JGonzalez
9da03ee0ea
Okay, so after going to Cartesian coordinantes, going back to spherical coordinates, reviewing Poisson and Vlasov equations in spherical coordinates (be careful on how you write Vlasov grad.(v f)).
668 lines
21 KiB
Fortran
668 lines
21 KiB
Fortran
!Physical and mathematical constants
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module constantParameters
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implicit none
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public
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integer, parameter:: dp = kind(0.d0) ! Precision
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real(dp), parameter:: PI = 4.0_dp*ATAN(1.0_dp) ! Number pi
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real(dp), parameter:: qe = 1.60217662e-19_dp ! Elementary charge
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real(dp), parameter:: kb = 1.38064852e-23_dp ! Boltzmann constants SI
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real(dp), parameter:: eV2J = qe ! Electron volt to Joule conversion
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real(dp), parameter:: eps_0 = 8.8542e-12_dp ! Epsilon_0
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real(dp), parameter:: eV_to_K = 11604.5_dp ! Convert eV to K
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real(dp), parameter:: cm3_to_m3 = 1.0e6_dp ! Convert cm^-3 to m^-3
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end module constantParameters
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module referenceValues
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use constantParameters, only: dp
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implicit none
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real(dp):: L_ref, t_ref, n_ref, u_ref, Temp_ref ! Reference values
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real(dp):: phi_ref ! Reference values
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end module referenceValues
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module output
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use constantParameters, only: dp
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implicit none
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public
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private:: dataRef_id, dataBC_id, dataF_id, dataPhi_id, dataCum_id
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private:: formatFloat, formatSep, formatTime
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integer:: everyOutput, everyWrite
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character(:), allocatable:: pathOutput
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integer, parameter:: dataRef_id = 10
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integer, parameter:: dataBC_id = 20
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integer, parameter:: dataF_id = 30
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integer, parameter:: dataPhi_id = 40
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integer, parameter:: dataCum_id = 50
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character(len=7), parameter:: formatFloat = 'ES0.6e3'
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character(len=3), parameter:: formatSep = '","'
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character(len=7):: formatTime
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contains
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subroutine setTimeFormat(nt)
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integer, intent(in):: nt
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integer:: l
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l=max(1,ceiling(log10(real(nt))))
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write(formatTime, '(A2,I0,".",I0,A1)') '(I',l,l,')'
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end subroutine setTimeFormat
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subroutine createPath()
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character(8) :: date_now
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character(10) :: time_now
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call date_and_time(date_now, time_now)
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!Compose the folder name
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pathOutput = date_now(1:4) // '-' // date_now(5:6) // '-' // date_now(7:8) // '_' // &
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time_now(1:2) // '.' // time_now(3:4) // '.' // time_now(5:6) // '/'
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call system('mkdir ' // pathOutput)
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end subroutine createPath
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subroutine writeOutputF(t, dt, nr, r, nv, v, f)
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use referenceValues, only: L_ref, n_ref, u_ref, t_ref
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integer, intent(in):: t
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integer, intent(in):: nr, nv
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real(dp), intent(in):: dt
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real(dp), intent(in):: r(1:nr)
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real(dp), intent(in):: v(1:nv)
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real(dp), intent(in):: f(1:nr,1:nv)
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character(len=30) :: myfmt
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character(:), allocatable:: filename
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integer:: i
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character(len=10):: timeString
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write (timeString, formatTime) t
