Research Article
An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model
Yinhua Xia,
S. C. Wong,
Mengping Zhang,
Chi-Wang Shu,
William H. K. Lam,
Yinhua Xia
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
Search for more papers by this authorCorresponding Author
S. C. Wong
Department of Civil Engineering, The University of Hong Kong, Hong Kong, China
Department of Civil Engineering, The University of Hong Kong, Hong Kong, ChinaSearch for more papers by this authorMengping Zhang
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
Search for more papers by this authorChi-Wang Shu
Division of Applied Mathematics, Brown University, Providence, RI 02912, U.S.A.
Search for more papers by this authorWilliam H. K. Lam
Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong, China
Search for more papers by this authorYinhua Xia,
S. C. Wong,
Mengping Zhang,
Chi-Wang Shu,
William H. K. Lam,
Yinhua Xia
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
Search for more papers by this authorCorresponding Author
S. C. Wong
Department of Civil Engineering, The University of Hong Kong, Hong Kong, China
Department of Civil Engineering, The University of Hong Kong, Hong Kong, ChinaSearch for more papers by this authorMengping Zhang
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
Search for more papers by this authorChi-Wang Shu
Division of Applied Mathematics, Brown University, Providence, RI 02912, U.S.A.
Search for more papers by this authorWilliam H. K. Lam
Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong, China
Search for more papers by this authorAbstract
In this paper, we develop a discontinuous Galerkin method on triangular meshes to solve the reactive dynamic user equilibrium model for pedestrian flows. The pedestrian density in this model is governed by the conservation law in which the flow flux is implicitly dependent on the density through the Eikonal equation. To solve the Eikonal equation efficiently at each time level, we use the fast sweeping method. Two numerical examples are then used to demonstrate the effectiveness of the algorithm. Copyright © 2008 John Wiley & Sons, Ltd.
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