Entropy stable boundary conditions for the Euler equations

We consider the initial-boundary value Euler equations with the aim to derive boundary conditions that yield an entropy bound for the physical (Navier-Stokes) entropy. We begin by reviewing the entropy bound obtained for standard no-penetration wall boundary conditions and propose a numerical implementation. The main results are the derivation of full-state boundary conditions (far-field, inlet, outlet) and the accompanying entropy stable implementations. We also show that boundary conditions obtained from linear theory are unable to bound the entropy and that non-linear bounds require additional boundary conditions. We corroborate our theoretical findings with numerical experiments. (C) 2020 The Author(s). Published by Elsevier Inc.