Approximating viscosity solutions of the Euler system

Bangwei She; Eduard Feireisl; M\'aria Luk\'a\v{c}ov\'a-Medvi\v{d}ov\'a; Simon Schneider

arxiv: 2102.07876 · v2 · pith:SXKUGBXJnew · submitted 2021-02-15 · 🧮 math.NA · cs.NA

Approximating viscosity solutions of the Euler system

Eduard Feireisl , M\'aria Luk\'a\v{c}ov\'a-Medvi\v{d}ov\'a , Simon Schneider , Bangwei She This is my paper

classification 🧮 math.NA cs.NA

keywords viscosityeulersolutionssystemnumericalapplyingapproximatingaveraging

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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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Approximating viscosity solutions of the Euler system

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