On a Nonlinear Pressure Algorithm for Dilute and Dense Granular Flow

Abstract

Granular flow is broadly classified into two distinct regimes. The first is rapid granular flow where particle collisions are assumed to be instantaneous and the second is dense granular flow where particles move together and slide on each other. Many contributions on the modelling of granular flow and the solving of such models numerically, restrict themselves to one of these distinct regimes. In some applications this is not possible. Because many features of granular media can be reproduced by a system of smooth hard spheres with inelastic collisions, it is tempting to extend the hydrodynamic modelling often used for rapid granular flow to the dense regime by means of algebraic relations. We present here a kinetic modelling approach inheriting a dynamic Coulomb friction for the dilute regime extended by a smooth transition to a full Coulomb friction for dense granular flow. The system of hydrodynamic equations together with strongly nonlinear, diverging algebraic relations for the system quantities pos...