Conditions aux limites fortement non lin{\'e}aires pour les {\'e}quations d'Euler de la dynamique des gaz

TL;DR

This paper investigates nonlinear boundary conditions for Euler equations in gas dynamics, combining mathematical analysis and numerical methods, including a new formulation that captures nonlinear effects at boundaries.

Contribution

It introduces a novel boundary condition formulation for Euler equations that accounts for nonlinear effects and integrates seamlessly with finite volume discretization.

Findings

Classical results based on linearized analysis are reviewed.

A new nonlinear boundary condition formulation is proposed.

A significant 1D test case demonstrates the approach.

Abstract

We study various formulations of the boundary conditions for the Euler equations of gas dynamics from a mathematical and numerical point of view. In the case of one space dimension, we recall the classical results, based on an analysis of the linearized problem. Then we present a more recent formulation of the problem, which allows for nonlinear effects at the boundary of the study domain. This formulation fits naturally into a finite volume discretization, and we present a significant one-dimensional test case.