Finite Volume approximations of the Euler system with variable congestion
It provides a numerical method for simulating crowd motion with individual congestion preferences, which is a specific application in fluid dynamics.
The paper develops an asymptotic preserving finite volume scheme for the Euler system with variable congestion, demonstrating second-order accuracy and validating it on 1D and 2D test cases that reproduce crowd dynamics.
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.