On a numerical flux for the pedestrian flow equations*

The pedestrian flow equations are formulated as the hyperbolic problem with a source term, completed by the eikonal equation yielding the desired direction of the pedestrian velocity. The operator splitting consisting of successive discretization of the eikonal equation, ordinary differential equation with the right hand side being the source term and the homogeneous hyperbolic system is proposed. The numerical flux of the Vijayasundaram type is proposed for the finite volume solution of the hyperbolic problem. The Vijayasundaram numerical flux, originally proposed for the hyperbolic problems possessing the homogeneity property is extended for pedestrian flow, where the homogeneity property is lost. The application of the proposed numerical flux is demonstrated on the physically relevant problem.