Approximating viscosity solutions of the Euler system

Feireisl, Eduard; Lukáčová-Medvid’ová, Mária; Schneider, Simon; She, Bangwei

doi:10.1090/mcom/3738

Approximating viscosity solutions of the Euler system
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by Eduard Feireisl, Mária Lukáčová-Medvid’ová, Simon Schneider and Bangwei She HTML | PDF

Math. Comp. 91 (2022), 2129-2164 Request permission

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.

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