Hybridizable discontinuous Galerkin methods for solving the two-fluid plasma model

TL;DR

This paper explores the use of Hybridizable Discontinuous Galerkin (HDG) methods to efficiently solve the two-fluid plasma model, addressing numerical stiffness and stability issues while maintaining high accuracy.

Contribution

It introduces an HDG framework tailored for the two-fluid plasma equations, demonstrating how it can bypass strict stability constraints and achieve high-order accuracy.

Findings

HDG methods provide stable solutions for stiff plasma equations.

The approach maintains high-order accuracy without strict stability restrictions.

Numerical stability conditions are quantified for the two-fluid model.

Abstract

The two-fluid plasma model has a wide range of timescales which must all be numerically resolved regardless of the timescale on which plasma dynamics occurs. The answer to solving numerically stiff systems is generally to utilize unconditionally stable implicit time advance methods. Hybridizable discontinuous Galerkin (HDG) methods have emerged as a powerful tool for solving stiff partial differential equations. The HDG framework combines the advantages of the discontinuous Galerkin (DG) method, such as high-order accuracy and flexibility in handling mixed hyperbolic/parabolic PDEs with the advantage of classical continuous finite element methods for constructing small numerically stable global systems which can be solved implicitly. In this research we quantify the numerical stability conditions for the two-fluid equations and demonstrate how HDG can be used to avoid the strict stability requirements while maintaining high order accurate results.