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An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model
Author(s) -
Xia Yinhua,
Wong S. C.,
Zhang Mengping,
Shu ChiWang,
Lam William H. K.
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2329
Subject(s) - polygon mesh , eikonal equation , discontinuous galerkin method , conservation law , galerkin method , mathematics , flow (mathematics) , eikonal approximation , mathematical optimization , pedestrian , computer science , mathematical analysis , finite element method , geometry , engineering , structural engineering , transport engineering
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.