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filename = 'time_' // trim(timeString) // '_f_i.csv'
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write (*, '(A, A)') 'Writing: ', filename
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open(unit=dataF_id, file=pathOutput // filename)
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write(dataF_id, '(A)') "t (s)"
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write(dataF_id, '('//formatFloat//')') t*dt*t_ref
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write(myfmt, "(I0)") nr
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myfmt = '(A,' // trim(myfmt) // '(' // formatSep // ',' // formatFloat // '))'
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write(dataF_id, myfmt) "v (m/s) / r (m)", r*L_ref
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write(myfmt, "(I0)") nr
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myfmt = '(' // formatFloat // ',' // trim(myfmt) // '(' // formatSep // ',' // formatFloat // '))'
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do i = 1, nv
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write(dataF_id, myfmt) v(i)*u_ref, f(:,i)*n_ref/u_ref
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end do
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close(unit=dataF_id)
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end subroutine writeOutputF
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subroutine writeOutputPhi(t, dt, nr, r, phi, E, n_e)
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use constantParameters, only: eV_to_K
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use referenceValues, only: L_ref, phi_ref, t_ref, n_ref
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integer, intent(in):: t
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integer, intent(in):: nr
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real(dp), intent(in):: dt
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real(dp), intent(in):: r(1:nr)
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real(dp), intent(in):: phi(1:nr)
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real(dp), intent(in):: E(1:nr)
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real(dp), intent(in):: n_e(1:nr)
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character(:), allocatable:: filename
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integer:: i
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character(len=10):: timeString
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write (timeString, formatTime) t
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filename = 'time_' // trim(timeString)//'_phi.csv'
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write (*, '(A, A)') 'Writing: ', filename
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open(unit=dataPhi_id, file=pathOutput//filename)
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write(dataPhi_id, '(A)') "t (s)"
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write(dataPhi_id, '('//formatFloat//')') t*dt*t_ref
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write(dataPhi_id, '(A,3('//formatSep//',A))') "r (m)","phi (V)","E (V m^-1)","n_e (m^-3)"
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do i = 1, nr
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write(dataPhi_id, '('//formatFloat//',3('//formatSep //','//formatFloat//'))') &
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r(i)*L_ref, &
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phi(i)*phi_ref, &
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E(i)*phi_ref/L_ref, &
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n_e(i)*n_ref
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end do
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close(unit=dataPhi_id)
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end subroutine writeOutputPhi
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subroutine writeOutputMom(t, dt, nr, r, n_i, u_i, T_i, Z)
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use constantParameters, only: eV_to_K
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use referenceValues, only: L_ref, t_ref, n_ref, u_ref, Temp_ref
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integer, intent(in):: t
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integer, intent(in):: nr
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real(dp), intent(in):: dt
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real(dp), intent(in):: r(1:nr)
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real(dp), intent(in):: n_i(1:nr)
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real(dp), intent(in):: u_i(1:nr)
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real(dp), intent(in):: T_i(1:nr)
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real(dp), intent(in):: Z(1:nr)
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character(:), allocatable:: filename
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integer:: i
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character(len=10):: timeString
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write (timeString, formatTime) t
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filename = 'time_' // trim(timeString)//'_mom_i.csv'
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write (*, '(A, A)') 'Writing: ', filename
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open(unit=dataPhi_id, file=pathOutput//filename)
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write(dataPhi_id, '(A)') "t (s)"
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write(dataPhi_id, '('//formatFloat//')') t*dt*t_ref
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write(dataPhi_id, '(A,4('//formatSep//',A))') "r (m)","n_i (m^-3)","u_i (m s^-1)", "T_i (eV)","Zave"
