Hybrid Entropy Stable HLL-Type Riemann Solvers for Hyperbolic Conservation Laws

TL;DR

This paper introduces hybrid entropy-stable HLL-type Riemann solvers for hyperbolic conservation laws, reducing dissipation while maintaining entropy stability, demonstrated through ideal MHD equations.

Contribution

It develops hybrid HLL-type Riemann solvers that are provably entropy stable and less dissipative, enhancing the accuracy of numerical solutions for hyperbolic systems.

Findings

Hybrid HLL-type methods are entropy stable.

Reduced dissipation demonstrated in ideal MHD simulations.

Convex combinations improve accuracy without losing stability.

Abstract

It is known that HLL-type schemes are more dissipative than schemes based on characteristic decompositions. However, HLL-type methods offer greater flexibility to large systems of hyperbolic conservation laws because the eigenstructure of the flux Jacobian is not needed. We demonstrate in the present work that several HLL-type Riemann solvers are provably entropy stable. Further, we provide convex combinations of standard dissipation terms to create hybrid HLL-type methods that have less dissipation while retaining entropy stability. The decrease in dissipation is demonstrated for the ideal MHD equations with a numerical example.