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A numerical study is presented to analyze the thermal mechanisms of unsteady,supersonic granular flow, by means of hydrodynamic simulations of theNavier-Stokes granular equations. For this purpose a paradigmatic problem ingranular dynamics such as the Faraday instability is selected. Two differentapproaches for the Navier-Stokes transport coefficients for granular materialsare considered, namely the traditional Jenkins-Richman theory for moderatelydense quasi-elastic grains, and the improved Garz\'o-Dufty-Lutsko theory forarbitrary inelasticity, which we also present here. Both solutions are comparedwith event-driven simulations of the same system under the same conditions, byanalyzing the density, the temperature and the velocity field. Importantdifferences are found between the two approaches leading to interestingimplications. In particular, the heat transfer mechanism coupled to the densitygradient which is a distinctive feature of inelastic granular gases, isresponsible for a major discrepancy in the temperature field and hence in thediffusion mechanisms.

A numerical study of the Navier-Stokes transport coefficients for 2D granular hydrodynamics