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do i = 1, nr
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write(dataPhi_id, '('//formatFloat//',4('//formatSep //','//formatFloat//'))') &
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r(i)*L_ref, &
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n_i(i)*n_ref, &
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u_i(i)*u_ref, &
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T_i(i)*Temp_ref/ev_to_K, &
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Z(i)
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end do
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close(unit=dataPhi_id)
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end subroutine writeOutputMom
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subroutine writeOutputBoundary(t, dt, n, u, Temp, Z)
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use constantParameters, only: eV_to_K
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use referenceValues, only: t_ref, n_ref, u_ref, Temp_ref
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integer, intent(in):: t
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real(dp), intent(in):: dt
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real(dp), intent(in):: n, u, Temp, Z
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character(len=6), parameter:: filename = 'bc.csv'
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logical:: res
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inquire(file=pathOutput // filename, exist=res)
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if (.not. res) then
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write (*, '(A, A)') 'Writing: ', filename
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open(unit=dataBC_id, file=pathOutput // filename, action='write', position='append')
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write(dataBC_id, '(A,4(' // formatSep // ',A))') 't (s)', 'n (m^-3)', 'u (m s^-1)', 'T (eV)', 'Z'
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close(dataBC_id)
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end if
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open(unit=dataBC_id, file=pathOutput // filename, action='write', position='append')
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write(dataBC_id, '(' // formatFloat // ',4('// formatSep // ',' // formatFloat // '))') &
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t*dt*t_ref, n*n_ref, u*u_ref, Temp*Temp_ref/eV_to_K, Z
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close(dataBC_id)
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end subroutine writeOutputBoundary
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subroutine writeOutputRef()
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use referenceValues, only: t_ref, L_ref, n_ref, u_ref, Temp_ref, phi_ref
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character(len=7), parameter:: filename = 'ref.csv'
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write (*, '(A, A)') 'Writing: ', filename
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open(unit=dataRef_id, file=pathOutput // filename)
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write(dataRef_id, '(A,5(' // formatSep // ',A))') 't_ref (s)', 'L_ref (m)', 'n_ref (m^-3)', &
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'u_ref (m s^-1)', 'T_ref (K)', 'phi_ref (V)'
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write(dataRef_id, '(' // formatFloat // ',5('// formatSep // ',' // formatFloat // '))') &
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t_ref, L_ref, n_ref, &
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u_ref, Temp_ref, phi_ref
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close(dataRef_id)
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end subroutine writeOutputRef
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subroutine writeOutputFCum(t, dt, r, nv, v, f)
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use referenceValues, only: L_ref, n_ref, u_ref, t_ref
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integer, intent(in):: t
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real(dp), intent(in):: dt
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integer, intent(in):: nv
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real(dp), intent(in):: r
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real(dp), intent(in):: v(1:nv)
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real(dp), intent(in):: f(1:nv)
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character(len=30) :: myfmt
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character(:), allocatable:: filename
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integer:: i
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character(len=10):: timeString
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write (timeString, formatTime) t
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filename = 'time_' // trim(timeString) // '_fCum_i.csv'
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write (*, '(A, A)') 'Writing: ', filename
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open(unit=dataCum_id, file=pathOutput // filename)
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write(dataCum_id, '(A)') "t (s)"
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write(dataCum_id, '('//formatFloat//')') t*dt*t_ref
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write(myfmt, "(I0)") 1
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myfmt = '(A,' // trim(myfmt) // '(' // formatSep // ',' // formatFloat // '))'
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write(dataCum_id, myfmt) "v (m/s) / r (m)", r*L_ref
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write(myfmt, "(I0)") 1
