Mathematical modeling of powder-snow avalanche flows

Denys Dutykh (1, 2, 3) , Céline Acary-Robert (1) , Didier Bresch (1)

1 LAMA - Laboratoire de Mathématiques
2 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
3 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc

Powder-snow avalanches are violent natural disasters which represent a major risk for infrastructures and populations in mountain regions. In this study we present a novel model for the simulation of avalanches in the aerosol regime. The second scope of this study is to get more insight into the interaction process between an avalanche and a rigid obstacle. An incompressible model of two miscible fluids can be successfully employed in this type of problems. We allow for mass diffusion between two phases according to the Fick's law. The governing equations are discretized with a contemporary fully implicit finite volume scheme. The solver is able to deal with arbitrary density ratios. Several numerical results are presented. Volume fraction, velocity and pressure fields are presented and discussed. Finally we point out how this methodology can be used for practical problems.

Mots clés: snow avalanche; gravity-driven flow; miscible fluids; two-phase flow; Fick's law; finite volumes

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Géophysique [physics.geo-ph]; Géophysique [physics.geo-ph]; Milieux et Changements globaux; Milieux fluides et réactifs; Analyse numérique [math.NA]; Physique Numérique [physics.comp-ph]; Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]; Glaciologie

Denys Dutykh, Céline Acary-Robert, Didier Bresch. Mathematical modeling of powder-snow avalanche flows. Studies in Applied Mathematics, 2011, 127 (1), pp.38-66. ⟨10.1111/j.1467-9590.2010.00511.x⟩. ⟨hal-00354000v4⟩