Implicit-Explicit Runge-Kutta schemes for hyperbolic systems with stiff relaxation and applications

TL;DR

This paper reviews Implicit-Explicit Runge-Kutta schemes for hyperbolic systems with stiff relaxation, highlighting recent advances in uniform accuracy and applications to thermodynamics models.

Contribution

It provides an overview of recent results on uniform accuracy of IMEX schemes for hyperbolic systems with stiff relaxation and introduces an original application in thermodynamics.

Findings

Demonstrates uniform accuracy for hyperbolic systems with stiff relaxation

Applies IMEX schemes to a thermodynamics model

Summarizes recent theoretical developments in the field

Abstract

In this paper we give an overview of Implicit-Explicit Runge-Kutta schemes applied to hyperbolic systems with stiff relaxation. In particular, we focus on some recent results on the uniform accuracy for hyperbolic systems with stiff relaxation [6], and hyperbolic system with diffusive relaxation [7, 5, 4]. In the latter case, we present an original application to a model problem arising in Extended Thermodynamics.