Entropy Stable Numerical Schemes for Two-Fluid Plasma Equations

TL;DR

This paper develops entropy stable finite difference schemes for two-fluid plasma equations, combining entropy conservative fluxes with IMEX-RK time-stepping to handle non-linearity and stiffness efficiently.

Contribution

It introduces a novel combination of entropy conservative fluxes and IMEX-RK schemes tailored for two-fluid plasma equations, improving stability and efficiency.

Findings

Schemes are robust and accurate in benchmark tests.

Efficient handling of stiff source terms with local linear solves.

Enhanced stability for high charge to mass ratios.

Abstract

Two-fluid ideal plasma equations are a generalized form of the ideal MHD equations in which electrons and ions are considered as separate species. The design of efficient numerical schemes for the these equations is complicated on account of their non-linear nature and the presence of stiff source terms, especially for high charge to mass ratios and for low Larmor radii. In this article, we design entropy stable finite difference schemes for the two-fluid equations by combining entropy conservative fluxes and suitable numerical diffusion operators. Furthermore, to overcome the time step restrictions imposed by the stiff source terms, we devise time-stepping routines based on implicit-explicit (IMEX)-Runge Kutta (RK) schemes. The special structure of the two-fluid plasma equations is exploited by us to design IMEX schemes in which only local (in each cell) linear equations need to be solved at each time step. Benchmark numerical experiments are presented to illustrate the robustness and accuracy of these schemes.