Approximating viscosity solutions of the Euler system

TL;DR

This paper introduces a novel approach using S-convergence to approximate viscosity solutions of the Euler system, combining theoretical analysis with efficient numerical methods and simulations of fluid instability phenomena.

Contribution

It presents a new framework for approximating viscosity solutions via S-convergence and demonstrates its effectiveness through numerical simulations of fluid instabilities.

Findings

Successful approximation of viscosity solutions using S-convergence

Efficient computation via Viscosity Finite Volume method

Numerical simulations illustrate theoretical results

Abstract

Applying the concept of S-convergence, based on averaging in the spirit of Strong Law of Large Numbers, the vanishing viscosity solutions of the Euler system are studied. We show how to efficiently compute a viscosity solution of the Euler system as the S-limit of numerical solutions obtained by the Viscosity Finite Volume method. Theoretical results are illustrated by numerical simulations of the Kelvin--Helmholtz instability problem.