Berlin 2008 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 19: Granular matter I

DY 19.2: Talk

Wednesday, February 27, 2008, 14:45–15:00, MA 004

A unified hydrodynamic model for dilute and dense granular flow — •Arnulf Latz and Sebastian Schmidt — Fraunhofer Institut für Techno- und Wirtschaftsmathematik, Kaiserslautern

A continuum model for granular flow is presented, which covers the regime of fast dilute flow as well as slow dense flow up to vanishing velocity. Our model is at small and intermediate densities equivalent to a kinetic model of granular flow. The existence of an inherent instability in the kinetic model due to the vanishing kinetic pressure for small granular temperatures requires a cross over from a kinetic pressure to an athermal yield pressure at densities close to random close packing. The viscosity diverges for small temperatures analogous to the diverging viscosities of liquids close to the glass transition. The model is able to recover many features of granular flow. As examples we show simulations of sandpiles with predictable slopes, Hopper simulations with mass and core flow and angle dependent critical sand heights in granular flow down an inclined plane. We solve the system of the strongly nonlinear singular hydrodynamic equations with the help of a newly developed nonlinear time stepping algorithm together with a finite volume space discretisation. The numerical algorithm is implemented using a finite volume solver framework developed by the authors which allows discretisation on cell-centred bricks in arbitrary domains.