Analysis and approximation of partially congested Navier-Stokes equations
In this talk, I will present and analyze a mathematical model for compressible flows subject to maximum density constraint. The aim is to model saturation phenomena (congestion) corresponding to the disappearance of one of the two phases of the mixture for two-phase mixtures. Given a fixed maximum density constraint, the solutions couple a compressible dynamic in the zones where the density is lower than this maximum density, with an incompressible dynamic in the zones where the critical value is reached, i.e. in the saturated zones. The presentation will focus on the discretization and numerical simulation of these equations by means of mixed finite volume / finite element schemes.
