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

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.

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