Convergence of a Hyperbolic Thermodynamically Compatible Finite Volume scheme for the Euler equations

TL;DR

This paper proves the convergence of a new thermodynamically compatible finite volume scheme for Euler equations, emphasizing entropy as a primary variable and ensuring energy conservation through compatible discretization.

Contribution

It introduces a novel HTC scheme that treats entropy as a main field and guarantees energy conservation via compatible discretization, advancing numerical methods for hyperbolic systems.

Findings

Scheme converges to dissipative weak solutions of Euler equations

Entropy is effectively incorporated as a main field

Energy conservation is achieved through compatible discretization

Abstract

We study the convergence of a novel family of thermodynamically compatible schemes for hyperbolic systems (HTC schemes) in the framework of dissipative weak solutions, applied to the Euler equations of compressible gas dynamics. Two key novelties of our method are i) entropy is treated as one of the main field quantities and ii) the total energy conservation is a consequence of compatible discretization and application of the Abgrall flux.