A Roe-type scheme for two-phase shallow granular flows over variable topography

A Roe-type Scheme for Two-phase Shallow Granular Flows over Variable Topography

We study a depth-averaged model of gravity-driven flows made of solid grains and fluid, moving over variable basal surface. In particular, we are interested in applications to geophysical flows such as avalanches and debris flows, which typically contain both solid material and interstitial fluid. The model system consists of mass and momentum balance equations for the solid and fluid component...

Shallow granular flows

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

1 Département de Mathématiques et Applications, École Normale Supérieure, 45, rue d’Ulm 75230 Paris cedex 05, France. [email protected] (M. Pelanti), [email protected] (F. Bouchut). 2 Département de Sismologie, Institut de Physique du Globe de Paris, 4, place Jussieu 75252 Paris cedex 05, France. [email protected] (A. Mangeney-Castelnau), [email protected] (J.-P. Vilotte).

Discontinuous Galerkin finite element method for shallow two-phase flows

We present a discontinuous Galerkin finite element method for two depth-averaged two-phase flow models. One of these models contains nonconservative products for which we developed a discontinuous Galerkin finite element formulation in Rhebergen et al. (2008) J. Comput. Phys. 227, 1887-1922. The other model is a new depth-averaged two-phase flow model we introduce for shallow two-phase flows th...

Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation

We present a class of augmented approximate Riemann solvers for the shallow water equations in the presence of a variable bottom surface. These belong to the class of simple approximate solvers that use a set of propagating jump discontinuities, or waves, to approximate the true Riemann solution. Typically, a simple solver for a system of m conservation laws uses m such discontinuities. We pres...