Numerical Modeling of Two-Phase Gravitational Granular Flows with Bottom Topography
Abstract
We study a depth-averaged model of gravity-driven mixtures of solid
grains and fluid moving over variable basal surface. The particular application we
are interested in is the numerical description of geophysical flows such as avalanches
and debris flows, which typically contain both solid material and interstitial fluid.
The depth-averaged mass and momentum equations for the solid and fluid components
form a non-conservative system, where non-conservative terms involving the
derivatives 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 velocities
of the two constituents is sufficiently small.
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.