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arXiv · 1705.00931

Finite Volume approximations of the Euler system with variable congestion

Pierre Degond·Piotr Minakowski·Laurent Navoret·Ewelina Zatorska
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Abstract

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. 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 extended here to higher order accuracy. We finally carry out two dimensional numerical simulations and show that the model exhibit typical crowd dynamics.

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Pierre Degond, Piotr Minakowski, Laurent Navoret, Ewelina Zatorska. 2017-05-02. Finite Volume approximations of the Euler system with variable congestion. https://doi.org/10.1016/j.compfluid.2017.09.007

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