Séminaire EDP-Analyse ICJ

Transport of congestion in two-phase compressible/incompressible flow

par Ewelina Zatorska (University College London)

Fokko Du Cloux (ICJ, Université Claude Bernard Lyon 1)

Fokko Du Cloux

ICJ, Université Claude Bernard Lyon 1

Campus de la Doua, Bâtiment Braconnier, Villeurbanne
Can the fluid equations be used to model pedestrian motion or traffic? In this talk, I will present the compressible-incompressible two phase system describing the flow in the free and in the congested regimes. I will show how to approximate such system by the compressible Navier-Stokes equations with singular pressure for the fixed barrier densities, together with some recent developments for the barrier densities varying in the space and time. At the end, I will present the numerical results showing that our macroscopic system captures some features characteristic for microscopic models of collective behaviour. This is a talk based on several papers in collaboration with: D. Bresch, C. Perrin, P. Degond, P. Minkowski, and L. Navoret.
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