CREUSÉ , Emmanuel

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...

This presentation is an overview on the development of numerical methods for the simulation of non homogeneous flows with incompressibility constraints. We are particularly interested in systems of PDEs describing certain mixture flows, like the Kazhikhov–Smagulov system which can be used to model powder–snow avalanches. It turns out that the...

When one solves PDEs modelling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. For instance, the underlying physical assumptions for the Euler equations are the positivity...