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 isdescribed through a single mass density and a velocity field, with an unusual constraint thatrelates the divergence of the velocity to derivatives of the density. We discuss a derivation ofthe model from a Eulerian-Lagrangian description of the mixture. We propose a numericalscheme based on a hybrid Finite Volume/Finite Element method. This approach is validatedby comparison to analytical solutions, numerical solutions and experimental data. The schemeworks on unstructured meshes and it can be advantageously coupled to mesh refnementsstrategies in order to follow fronts of high density variation. We explore numerically therole of the leading coeffcients that characterize the flow: the Froude, the Reynolds and theSchmidt numbers.