Abstract
We consider the Pedestrian Flow Equations (PFEs) to model evacuation scenarios as a coupled system formed by a functional minimization problem for the desired direction of movement and a first order hyperbolic system with source term. The operator splitting is proposed for the numerical solution of the coupled system. The functional minimization is based on the modified Dijkstra’s algorithm for the fastest path in a graph. The hyperbolic system is discretized by the combination of the Finite Volume Method (FVM) for the space discretization and the Discontinuous Galerkin Method (DGM) for the implicit time discretization. The original numerical flux of the Vijayasundaram type is used in the FVM. The standard approach for the desired direction of motion of pedestrians based on the solution of the Eikonal Equation is replaced by the functional minimization, which, together with the implicit time discontinuous Galerkin method, is the novelty of this paper. The relation between the proposed functional minimization and the Eikonal Equation is mentioned. The numerical examples of the solution of the PFEs are presented.
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