<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The pedestrian flow equations are formulated as the hyperbolic problem with a source term, completed by the eikonal equation yielding the desired direction of the pedestrian velocity. The operator splitting consisting of successive discretization of the eikonal equation, ordinary differential equation with the right hand side being the source term and the homogeneous hyperbolic system is proposed. The numerical flux of the Vijayasundaram type is proposed for the finite volume solution of the hyperbolic problem. The Vijayasundaram numerical flux, originally proposed for the hyperbolic problems possessing the homogeneity property is extended for pedestrian flow, where the homogeneity property is lost. The application of the proposed numerical flux is demonstrated on the physically relevant problem.</p></abstract>

The pedestrian flow equations are formulated as the hyperbolic problem with a source term, completed by the eikonal equation yielding the desired direction of the pedestrian velocity. The operator splitting consisting of successive discretization of the eikonal equation, ordinary differential equation with the right hand side being the source term and the homogeneous hyperbolic system is proposed. The numerical flux of the Vijayasundaram type is proposed for the finite volume solution of the hyperbolic problem. The Vijayasundaram numerical flux, originally proposed for the hyperbolic problems possessing the homogeneity property is extended for pedestrian flow, where the homogeneity property is lost. The application of the proposed numerical flux is demonstrated on the physically relevant problem.

On a numerical flux for the pedestrian flow equations<xref ref-type="fn" rid="fn1_w2aab2b8b9b1b7b1ab1aaAa">*</xref>

Jan Evengelista Purkyně University Faculty of Science, Department of Informatics and Czech Technical University in Prague Faculty of Nuclear Sciences and Physical Engineering Department of Informatics

Charles University in Prague Faculty of Mathematics and Physics Department of Numerical Mathematics

Journal of Applied Mathematics, Statistics and Informatics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On a numerical flux for the pedestrian flow equations

The pedestrian flow equations are formulated as the hyperbolic problem with a source term, completed by the eikonal equation yielding the desired direction of...

On a numerical flux for the pedestrian flow equations*

Published Online: Dec 30, 2015

Page range: 79 - 96

DOI: https://doi.org/10.1515/jamsi-2015-0014

© 2015 Faculty of Natural Sciences, University of Saint Cyril and Metodius

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.