Two-fluid barotropic models for powder-snow avalanche flows

TL;DR

This paper develops and analyzes two-fluid barotropic models for powder-snow avalanches, addressing hyperbolicity and simplifying the model to a single velocity and incompressible limit for better numerical handling.

Contribution

It introduces a relaxation-based single velocity model that remains hyperbolic, improving the mathematical and numerical treatment of powder-snow avalanche flows.

Findings

The compressible two-velocity model can be non-hyperbolic.

The relaxation process yields a hyperbolic single velocity model.

An incompressible limit of the model is derived.

Abstract

In the present study we discuss several modeling issues of powder-snow avalanche flows. We take a two-fluid modeling paradigm. For the sake of simplicity, we will restrict our attention to barotropic equations. We begin the exposition by a compressible model with two velocities for each fluid. However, this model may become non-hyperbolic and thus, represents serious challenges for numerical methods. To overcome these issues, we derive a single velocity model as a result of a relaxation process. This model can be easily shown to be hyperbolic for any reasonable equation of state. Finally, an incompressible limit of this model is derived.