Numerical Approximation of Hyperbolic Systems Containing an Interface

TL;DR

This paper introduces a numerical method for coupled hyperbolic conservation laws with interfaces, using central schemes that balance wave effects and preserve equilibrium and conservation properties, demonstrated through various applications.

Contribution

The paper presents a novel central scheme approach for hyperbolic systems with interfaces that does not rely on Riemann problem structures and maintains equilibrium and conservation.

Findings

The method accurately approximates solutions with interface conditions.

It preserves equilibrium states exactly.

Numerical tests confirm the scheme's effectiveness in different applications.

Abstract

In this paper we present an approach to approximate numerically the solution of coupled hyperbolic conservation laws. The coupling is achieved through a fixed interface, in which interface conditions are linking the traces of both sides. The numerical solver is based on central methods, like the Rusanov scheme, and does not use the structure of the Riemann Problem. It consists in balancing the effects of the waves that enter the interface. The scheme is well balanced with respect to all the piecewise constant equilibria associated with the interface condition and is able to maintain exactly conservation properties of the interface conditions. A detailed analysis and several numerical tests show the quality of the method. Different applications, including sonic and transsonic flows and a multiphysic model are studied.