A minimum entropy principle in the compressible multicomponent Euler equations

Abstract

In this work, the space of admissible entropy functions for the compressible multicomponent Euler equations is explored, following up on [Harten, \textit{J. Comput. Phys.}, 49 (1), 1983, pp. 151-164]. This effort allows us to prove a minimum entropy principle on entropy solutions, whether smooth or discrete, in the same way it was originally demonstrated for the compressible Euler equations by [Tadmor, \textit{Appl. Numer. Math.}, 49 (3-5), 1986, pp. 211-219].

References in corpus (4)

• Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems
• Fast estimation from above of the maximum wave speed in the Riemann problem for the Euler equations
• Entropy-Bounded Discontinuous Galerkin Scheme for Euler Equations
• An Efficient Algorithm for the Multicomponent Compressible Navier-Stokes Equations in Low- and High-Mach Number Regimes

Cited by in corpus (4)

• Formulation of Entropy-Stable schemes for the multicomponent compressible Euler equations
• Positivity-preserving and entropy-bounded discontinuous Galerkin method for the chemically reacting, compressible Euler equations. Part I: The one-dimensional case
• Positivity-preserving and entropy-bounded discontinuous Galerkin method for the chemically reacting, compressible Euler equations. Part II: The multidimensional case
• Entropy-Stable Schemes in the Low-Mach-Number Regime: Flux-Preconditioning, Entropy Breakdowns, and Entropy Transfers