Finite volume approximations of the Euler system with variable congestion

We are interested in the numerical simulations of the Euler system with variable congestion encoded by a singular pressure (Degond et al., 2016). 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-dimensionnal test-cases and compare it with a scheme previously proposed in Degond et al. (2016) and extended here to higher order accuracy. We finally carry out two dimensional numerical simulations and show that the model exhibit typical crowd dynamics.