| Issue |
Math. Model. Nat. Phenom.
Volume 6, Number 4, 2011
Granular hydrodynamics
|
|
|---|---|---|
| Page(s) | 151 - 174 | |
| DOI | https://doi.org/10.1051/mmnp/20116407 | |
| Published online | 18 July 2011 | |
Application of the Method of Generating Functions to the Derivation of Grad’s N-Moment Equations for a Granular Gas
1
School of Mechanical Engineering, Faculty of engineering, Tel-Aviv
University, Ramat-Aviv, Tel-Aviv
69978,
Israel
2
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
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.
Mathematics Subject Classification: 82C40 / 82D05
Key words: Grad’s method of moments / granular gas / generating function / computer aided
© EDP Sciences, 2011
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