Pressureless Euler equations with maximal density constraint : a time-splitting scheme

Schéma de discrétisation en temps pour les équations d'Euler sans pression avec contrainte de densité maximale

Bertrand Maury (1, 2) , Anthony Preux (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 DMA - Département de Mathématiques et Applications - ENS Paris

In this paper, we consider the pressureless Euler equations with a congestion constraint. This system still raises many open questions and, aside from its one-dimensional version, very few is known concerning its solutions. The strategy that we propose relies on previous works on crowd motion models with congestion in the framework of the Wasserstein space, and on a microscopic granular model with nonelastic collisions. We illustrate the approach by preliminary numerical simulations in the two-dimensional setting.

Mots clés: Pressureless Euler equations; congestion; optimal transportation

Domaines: Analyse numérique [math.NA]

Bertrand Maury, Anthony Preux. Pressureless Euler equations with maximal density constraint : a time-splitting scheme. 2015. ⟨hal-01224008⟩