This article is cited in 9 papers

Method of adaptive artificial viscosity for solving the Navier–Stokes equations

I. V. Popov^ab, I. V. Fryazinov<sup>a

a</sup> Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia
^b National Research Nuclear University MEPhI, Kashirskoe shosse 31, Moscow, 115409, Russia

Abstract: A numerical technique based on the method of adaptive artificial viscosity is proposed for solving the viscous compressible Navier–Stokes equations in two dimensions. The Navier–Stokes equations is approximated on unstructured meshes, namely, on triangular or tetrahedral elements. The monotonicity of the difference scheme according to the Friedrichs criterion is achieved by adding terms with adaptive artificial viscosity to the scheme. The adaptive artificial viscosity is determined by satisfying the maximum principle conditions. An external flow around a cylinder at various Reynolds numbers is computed as a numerical experiment.

Key words: difference scheme, Navier–Stokes equations, adaptive artificial viscosity, numerical method.

UDC: 519.63

Received: 09.02.2015

DOI: 10.7868/S0044466915080141

 English version: Computational Mathematics and Mathematical Physics, 2015, 55:8, 1324–1329

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