Numerical Modeling of Two-Phase Gravitational Granular Flows with Bottom Topography

International audience ; We study a depth-averaged model of gravity-driven mixtures of solidgrains and fluid moving over variable basal surface. The particular application weare interested in is the numerical description of geophysical flows such as avalanchesand debris flows, which typically contain both solid material and interstitial fluid.The depth-averaged mass and momentum equations for the solid and fluid componentsform a non-conservative system, where non-conservative terms involving thederivatives of the unknowns couple together the sets of equations of the two phases.The system can be shown to be hyperbolic at least when the difference of velocitiesof the two constituents is sufficiently small.We numerically solve the model equations in one dimension by a finite volumescheme based on a Roe-type Riemann solver. Well-balancing of topography sourceterms is obtained via a technique that includes these contributions into the wavestructure of the Riemann solution.