Second order divergence constraint preserving entropy stable finite difference schemes for ideal two-fluid plasma flow equations

TL;DR

This paper introduces second-order finite difference schemes for ideal two-fluid plasma flow equations that preserve divergence constraints, are entropy stable, and ensure divergence-free magnetic fields, validated through various test cases.

Contribution

The paper develops a novel divergence constraint-preserving, entropy-stable finite difference scheme for ideal two-fluid plasma equations, combining Maxwell's solver with fluid discretization.

Findings

Schemes are second-order accurate and entropy stable.

Numerical results confirm divergence constraint preservation.

Compared favorably with existing divergence cleaning methods.

Abstract

Two-fluid plasma flow equations describe the flow of ions and electrons with different densities, velocities, and pressures. We consider the ideal plasma flow i.e. we ignore viscous, resistive, and collision effects. The resulting system of equations has flux consisting of three independent components, one for ions, one for electrons, and a linear Maxwell's equation flux for the electromagnetic fields. The coupling of these components is via source terms. In this article, we present {conservative} second-order finite difference schemes that ensure the consistent evolution of the divergence constraints on the electric and magnetic fields. The key idea is to design a numerical solver for Maxwell's equations using the multidimensional Riemann solver at the vertices, ensuring discrete divergence constraints; for the fluid parts, we use an entropy-stable discretization. The proposed schemes are co-located, second-order accurate, entropy stable, and ensure divergence-free evolution of the magnetic field. We use explicit and IMplicit-EXplicit (IMEX) schemes for time discretizations. To demonstrate the accuracy, stability, and divergence constraint-preserving ability of the proposed schemes, we present several test cases in one and two dimensions. We also compare the numerical results with those obtained from schemes with no divergence cleaning and those employing perfectly hyperbolic Maxwell (PHM) equations-based divergence cleaning methods for Maxwell's equations.