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Section: New Results

Finite Volume approximations of the Euler system with variable congestion

Participants : Pierre Degond, Piotr Minakowski, Laurent Navoret, Ewelina Zatorska.

We are interested in the numerical simulations of the Euler system with variable congestion encoded by a singular pressure. This model describes for instance the macroscopic motion of a crowd with individual congestion preferences. In [3] we propose an asymptotic preserving (AP) scheme based on a conservative formulation of the system in terms of density, momentum and density fraction. A second order accuracy version of the scheme is also presented. We validate the scheme on one-dimensional test cases and compare it with a scheme developed in a previous work and extended here to higher order accuracy. We finally carry out two-dimensional numerical simulations and show that the model exhibits typical crowd dynamics.