Modélisation des avalanches denses Approches théorique et numérique

Modelling flowing avalanches

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Abstract

This paper focuses on physical and numerical modelling of flowing avalanches. The first part of this investigation examines previous models : it is shown that our sound knowledge of avalanches are insufficient, be it through the rheology of snow or through the accuracy of models. The second part presents a mathematical model based on mass and momentum equations. As constitutive relation, we use a Bingham law. Equations are written in curvilinear coordinates for one-dimensional simply sheared flow. For transient laminar regime, wall friction is calculated using the formula of corresponding uniform steady regime. The numerical resolution of this hyperbolic system is performed by a Godunov's scheme. Numerical simulations show that density variations during flow have no influence on large avalanches and that the determination of yield stress is essential for a correct velocity estimation.