On a nonlinear pressure algorithm for dilute and dense granular flow
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 rel ations for the system quantities pose, in discretised form, a challenging numerical problem. We present a nonlinear predictor corrector algorithm to advance this system in time together with a finite volume space discretisation. The numerical algorithm is implemented using a finite volume solver framework developed by the first author which allows discretisation on cell-centred bricks in arbitrary domains.