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JOURNALS // Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie // Archive

Vestnik YuUrGU. Ser. Mat. Model. Progr., 2013 Volume 6, Issue 1, Pages 72–84 (Mi vyuru34)

Mathematical Modelling

The New Hyperbolic Models of Heterogeneous Environments

V. S. Surov, I. V. Berezansky

South Ural State University, Chelyabinsk, Russian Federation

Abstract: Invention mathematically and physically correct models multiphase environment is an important problem, since many of the available models of heterogeneous environment are not such. In this paper, for multi-component environment offers two new models - single- and multi-velocity approximations. The models are based on the laws of conservation. Viscous and heat-conducting properties of the mixture are considered. For the described models is constructed automodels solution kind of traveling wave. On the example of a binary mixture have done of calculations for single- and multi-velocity approximations. It is shown that, if the use of the relaxation of the laws for the dissipative processes then the system of equations are hyperbolic.

Keywords: multicomponent viscous heat-conducting mixture, singlevelocity and multivelocity multicomponent medium, hyperbolic systems of partial differential equations, automodel solutions.

UDC: 532.529.5

MSC: 35Q35

Received: 21.11.2012



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