Finite Volume approximations of the Euler system with variable congestion
Numerical Analysis
2021-02-04 v1
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.
Keywords
Cite
@article{arxiv.1705.00931,
title = {Finite Volume approximations of the Euler system with variable congestion},
author = {Pierre Degond and Piotr Minakowski and Laurent Navoret and Ewelina Zatorska},
journal= {arXiv preprint arXiv:1705.00931},
year = {2021}
}