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

Please always quote using this URN: urn:nbn:de:bvb:29-opus-38642
  • 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.

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Author:S. H. Noskowicza, Dan Serero
Document Type:Article
Year of Completion:2011
Publishing Institution:Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Release Date:2012/11/15
Tag:Grad’s method of moments; computer aided; generating function; granular gas
Original publication:Mathematical Modelling of Natural Phenomena 6.4 (2011): S. 151-174. 09.11.2012 <>
Institutes:Naturwissenschaftliche Fakultät / Naturwissenschaftliche Fakultät -ohne weitere Spezifikation-
Dewey Decimal Classification:Naturwissenschaften und Mathematik / Naturwissenschaften / Naturwissenschaften und Mathematik
MSC-Classification:82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) / 82C40 Kinetic theory of gases
82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Dxx Applications to specific types of physical systems / 82D05 Gases
open_access (DINI-Set):open_access
Collections:Universität Erlangen-Nürnberg / Allianzlizenzen: Alle Beiträge sind mit Zustimmung der Rechteinhaber aufgrund einer DFG-geförderten Allianzlizenz frei zugänglich. / Allianzlizenzen 2011