High-order finite-difference entropy stable schemes for two-fluid relativistic plasma flow equations

TL;DR

This paper develops high-order entropy stable finite-difference schemes for two-fluid relativistic plasma flow equations, ensuring stability and efficiency in simulating complex plasma dynamics with coupled ion, electron, and electromagnetic components.

Contribution

The paper introduces a novel high-order entropy stable finite-difference scheme for two-fluid relativistic plasma equations, extending existing methods and incorporating efficient treatment of stiff source terms.

Findings

Schemes demonstrate stability and accuracy in test problems.

Efficient solution of nonlinear algebraic equations via Newton's method.

Effective coupling of relativistic hydrodynamics and Maxwell's equations.

Abstract

In this article, we propose high-order finite-difference entropy stable schemes for the two-fluid relativistic plasma flow equations. This is achieved by exploiting the structure of the equations, which consists of three independent flux components. The first two components describe the ion and electron flows, which are modeled using the relativistic hydrodynamics equation. The third component is Maxwell's equations, which are linear systems. The coupling of the ion and electron flows, and electromagnetic fields is via source terms only. Furthermore, we also show that the source terms do not affect the entropy evolution. To design semi-discrete entropy stable schemes, we extend the RHD entropy stable schemes in Bhoriya et al. to three dimensions. This is then coupled with entropy stable discretization of the Maxwell's equations. Finally, we use SSP-RK schemes to discretize in time. We also propose ARK-IMEX schemes to treat the stiff source terms; the resulting nonlinear set of algebraic equations is local (at each discretization point). These equations are solved using the Newton's Method, which results in an efficient method. The proposed schemes are then tested using various test problems to demonstrate their stability, accuracy and efficiency.