Fluid model

TwoFluidQuasiNeutralToy

Linearized, quasi-neutral two-fluid model with zero electron inertia.

Overview

TwoFluidQuasiNeutralToy is a reduced linear two-fluid benchmark with

zero electron inertia. It is meant for studying the quasi-neutral solve and the coupled ion/electron velocity response in a simplified setting.

References

[1] Juan Vicente Gutiérrez-Santacreu, Omar Maj, Marco Restelli: Finite element discretization of a Stokes-like model arising in plasma physics, Journal of Computational Physics 2018.

Use cases

This model is appropriate for:

linear quasi-neutral two-fluid benchmarks
Stokes-like plasma model verification
testing coupled velocity-potential FEEC solvers

Governing equations

PDEs solved by model:

Ion momentum:

\frac{\partial u}{\partial t} = - \nabla ϕ + \frac{u \times B _{0}}{ε} + ν Δ u + f

Electron momentum:

0 = \nabla ϕ - \frac{u _{e} \times B _{0}}{ε} + ν_{e} Δ u_{e} + f_{e}

Quasi-neutrality constraint:

\nabla \cdot (u - u_{e}) = 0

where $B_{0}$ is a static magnetic field and $f, f_{e}$ are given forcing terms.

Normalization

Thermal-speed scaling is used:

u^= v^_{th}, e ϕ^= m v^_{th}^{2} .

Discretization

Time integration is performed by the following propagators (in sequence):

struphy.propagators.two_fluid_quasi_neutral_full.TwoFluidQuasiNeutralFull

Diagnostics

The following scalars are tracked during simulation:

No default scalar diagnostics are defined by this model.

Example

Create and initialize the quasi-neutral toy model:

from struphy.models import TwoFluidQuasiNeutralToy

model = TwoFluidQuasiNeutralToy()
model.em_fields.phi
model.ions.u

model.electrons.u