Approximating viscosity solutions of the Euler system

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.