Entropy-stable in- and outflow boundary conditions for the compressible Navier-Stokes equations

TL;DR

This paper introduces entropy-stable inflow and outflow boundary conditions for the compressible Navier-Stokes equations, ensuring stability and robustness in numerical simulations.

Contribution

It develops new boundary conditions that guarantee a priori entropy, mass, and energy estimates and demonstrates their implementation with entropy-stable finite-volume schemes.

Findings

Boundary conditions allow a priori entropy estimates.

Numerical scheme demonstrates robustness.

Applicable to various entropy-stable schemes.

Abstract

We propose inflow and outflow boundary conditions for the compressible Navier-Stokes equations and prove that they allow a priori estimates of the entropy, mass and total energy. Furthermore, we demonstrate how to approximate these boundary conditions in conjunction with an entropy-stable finite-volume scheme. The method is also applicable to other types of entropy-stable schemes. Finally, we carry out some numerical computations with the finite-volume scheme and demonstrate their robustness.