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Numerical simulation of a continuum model for bi-directional pedestrian flow. (English) Zbl 1425.90027

Summary: An algorithm for an extended reactive dynamic user equilibrium model of pedestrian counterflow as a continuum is developed. It is based on a cell-centered high-resolution finite volume scheme with a fast sweeping method for an Eikonal-type equation on an orthogonal grid. A high-order total variation diminishing Runge-Kutta method is adopted for the time integration of semi-discrete equations. The numerical results demonstrate the rationality of the model and efficiency of the algorithm. Some crowd pedestrian flow phenomena, such as dynamic lane formation in bi-directional flow, are observed which are helpful for a global comprehension of pedestrian dynamics. Also, the model can be utilized with different potential applications.

MSC:

90B20 Traffic problems in operations research
76M12 Finite volume methods applied to problems in fluid mechanics
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