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Hyperbolic Moment Equations in Kinetic Gas Theory Based on Multi-Variate Pearson-IV-Distributions

Hyperbolic Moment Equations in Kinetic Gas Theory Based on Multi-Variate Pearson-IV-Distributions
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Year:    2010

Communications in Computational Physics, Vol. 7 (2010), Iss. 4 : pp. 639–673

Abstract

In this paper we develop a new closure theory for moment approximations in kinetic gas theory and derive hyperbolic moment equations for 13 fluid variables including stress and heat flux. Classical equations have either restricted hyperbolicity regions like Grad's moment equations or fail to include higher moments in a practical way like the entropy maximization approach. The new closure is based on Pearson-Type-IV distributions which reduce to Maxwellians in equilibrium, but allow anisotropies and skewness in non-equilibrium. The closure relations are essentially explicit and easy to evaluate. Hyperbolicity is shown numerically for a large range of values. Numerical solutions of Riemann problems demonstrate the capability of the new equations to handle strong non-equilibrium.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.2009.09.049

Communications in Computational Physics, Vol. 7 (2010), Iss. 4 : pp. 639–673

Published online:    2010-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    35

Keywords:   

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  10. Numerical Study of Partially Conservative Moment Equations in Kinetic Theory

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

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  12. Theory, Numerics and Applications of Hyperbolic Problems II

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