Preserving the minimum principle on the entropy for the compressible Euler Equations with general equations of state

This paper is concerned with constructing an invariant-domain preserving approximation technique for the compressible Euler equations with general equations of state that preserves the minimum principle on the physical entropy. We derive a sufficient wave speed estimate for the Riemann problem under some mild thermodynamic assumptions on the equation of state. This minimum principle is guaranteed through the use of discrete auxiliary states which are in the invariant domain when using this new wave speed estimate. Finally, we numerically illustrate the proposed methodology.