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Application of the Method of Generating Functions to the Derivation of Grad’s N-Moment Equations for a Granular Gas

Published online by Cambridge University Press:  18 July 2011

S. H. Noskowicz  and
D. Serero
S. H. Noskowicz*
Affiliation:
School of Mechanical Engineering, Faculty of engineering, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, Israel
D. Serero
Affiliation:
Institute for Multiscale Simulation, Universität Erlangen-Nürnberg, Nägelsbachstraße 49b, 91052 Erlangen, Germany
*
⋆ Corresponding author. E-mail: henri@eng.tau.ac.il and sh.noskowicz@gmail.com
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Abstract

A computer aided method using symbolic computations that enables the calculation of the source terms (Boltzmann) in Grad’s method of moments is presented. The method is extremely powerful, easy to program and allows the derivation of balance equations to very high moments (limited only by computer resources). For sake of demonstration the method is applied to a simple case: the one-dimensional stationary granular gas under gravity. The method should find applications in the field of rarefied gases, as well. Questions of convergence, closure are beyond the scope of this article.

Keywords

Grad’s method of momentsgranular gasgenerating functioncomputer aided
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 4: Granular hydrodynamics , 2011 , pp. 151 - 174
Copyright
© EDP Sciences, 2011

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