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

S. H. Noskowicz;  D. Serero — 2011

Mathematical Modelling of Natural Phenomena

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...

Theory of Dilute Binary Granular Gas Mixtures

D. Serero;  S. H. Noskowicz;  I. Goldhirsch — 2010

Mathematical Modelling of Natural Phenomena

A computer-aided method for accurately carrying out the Chapman-Enskog expansion of the Boltzmann equation, including its inelastic variant, is presented and employed to derive a hydrodynamic description of a dilute binary mixture of smooth inelastic spheres. Constitutive relations, formally valid for all physical values of the coefficients of restitution, are calculated by carrying out the pertinent Chapman-Enskog expansion to sufficient high orders in the Sonine polynomials to ensure numerical...

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