diff --git a/src/vlaplex.f90 b/src/vlaplex.f90 index 21b3b6c..7fc9ebe 100644 --- a/src/vlaplex.f90 +++ b/src/vlaplex.f90 @@ -14,7 +14,6 @@ program VlaPlEx real(dp), parameter:: gamma_e_exp = 1.0_dp /(gamma_e - 1.0_dp) ! Exponent for polytropic electrons real(dp), parameter:: gamma_e_dexp = (2.0_dp - gamma_e)/(gamma_e - 1.0_dp) ! Exponent for polytropic db_dphi real(dp), parameter:: n_epsilon = 1.0e-16_dp - real(dp), parameter:: cosTheta = 0.995_dp real(dp):: r0, rf real(dp), allocatable, dimension(:):: r @@ -54,7 +53,7 @@ program VlaPlEx real(dp), allocatable, dimension(:):: phi, phi_old, E, db_dphi real(dp):: phiConv real(dp):: phi0 - real(dp):: T_e0 + real(dp):: T_e ! real(dp):: phiF integer:: k @@ -146,7 +145,7 @@ program VlaPlEx E_i = 0.0_dp T_i = 0.0_dp n_e = 0.0_dp - T_e0 = 0.0_dp + T_e = 0.0_dp Zave = 0.0_dp Zave_bc_old = 0.0_dp phi = 0.0_dp @@ -164,8 +163,8 @@ program VlaPlEx b = 0.0_dp db_dphi = 0.0_dp diag = -2.0_dp / dr**2 - diag_low = 1.0_dp / dr**2! - 1.0_dp / (r(2:nr) * dr) - diag_high = 1.0_dp / dr**2! + 1.0_dp / (r(1:nr-1) * dr) + diag_low = 1.0_dp / dr**2 - 1.0_dp / (r(2:nr) * dr) + diag_high = 1.0_dp / dr**2 + 1.0_dp / (r(1:nr-1) * dr) diag(1) = 1.0_dp ! Dirichlet diag_high(1) = 0.0_dp ! Dirichlet ! diag_high(1) = 2.0_dp / dr**2 ! Neumann @@ -212,7 +211,7 @@ program VlaPlEx ! Get boundary conditions for specific time call boundaryConditions%get(time, n_bc, u_bc, Temp_bc) - ! Find new \bar{Z}_i based on T_e0 = Temp_bc and n_e = n_bc + ! Find new \bar{Z}_i based on T_e = Temp_bc and n_e = n_bc call Tene_to_Z%get(Temp_bc, n_bc, Zave_bc) ! Assign Z(T,n) to bin z_inj = minloc(abs(Zlist - Zave_bc),1) @@ -230,7 +229,7 @@ program VlaPlEx f_i_old(z_inj,1,j0:nv) = f0 f_i(:,1,j0:nv) = f_i_old(:,1,j0:nv) - T_e0 = Temp_bc + T_e = Temp_bc ! r = rf, v<0 f_i_old(:,nr,1:j0-1) = 0.0_dp @@ -248,13 +247,13 @@ program VlaPlEx do i = 1, nr ! Advect negative velocity if (i < nr) then - f_i(iz,i,1:j0-1) = f_i_old(iz,i,1:j0-1) - v(1:j0-1)*cosTheta*dt/dr*(f_i_old(iz,i+1,1:j0-1) - & - f_i_old(iz,i ,1:j0-1)) + f_i(iz,i,1:j0-1) = f_i_old(iz,i,1:j0-1) - v(1:j0-1)*dt/dr/r(i)**2*(r(i+1)**2*f_i_old(iz,i+1,1:j0-1) - & + r(i )**2*f_i_old(iz,i ,1:j0-1)) end if ! Advect positive velocity if (i > 1) then - f_i(iz,i,j0:nv) = f_i_old(iz,i, j0:nv) - v( j0:nv)*cosTheta*dt/dr*(f_i_old(iz,i , j0:nv) - & - f_i_old(iz,i-1, j0:nv)) + f_i(iz,i,j0:nv) = f_i_old(iz,i, j0:nv) - v( j0:nv)*dt/dr/r(i)**2*(r(i )**2*f_i_old(iz,i , j0:nv) - & + r(i-1)**2*f_i_old(iz,i-1, j0:nv)) end if n_i(iz,i) = sum(f_i(iz,i,:))*dv @@ -284,8 +283,8 @@ program VlaPlEx phi_old = phi diag = -2.0_dp / dr**2 - db_dphi - diag_low = 1.0_dp / dr**2! - 1.0_dp / (r(2:nr) * dr) - diag_high = 1.0_dp / dr**2! + 1.0_dp / (r(1:nr-1) * dr) + diag_low = 1.0_dp / dr**2 - 1.0_dp / (r(2:nr) * dr) + diag_high = 1.0_dp / dr**2 + 1.0_dp / (r(1:nr-1) * dr) diag(1) = 1.0_dp ! Dirichlet diag_high(1) = 0.0_dp ! Dirichlet ! diag(nr) = 1.0_dp ! Dirichlet @@ -309,12 +308,12 @@ program VlaPlEx ! phi0=phi(1) ! Neumann ! Calculate distribution of electrons - ! n_e = sum_ni(1) * exp((phi- phi0) / T_e0) ! Isothermal (Boltzmann) - n_e = sum_ni(1) * (1.0_dp + (gamma_e - 1.0_dp)/gamma_e*(phi-phi0)/T_e0)**gamma_e_exp !Polytropic + ! n_e = sum_ni(1) * exp((phi- phi0) / T_e) ! Isothermal (Boltzmann) + n_e = sum_ni(1) * (1.0_dp + (gamma_e - 1.0_dp)/gamma_e*(phi-phi0)/T_e)**gamma_e_exp !Polytropic ! Diagonal matrix for Newton integration scheme - ! db_dphi = n_e / T_e0 ! Isothermal (Boltzmann) - db_dphi = sum_ni(1) / (gamma_e * T_e0) * & - (1.0_dp + (gamma_e - 1.0_dp)/gamma_e*(phi-phi0)/T_e0)**gamma_e_dexp !Polytropic + ! db_dphi = n_e / T_e ! Isothermal (Boltzmann) + db_dphi = sum_ni(1) / (gamma_e * T_e) * & + (1.0_dp + (gamma_e - 1.0_dp)/gamma_e*(phi-phi0)/T_e)**gamma_e_dexp !Polytropic ! Check if the solution has converged phiConv = maxval(abs(Res),1) @@ -323,6 +322,15 @@ program VlaPlEx end if + ! ! Calculate new potential to ensure 0 current at the edge + ! if (n_i(nr) > n_epsilon) then + ! phiF = phi0 + T_e * log((2.0_dp*sqrt(pi)*Zave(nr)*n_i(nr)*u_i(nr)) / (Zave(1)*n_i(1)*sqrt(m_i*T_e/m_e))) + ! + ! else + ! phiF = phi(nr-5) + ! + ! end if + end do ! Calculate electric field