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Convergence Study of Moment Approximations for Boundary Value Problems of the Boltzmann-BGK Equation

Part of: Equilibrium statistical mechanics Rarefied gas flows, Boltzmann equation Hyperbolic equations and systems

Published online by Cambridge University Press:  14 September 2015

Manuel Torrilhon
Manuel Torrilhon*
Affiliation:
Center for Computational Engineering Science, RWTH Aachen University, Germany
*
*Corresponding author. Email address: [email protected] (M. Torrilhon)
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Abstract

The accuracy of moment equations as approximations of kinetic gas theory is studied for four different boundary value problems. The kinetic setting is given by the BGK equation linearized around a globally constant Maxwellian using one space dimension and a three-dimensional velocity space. The boundary value problems include Couette and Poiseuille flow as well as heat conduction between walls and heat conduction based on a locally varying heating source. The polynomial expansion of the distribution function allows for different moment theories of which two popular families are investigated in detail. Furthermore, optimal approximations for a given number of variables are studied empirically. The paper focuses on approximations with relatively low number of variables which allows to draw conclusions in particular about specific moment theories like the regularized 13-moment equations.

Keywords

Kinetic gas theoryHermite expansionchannel flow

MSC classification

Secondary: 82B40: Kinetic theory of gases 76P05: Rarefied gas flows, Boltzmann equation 35L65: Conservation laws
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 3 , September 2015 , pp. 529 - 557
Copyright
Copyright © Global-Science Press 2015 

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