Visco-plastic fluids and free-surface
are natural phenomena that occur in mountainous regions such as Alps in
France. As usually in complex phenomena, it is very difficult to
postulate a constitutive relation for the stress tensor in terms of a
deformation measure that correctly descrives avalanches behavior.
During the last few year, more and more efforts have been devoted to the physical understanding of avalanche formation.
this talk, we will derive an example of compressible visco-plastic
model occuring as a depth averaged system. Then we present a
generalization to compressible flows of the Augmented Lagrangian method
for incompressible Bingham visco-plastic flow initiated by R.
Glowinski. We will see on several numerical tests that there exists a
real interaction between the finite volume scheme and the Augmented
Lagrangian procedure. We will also present some other models sometimes
used in Avalanches and the mathematical difficulties encountoured for
instance to establish the existence of global weak solutions. Part of
this talk is a joint work with E. Fernandez-Nieto, I. Ionescu, P.