A Roe-type scheme for two-phase shallow granular flows with bottom topography

M. Pelanti, ENS Paris, France

Wednesday, February 20
at 16.15
in HG E1.2

We study a depth-averaged model of gravity-driven flows made of solid granular material and fluid, moving over variable basal surface. In particular, we are interested in applications to geophysical flows such as avalanches and debris flows, which often contain both solid components and interstitial fluid.

The model system consists of mass and momentum balance equations for the solid and fluid constituents, and it includes inter-phase drag effects. The system can be shown to be hyperbolic at least for flow regimes characterized by sufficiently small phase velocity differences.

Difficulties in the numerical approximation of this two-phase model arise from the presence of non-conservative products involving the derivatives of the unknowns that couple together the sets of equations of the two components. Here we numerically solve the model equations in one dimension by a finite volume scheme based on a Roe-type Riemann solver. Well-balancing of topography source terms is obtained via a technique that includes these contributions into the wave structure of the Riemann solution. Several numerical
experiments are presented, including problems of perturbed steady flows over non-flat bottom surface that show the efficient modeling of disturbances of equilibrium conditions.