ABSTRACT
Since recently, computational hydrodynamics is being widely applied to study flow and instabilities in granular media. The microscopic foundation lies on hydrodynamic descriptions derived from Boltzmann equations for granular gases by following standard moment methods or expansions around either local Maxwellians or homogeneous cooling states. Inelasticity is incorporated via a constant or velocity dependent restitution coefficient in the collision model. At the macroscopic level, there is a huge set of transport equations for granular gases in the literature, depending on the assumptions on the restitution coefficient, the type of expansion and the equation of state considered (Jenkins and Richman 1985; Goldshtein and Shapiro 1995; Sela and Goldhirsch 1998). While strictly, hydrodynamic descriptions cease to be valid approaching close-packing situations, such models have however been used successfully in situations far from their supposed limits of validity, to describe for instance shock waves in granular gases (Rericha et al. 2002; Bougie et al. 2002; Bougie et al. 2002) or clustering (Hill and Mazenko 2003; Brilliantov et al. 2004).
