Two-fluid barotropic models for powder-snow avalanche flows

Yannick Meyapin (1) , Denys Dutykh (1, 2, 3) , Marguerite Gisclon (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

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.

Mots clés: two-phase flow; two-fluid flow; powder snow avalanche; Chapman-Enskog expansion

Domaines: Mécanique des fluides [physics.class-ph]; Equations aux dérivées partielles [math.AP]; Géophysique [physics.geo-ph]; Dynamique des Fluides [physics.flu-dyn]; Physique Numérique [physics.comp-ph]; Milieux fluides et réactifs; Glaciologie

Yannick Meyapin, Denys Dutykh, Marguerite Gisclon. Two-fluid barotropic models for powder-snow avalanche flows. Computational Science and High Performance Computing IV, Springer Berlin Heidelberg, pp.219-232, 2011, 978-3-642-17770-5. ⟨10.1007/978-3-642-17770-5_17⟩. ⟨hal-00394437⟩