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myfmt = '(' // formatFloat // ',' // trim(myfmt) // '(' // formatSep // ',' // formatFloat // '))'
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do i = 1, nv
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write(dataCum_id, myfmt) v(i)*u_ref, f(i)*n_ref/u_ref
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end do
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close(unit=dataCum_id)
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end subroutine writeOutputFCum
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end module output
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module eos
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use constantParameters, only: dp
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implicit none
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private
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public:: T_to_Z
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contains
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pure function T_to_Z(T) result(Z)
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use constantParameters, only: eV_to_K
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use referenceValues, only: Temp_ref
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implicit none
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real(dp), intent(in):: T
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real(dp):: Z
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! Z = (Temp_ref * T / eV_to_K)**0.6
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! Z = max(Z, 1.0_dp)
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! Z = min(Z, 22.0_dp)
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Z = 12.0_dp
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end function T_to_Z
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end module eos
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program plasmaExpansion
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use constantParameters, only: dp, kb, qe, eps_0, ev_to_K, cm3_to_m3, PI
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use output
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use referenceValues
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use eos, only: T_to_Z
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use omp_lib
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implicit none
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real(dp), parameter:: m_i = 1.9712258e-25_dp ! Tin atom mass in kg
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real(dp), parameter:: m_e = 9.1093837e-31_dp ! Electron mass in kg
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real(dp), parameter:: gam = 1.0_dp ! Adiabatic coefficient
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real(dp):: r0, rf
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real(dp), allocatable, dimension(:):: r
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real(dp):: v0, vf
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real(dp), allocatable, dimension(:):: v
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real(dp):: t0, tf
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real(dp):: dr, dv, dt
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integer:: nr, nv, nt
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integer:: i, j, t
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integer:: j0 ! First integer of positive velocity
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real(dp):: Temp_bc ! Temperature
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real(dp):: Temp0, TempF
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real(dp):: n_ecr ! Electron critical density for the laser
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real(dp):: c_s ! Ion sound speed
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real(dp):: u_bc ! Injection velocity
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real(dp):: u_bc0, u_bcF
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real(dp):: n_bc ! Injection density
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real(dp):: n_bc0, n_bcF
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integer:: t_bc0, t_bcF
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real(dp), allocatable, dimension(:,:):: f_i, f_i_old
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real(dp), allocatable, dimension(:):: f0 ! Boundary at r = x_0
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real(dp), allocatable, dimension(:):: n_i
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real(dp), allocatable, dimension(:):: u_i
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real(dp), allocatable, dimension(:):: E_i
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real(dp), allocatable, dimension(:):: T_i
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real(dp), allocatable, dimension(:):: n_e
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real(dp), allocatable, dimension(:):: Zave
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real(dp), allocatable, dimension(:):: diag, diag_low, diag_high
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real(dp), allocatable, dimension(:,:):: A
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real(dp), allocatable, dimension(:):: Res
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real(dp), allocatable, dimension(:):: b
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integer:: info
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real(dp), allocatable, dimension(:):: phi, phi_old, E
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real(dp):: phiConv
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real(dp):: phi0, phiF
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integer:: k
