Hybrid Entropy Stable HLL-Type Riemann Solvers for Hyperbolic Conservation Laws
Provides entropy-stable, less dissipative HLL-type solvers for hyperbolic conservation laws, benefiting computational fluid dynamics and MHD simulations.
The authors prove that several HLL-type Riemann solvers are entropy stable and propose hybrid methods that reduce dissipation while maintaining entropy stability, demonstrated on ideal MHD equations.
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.