A higher-order macroscopic model for bi-direction pedestrian flow

In this paper, a higher-order macroscopic model for bi-direction pedestrian flow is presented to investigate macroscopic crowd patterns of bi-direction pedestrian movement. For each group, the macroscopic model consists of two-dimensional Euler equations with relaxation and an Eikonal-type equation. The magnitude of the desired velocity is described by an empirical relation between density and speed, while its direction is chosen to minimize the total instantaneous walking cost which satisfies a reactive user equilibrium assignment pattern. The dynamic model is numerically solved by a splitting technique and a cell-centered finite volume method on an orthogonal grid. Typical numerical examples of bi-direction pedestrian flow walking in a channel are designed to validate the rationality of the dynamic model and the effectiveness of the numerical algorithm.