Modeling and simulation of mixture flows: Application to powder-snow avalanches

We are concerned with the numerical simulation of certain multi-fluids flows, which in particular arise in the modeling of powder-snow avalanches. The behavior of the mixture is described through a single mass density and a velocity field, with an unusual constraint that relates the divergence of the velocity to derivatives of the density. We discuss a derivation of the model from a Eulerian-Lagrangian description of the mixture. We propose a numerical scheme based on a hybrid Finite Volume/Finite Element method. This approach is validated by comparison to analytical solutions, numerical solutions and experimental data. The scheme works on unstructured meshes and it can be advantageously coupled to mesh refinements strategies in order to follow fronts of high density variation. We explore numerically the role of the leading coefficients that characterize the flow: the Froude, the Reynolds and the Schmidt numbers. (C) 2014 Elsevier Ltd. All rights reserved.