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real(dp), allocatable, dimension(:):: fCum_i
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real(dp):: rCum
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integer:: rCum_index
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! Set number of threads
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call omp_set_num_threads(8)
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! Set reference numbers (in SI units)
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Temp_ref = 60.0_dp * eV_to_K
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n_ref = 1.0e19_dp * cm3_to_m3
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t_ref = sqrt(eps_0 * m_i / (n_ref * 1.0_dp * qe**2)) ! 1.0_dp represents Z = 1 for reference values
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u_ref = sqrt(kb * Temp_ref / m_i)
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L_ref = u_ref * t_ref
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phi_ref = kb * Temp_ref / qe
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! Set position to calculate cumulative sum of f (non-dimensional units)
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rCum = 5.0e-3 / L_ref
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! Set input parameters (remember these have to be in non-dimensional units)
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Temp0 = 60.0_dp * eV_to_K / Temp_ref
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TempF = 60.0_dp * eV_to_K / Temp_ref
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n_ecr = 1.0e19_dp * cm3_to_m3 / n_ref
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c_s = sqrt(T_to_Z(Temp0) * gam * Temp0)
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u_bc0 = c_s!sqrt(Temp0)
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u_bcF = u_bc0!sqrt(TempF)
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n_bc0 = n_ecr / T_to_Z(Temp0)
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n_bcF = n_bc0!n_ecr*1.0e-1 / T_to_Z(Temp0)
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! Set domain boundaries (non-dimensional units)
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r0 = 200.0e-6_dp / L_ref
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rf = 6.0e-3_dp / L_ref
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dr = 1.0e3_dp
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nr = nint((rf - r0) / dr) + 1
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dr = (rf - r0) / float(nr-1)
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allocate(r(1:nr))
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do i = 1, nr
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r(i) = dr * float(i-1) + r0
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end do
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! Index for cumulative sum
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rCum_index = minloc(abs(r - rCum), 1)
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v0 =-1.0e1_dp*c_s
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vf = 2.0e1_dp*c_s
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dv = 1.0e-1_dp
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nv = nint((vf - v0) / dv) + 1
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dv = (vf - v0) / float(nv-1)
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allocate(v(1:nv))
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do j = 1, nv
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v(j) = dv * float(j-1) + v0
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end do
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! Shift v mesh so it passes by 0
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v = v - (minval(abs(v)))
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j0 = minloc(abs(v), 1)
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if (v(j0) < 0.0_dp) then
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j0 = j0 + 1
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end if
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t0 = 0.0_dp
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tf = 1.0e-6_dp / t_ref
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! tf = 1.0e1_dp * (rf - r0) / c_s
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dt = 1.0e-1_dp*dr/(10.0_dp*c_s)
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nt = nint((tf - t0) / dt)
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dt = (tf - t0) / float(nt)
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t_bc0 = nint(100.0e-9_dp / t_ref / dt)
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t_bcF = nint(105.0e-9_dp / t_ref / dt)
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everyOutput = nint(1.0e-9_dp/t_ref/dt)
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if (everyOutput == 0) then
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everyOutput = 1
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end if
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everyWrite = everyOutput/10
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if (everyWrite == 0) then
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everyWrite = 1
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end if
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write(*, '(A,ES0.4e3)') 'CFL: ', dt*vf/dr
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! Allocate vectors
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allocate(f_i(1:nr,1:nv), f_i_old(1:nr,1:nv))
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allocate(n_i(1:nr))
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allocate(u_i(1:nr), E_i(1:nr), T_i(1:nr))
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allocate(Zave(1:nr))
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allocate(n_e(1:nr))
