Boundary layers and shock profiles for the discrete Boltzmannequation for mixtures

Niclas Bernhoff

doi:10.3934/krm.2012.5.1

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2012, Volume 5, Issue 1: 1-19. Doi: 10.3934/krm.2012.5.1

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Boundary layers and shock profiles for the discrete Boltzmann equation for mixtures

Niclas Bernhoff^1,

1.
Department of Mathematics, Karlstad University, 651 88 Karlstad

Received: December 31, 2010

Revised: May 31, 2011

Published: February 2012

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Abstract

We consider the discrete Boltzmann equation for binary gas mixtures. Some known results for half-space problems and shock profile solutions of the discrete Boltzmann for single-component gases are extended to the case of two-component gases. These results include well-posedness results for half-space problems for the linearized discrete Boltzmann equation, existence results for half-space problems for the weakly non-linear discrete Boltzmann equation, and existence results for shock profile solutions of the discrete Boltzmann equation. A characteristic number, corresponding to the speed of sound in the continuous case, is calculated for a class of symmetric models. Some explicit calculations are also made for a simplified 6 + 4 -velocity model.

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Mathematics Subject Classification: Primary: 82C40; Secondary: 35Q20, 76P05.

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