Hybrid Riemann Solvers for Large Systems of Conservation Laws

TL;DR

This paper introduces a new family of approximate Riemann solvers designed for large systems of hyperbolic conservation laws, which are more efficient and less dissipative by only requiring estimates of the fastest wave speeds without eigensystem computations.

Contribution

The paper presents a novel family of Riemann solvers that avoid characteristic decomposition, improving efficiency and reducing dissipation for large systems of conservation laws.

Findings

Reproduces all waves with less dissipation than HLL

Requires only estimates of the fastest wave speeds

Avoids computing characteristic decomposition

Abstract

In this paper we present a new family of approximate Riemann solvers for the numerical approximation of solutions of hyperbolic conservation laws. They are approximate, also referred to as incomplete, in the sense that the solvers avoid computing the characteristic decomposition of the flux Jacobian. Instead, they require only an estimate of the globally fastest wave speeds in both directions. Thus, this family of solvers is particularly efficient for large systems of conservation laws, i.e. with many different propagation speeds, and when no explicit expression for the eigensystem is available. Even though only fastest wave speeds are needed as input values, the new family of Riemann solvers reproduces all waves with less dissipation than HLL, which has the same prerequisites, requiring only one additional flux evaluation.