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allocate(phi(1:nr), phi_old(1:nr), E(1:nr))
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allocate(fCum_i(1:nv))
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f_i = 0.0_dp
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f_i_old = 0.0_dp
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n_i = 0.0_dp
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u_i = 0.0_dp
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E_i = 0.0_dp
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T_i = 0.0_dp
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n_e = 1.0_dp
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Zave = 0.0_dp
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phi = 0.0_dp
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phi_old = 0.0_dp
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E = 0.0_dp
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fCum_i = 0.0_dp
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! Allocate matrix for Poisson equation
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allocate(diag(1:nr), diag_low(1:nr-1), diag_high(1:nr-1))
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allocate(b(1:nr))
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diag = 0.0_dp
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diag_low = 0.0_dp
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diag_high = 0.0_dp
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b = 0.0_dp
|
|
diag = -2.0_dp / dr**2
|
|
diag_low = 1.0_dp / dr**2 - 1.0_dp / (r(2:nr) * 2.0_dp * dr)
|
|
diag_high = 1.0_dp / dr**2 + 1.0_dp / (r(1:nr-1) * 2.0_dp * dr)
|
|
diag(1) = 1.0_dp ! Dirichlet
|
|
diag_high(1) = 0.0_dp ! Dirichlet
|
|
! diag_high(1) = 2.0_dp / dr**2 ! Neumann
|
|
! diag(nr) = 1.0_dp ! Dirichlet
|
|
! diag_low(nr-1) = 0.0_dp ! Dirichlet
|
|
diag_low(nr-1) = 2.0_dp / dr**2 ! Neumann
|
|
|
|
allocate(A(1:nr,1:nr))
|
|
A = 0.0_dp
|
|
A(1,1) = diag(1)
|
|
A(1,2) = diag_high(1)
|
|
do i = 2, nr - 1
|
|
A(i, i-1) = diag_low(i-1)
|
|
A(i, i) = diag(i)
|
|
A(i, i+1) = diag_high(i)
|
|
end do
|
|
A(nr,nr-1) = diag_low(nr-1)
|
|
A(nr,nr) = diag(nr)
|
|
|
|
allocate(Res(1:nr))
|
|
Res = 0.0_dp
|
|
|
|
! Set boundary values
|
|
phi0 = 0.0_dp / phi_ref ! Dirichlet
|
|
! phi0 = phi(1) ! Neumann
|
|
! phiF = 0.0_dp ! Dirichlet
|
|
allocate(f0(j0:nv))
|
|
f0 = 0.0_dp
|
|
|
|
! Output initial values
|
|
call createPath()
|
|
call setTimeFormat(nt)
|
|
t = 0
|
|
call writeOutputRef()
|
|
call writeOutputF(t, dt, nr, r, nv, v, f_i_old)
|
|
call writeOutputPhi(t, dt, nr, r, phi, E, n_e)
|
|
call writeOutputMom(t, dt, nr, r, n_i, u_i, T_i, Zave)
|
|
|
|
! Main loop
|
|
Temp_bc = Temp0
|
|
u_bc = u_bc0
|
|
n_bc = n_bc0
|
|
do t = 1, nt
|
|
if (t > t_bc0 .and. t <= t_bcF) then
|
|
Temp_bc = (TempF - Temp0) / float(t_bcF - t_bc0)*(t - t_bc0) + Temp0
|
|
u_bc = (u_bcF - u_bc0) / float(t_bcF - t_bc0)*(t - t_bc0) + u_bc0
|
|
n_bc = (n_bcF - n_bc0) / float(t_bcF - t_bc0)*(t - t_bc0) + n_bc0
|
|
else if (t > t_bcF) then
|
|
Temp_bc = TempF
|
|
u_bc = u_bcF
|
|
n_bc = n_bcF
|
|
end if
|
|
call writeOutputBoundary(t, dt, n_bc, u_bc, Temp_bc, T_to_Z(Temp_bc))
|
|
f0(j0:nv) = n_bc / sqrt(PI*Temp_bc) * exp(-(v(j0:nv) - u_bc)**2 / Temp_bc)
|
|
|
|
! Boundary conditions
|
|
! r = r0, v>0
|
|
f_i_old(1,j0:nv) = f0
|
|
f_i(1,j0:nv) = f_i_old(1,j0:nv)
|
|
T_i(1) = Temp_bc
|
|
Zave(1) = T_to_Z(Temp_bc)
|
|
! r = rf, v<0
|
|
f_i_old(nr,1:j0-1) = 0.0_dp
|
|
f_i(nr,1:j0-1) = f_i_old(nr,1:j0-1)
|
|
! set edge velocities to 0
|
|
f_i_old(:,1) = 0.0_dp
|
|
f_i_old(:,nv) = 0.0_dp
|
|
! Advect in the r direction
|
|
!$omp parallel do
|
|
do i = 1, nr
|
|
! Advect negative velocity
|
|
if (i < nr) then
|
|
f_i(i,1:j0-1) = f_i_old(i,1:j0-1) - v(1:j0-1)*dt/dr/r(i)**2*(r(i+1)**2*f_i_old(i+1,1:j0-1) - &
|
|
r(i )**2*f_i_old(i ,1:j0-1))
|
|
end if
|
|
! Advect positive velocity
|
|
if (i > 1) then
|
|
f_i(i,j0:nv) = f_i_old(i, j0:nv) - v( j0:nv)*dt/dr/r(i)**2*(r(i )**2*f_i_old(i , j0:nv) - &
|
|
r(i-1)**2*f_i_old(i-1, j0:nv))
|
|
end if
|
|
|
|
n_i(i) = sum(f_i(i,:)*dv)
|
|
if (n_i(i) > 1.0e-10_dp) then
|
|
u_i(i) = sum(v(:) *f_i(i,:)*dv) / n_i(i)
|
|
E_i(i) = sum(v(:)**2*f_i(i,:)*dv) / n_i(i)
|
|
T_i(i) = 2.0_dp*E_i(i) - 2.0_dp*u_i(i)**2
|
|
Zave(i) = T_to_Z(T_i(i))
|
|
|
|
else
|
|
u_i(i) = 0.0_dp
|
|
T_i(i) = 0.0_dp
|
|
Zave(i) = 0.0_dp
|
|
end if
|
|
|
|
end do
|
|
!$omp end parallel do
|
|
|
|
! Solve Poission (maximum number of iterations, break if convergence is reached before)
|
|
do k = 1, 1000
|
|
! Store previous value
|
|
phi_old = phi
|
|
|
|
! Diagonal matrix for Newton integration scheme
|
|
diag = -2.0_dp / dr**2 - n_e
|
|
diag_low = 1.0_dp / dr**2 - 1.0_dp / (r(2:nr) * 2.0_dp * dr)
|
|
diag_high = 1.0_dp / dr**2 + 1.0_dp / (r(1:nr-1) * 2.0_dp * dr)
|
|
diag(1) = 1.0_dp ! Dirichlet
|
|
diag_high(1) = 0.0_dp ! Dirichlet
|
|
! diag_high(1) = 2.0_dp / dr**2 - n_e(1) ! Neumann
|
|
! diag(nr) = 1.0_dp ! Dirichlet
|
|
! diag_low(nr-1) = 0.0_dp ! Dirichlet
|
|
diag_low(nr-1) = 2.0_dp / dr**2 - n_e(nr) ! Neumann
|
|
|
|
! Calculate charge density
|
|
b = -(Zave*n_i - n_e)
|
|
! Apply boundary conditions
|
|
b(1) = phi0 ! Dirichlet
|
|
! b(nr) = phiF ! Dirichlet
|
|
|
|
! Calculate residual
|
|
!$omp parallel workshare
|
|
Res = -(MATMUL(A, phi_old) - b)
|
|
!$omp end parallel workshare
|
|
|
|
! Iterate system
|
|
call dgtsv(nr, 1, diag_low, diag, diag_high, Res, nr, info)
|
|
phi = phi_old + Res
|
|
! phi0=phi(1)
|
|
|
|
! Calculate distribution of electrons
|
|
n_e = Zave(1) * n_i(1) * exp((phi - phi0) / T_i(1))
|
|
|
|
! Check if the solution has converged
|
|
phiConv = maxval(abs(Res),1)
|
|
if (phiConv < 1.0e-3_dp) then
|
|
exit
|
|
|
|
end if
|
|
|
|
! ! Calculate new potential to ensure 0 current at the edge
|
|
! if (n_i(nr) > 1.0e-10_dp) then
|
|
! phiF = phi0 + T_i(1) * log((2.0_dp*sqrt(pi)*Zave(nr)*n_i(nr)*u_i(nr)) / (Zave(1)*n_i(1)*sqrt(m_i*T_i(1)/m_e)))
|
|
!
