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On Singular Closures for the 5-Moment System in Kinetic Gas Theory

Published online by Cambridge University Press:  22 January 2015

Roman Pascal Schaerer  and
Manuel Torrilhon
Roman Pascal Schaerer*
Affiliation:
Center for Computational Engineering Science, RWTH Aachen University, Schinkelstr. 2, 52062 Aachen, Germany
Manuel Torrilhon
Affiliation:
Center for Computational Engineering Science, RWTH Aachen University, Schinkelstr. 2, 52062 Aachen, Germany
*
*Email addresses: schaerer@mathcces.rwth-aachen.de (R. P. Schaerer), mt@mathcces.rwth-aachen.de (M. Torrilhon)
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Abstract

Moment equations provide a flexible framework for the approximation of the Boltzmann equation in kinetic gas theory. While moments up to second order are sufficient for the description of equilibrium processes, the inclusion of higher order moments, such as the heat flux vector, extends the validity of the Euler equations to non-equilibrium gas flows in a natural way.

Unfortunately, the classical closure theory proposed by Grad leads to moment equations, which suffer not only from a restricted hyperbolicity region but are also affected by non-physical sub-shocks in the continuous shock-structure problem if the shock velocity exceeds a critical value. Amore recently suggested closure theory based on the maximum entropy principle yields symmetric hyperbolic moment equations. However, if moments higher than second order are included, the computational demand of this closure can be overwhelming. Additionally, it was shown for the 5-moment system that the closing flux becomes singular on a subset of moments including the equilibrium state.

Motivated by recent promising results of closed-form, singular closures based on the maximum entropy approach, we study regularized singular closures that become singular on a subset of moments when the regularizing terms are removed. In order to study some implications of singular closures, we use a recently proposed explicit closure for the 5-moment equations. We show that this closure theory results in a hyperbolic system that can mitigate the problem of sub-shocks independent of the shock wave velocity and handle strongly non-equilibrium gas flows.

Keywords

35Q2035Q35Non-equilibrium gas dynamicshyperbolic moment equationskinetic theorymaximum entropy closures

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Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 2 , February 2015 , pp. 371 - 400
Copyright
Copyright © Global Science Press Limited 2015 

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