Edit on GitHub

DynamicElectricSheath

Documentation for DynamicElectricSheath

DynamicElectricSheath.Discretization — Type
struct Discretization

Grid in velocity corresponds to the electronic one which contains the support of boths ions and electron density function

  • Nx::Int64

    Number of points of the space mesh

  • Nv::Int64

    Number of points of the speed mesh

  • dx::Float64

    Space step

  • dv::Float64

    Speed step

  • CFL_x::Float64

    CFL in x

  • CFL_v::Float64

    CFL in v

  • Nt::Int64

    Number of time steps

  • dt::Float64

    Time step

source
DynamicElectricSheath.Physics — Type
struct Physics

  • ν::Float64

    Collision frequency Default: 20.0

  • λ::Float64

    Debye length Default: 0.5

  • T::Float64

    Time horizon Default: 10.0

  • μ::Float64

    Thermal speed Default: 0.5

  • xmin::Float64

    Lower bound space Default: -1.0

  • xmax::Float64

    Upper bound space Default: 1.0

  • vmin::Float64

    Lower bound speed Default: -10.0

  • vmax::Float64

    Uupper bound speed Default: 10.0

source
DynamicElectricSheath.advection! — Method
advection!(
    fi,
    fe,
    vv_plus,
    vv_minus,
    EE_plus,
    EE_minus,
    nu,
    mu,
    dx,
    dv,
    dt
)

\[\frac{d f_i}{dt} + v \frac{d f_i}{dx} + E \frac{d f_i}{dv} = \nu * f_e\]

\[\frac{d f_e}{dt} + v \frac{d f_e}{dx} + \frac{1}{\mu} E \frac{d f_e}{dv} = 0\]

source
DynamicElectricSheath.compute_e! — Method
compute_e!(EE, rho, lambda, J_l, J_r, dx, dt)

Update electric field : use formula

\[E(x) = 0.5*(E(1) + E(-1)) + \nu/2 * ( \int_{-1}^{x} rho(y)dy - \int_{x}^{1} \rho(y)dy )\]

with $E(t^{n+1},1) + E(t^{n+1},-1)$ approximated by $E(t^n,1) + E(t^n,-1) + dt/\lambda^2 * (J_l + J_r)$ (Ampère boundary conditions)

source