|
|
! else
|
|
! phiF = phi(nr-5)
|
|
!
|
|
! end if
|
|
|
|
end do
|
|
|
|
! Calculate electric field
|
|
E(1) = - (phi(2) - phi(1)) / dr ! Dirichlet
|
|
! E(1) = 0.0_dp ! Neumann
|
|
!$omp parallel do
|
|
do i = 2, nr-1
|
|
E(i) = - 0.5_dp*(phi(i+1) - phi(i-1)) / dr
|
|
|
|
end do
|
|
!$omp end parallel do
|
|
! E(nr) = - (phi(nr) - phi(nr-1)) / dr ! Dirichlet
|
|
E(nr) = 0.0_dp ! Neumann
|
|
|
|
! Update intermediate f
|
|
f_i_old = f_i
|
|
|
|
! Advect in the v direction
|
|
! i = 1, v<0
|
|
i = 1
|
|
if (E(i) >= 0.0_dp) then
|
|
f_i(i,2:j0-2) = f_i_old(i,2:j0-2) - Zave(i)*E(i)*dt/dv*(f_i_old(i,2:j0-2) - f_i_old(i,1:j0-3))
|
|
else
|
|
f_i(i,2:j0-2) = f_i_old(i,2:j0-2) - Zave(i)*E(i)*dt/dv*(f_i_old(i,3:j0-1) - f_i_old(i,2:j0-2))
|
|
|
|
end if
|
|
! i = 2, nr-1; all v
|
|
!$omp parallel do
|
|
do i = 2, nr-1
|
|
if (E(i) >= 0.0_dp) then
|
|
f_i(i,2:nv-1) = f_i_old(i,2:nv-1) - Zave(i)*E(i)*dt/dv*(f_i_old(i,2:nv-1) - f_i_old(i,1:nv-2))
|
|
else
|
|
f_i(i,2:nv-1) = f_i_old(i,2:nv-1) - Zave(i)*E(i)*dt/dv*(f_i_old(i,3:nv) - f_i_old(i,2:nv-1))
|
|
|
|
end if
|
|
|
|
end do
|
|
!$omp end parallel do
|
|
! i = nr, v>=0
|
|
i = nr
|
|
if (E(i) >= 0.0_dp) then
|
|
f_i(i,j0+1:nv-1) = f_i_old(i,j0+1:nv-1) - Zave(i)*E(i)*dt/dv*(f_i_old(i,j0+1:nv-1) - f_i_old(i,j0:nv-2))
|
|
else
|
|
f_i(i,j0+1:nv-1) = f_i_old(i,j0+1:nv-1) - Zave(i)*E(i)*dt/dv*(f_i_old(i,j0+2:nv) - f_i_old(i,j0+1:nv-1))
|
|
|
|
end if
|
|
|
|
! Reset values for next iteration
|
|
f_i_old = f_i
|
|
fCum_i = fCum_i + f_i_old(rCum_index,:)
|
|
|
|
! Write output
|
|
if (mod(t,everyOutput) == 0 .or. t == nt) then
|
|
call writeOutputF(t, dt, nr, r, nv, v, f_i_old)
|
|
call writeOutputPhi(t, dt, nr, r, phi, E, n_e)
|
|
call writeOutputMom(t, dt, nr, r, n_i, u_i, T_i, Zave)
|
|
call writeOutputFCum(t, dt, r(rCum_index), nv, v, fCum_i)
|
|
|
|
end if
|
|
|
|
! Write progress
|
|
if (mod(t,everyWrite) == 0) then
|
|
write (*, '(I10, A, I10)' ) t, '/', nt
|
|
write (*, '(A, ES0.4e3,","ES0.4e3)') 'phi max,min: ', maxval(phi)*phi_ref, minval(phi)*phi_ref
|
|
|
|
end if
|
|
|
|
end do
|
|
|
|
end program plasmaExpansion
|
|
|