .AND. (ij .EQ. 2) ) THEN ! kronecker p0 * j1
TColl01 = 2.0/3.0*(SQRT2*moments_i(3,1,ikr,ikz,updatetlevel)&
- 2.0*moments_i(1,2,ikr,ikz,updatetlevel))
TColl20 = 0.0; TColl10 = 0.0;
ELSEIF ( (ip .EQ. 3) .AND. (ij .EQ. 1) ) THEN ! kronecker p2 * j0
TColl20 = -SQRT2/3.0*(SQRT2*moments_i(3,1,ikr,ikz,updatetlevel)&
- 2.0*moments_i(1,2,ikr,ikz,updatetlevel))
TColl10 = 0.0; TColl01 = 0.0;
ELSEIF ( (ip .EQ. 2) .AND. (ij .EQ. 1) ) THEN ! kronecker p1 * j0
TColl10 = moments_i(2,1,ikr,ikz,updatetlevel)
TColl20 = 0.0; TColl01 = 0.0;
ELSE
TColl10 = 0.0; TColl20 = 0.0; TColl01 = 0.0;
ENDIF
! x phi ! x phi
IF (ip .EQ. 1) THEN !(krokecker delta_p^0) IF (ip .EQ. 1) THEN !(krokecker delta_p^0)
...@@ -197,14 +227,14 @@ SUBROUTINE moments_eq_rhs ...@@ -197,14 +227,14 @@ SUBROUTINE moments_eq_rhs
factj = REAL(Factorial(ij-1),dp) factj = REAL(Factorial(ij-1),dp)
ELSE IF (ip .EQ. 3) THEN !(krokecker delta_p^2) ELSE IF (ip .EQ. 3) THEN !(krokecker delta_p^2)
xphij = (eta_T/SQRT2 - SQRT2*eta_B) xphij = (eta_T/SQRT2 - SQRT2*eta_B)
factj = REAL(Factorial(ij-1),dp) factj = REAL(Factorial(ij-1),dp)
ELSE ELSE
xphij = 0.; xphijp1 = 0.; xphijm1 = 0. xphij = 0.; xphijp1 = 0.; xphijm1 = 0.
factj = 1. factj = 1.
ENDIF ENDIF
! Loop on kspace ! Loop on kspace
krloopi : DO ikr = ikrs,ikre krloopi : DO ikr = ikrs,ikre
kzloopi : DO ikz = ikzs,ikze kzloopi : DO ikz = ikzs,ikze
kr = krarray(ikr) ! Poloidal wavevector kr = krarray(ikr) ! Poloidal wavevector
kz = kzarray(ikz) ! Toroidal wavevector kz = kzarray(ikz) ! Toroidal wavevector
...@@ -213,25 +243,25 @@ SUBROUTINE moments_eq_rhs ...@@ -213,25 +243,25 @@ SUBROUTINE moments_eq_rhs
!! Compute moments and mixing terms !! Compute moments and mixing terms
! term propto N_i^{p,j} ! term propto N_i^{p,j}
TNapj = moments_i(ip,ij,ikr,ikz,updatetlevel) * xNapj TNapj = moments_i(ip,ij,ikr,ikz,updatetlevel) * xNapj
! term propto N_i^{p+2,j} ! term propto N_i^{p+2,j}
IF (ip+2 .LE. ipe_i) THEN IF (ip+2 .LE. ipe_i) THEN
TNapp2j = moments_i(ip+2,ij,ikr,ikz,updatetlevel) * xNapp2j TNapp2j = moments_i(ip+2,ij,ikr,ikz,updatetlevel) * xNapp2j
ELSE ELSE
TNapp2j = 0. TNapp2j = 0.
ENDIF ENDIF
! term propto N_i^{p-2,j} ! term propto N_i^{p-2,j}
IF (ip-2 .GE. ips_i) THEN IF (ip-2 .GE. ips_i) THEN
TNapm2j = moments_i(ip-2,ij,ikr,ikz,updatetlevel) * xNapm2j TNapm2j = moments_i(ip-2,ij,ikr,ikz,updatetlevel) * xNapm2j
ELSE ELSE
TNapm2j = 0. TNapm2j = 0.
ENDIF ENDIF
! xterm propto N_i^{p,j+1} ! xterm propto N_i^{p,j+1}
IF (ij+1 .LE. ije_i) THEN IF (ij+1 .LE. ije_i) THEN
TNapjp1 = moments_i(ip,ij+1,ikr,ikz,updatetlevel) * xNapjp1 TNapjp1 = moments_i(ip,ij+1,ikr,ikz,updatetlevel) * xNapjp1
ELSE ELSE
TNapjp1 = 0. TNapjp1 = 0.
ENDIF ENDIF
! term propto N_i^{p,j-1} ! term propto N_i^{p,j-1}
IF (ij-1 .GE. ijs_i) THEN IF (ij-1 .GE. ijs_i) THEN
TNapjm1 = moments_i(ip,ij-1,ikr,ikz,updatetlevel) * xNapjm1 TNapjm1 = moments_i(ip,ij-1,ikr,ikz,updatetlevel) * xNapjm1
...@@ -239,12 +269,8 @@ SUBROUTINE moments_eq_rhs ...@@ -239,12 +269,8 @@ SUBROUTINE moments_eq_rhs
TNapjm1 = 0. TNapjm1 = 0.
ENDIF ENDIF
! Collision term completed (Lenard-Bernstein) ! Collision term completed (Dougherty)
IF (ip+2 .LE. ipe_i) THEN TColl = -nu* (xColl * moments_i(ip,ij,ikr,ikz,updatetlevel))
TColl = nu*(xColl - b_i2) * moments_i(ip+2,ij,ikr,ikz,updatetlevel)
ELSE
TColl = 0.
ENDIF
!! Electrical potential term !! Electrical potential term
Tphi = 0 Tphi = 0
......
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