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Bound-Preserving High Order Finite Volume Schemes for Conservation Laws and Convection-Diffusion Equations Read chapter Read first chapter

2017 | OriginalPaper | Chapter

A Simple Finite-Volume Method on a Cartesian Mesh for Pedestrian Flows with Obstacles

Authors : Yuanzhen Cheng, Alina Chertock, Alexander Kurganov

Published in: Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects

Publisher: Springer International Publishing

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Abstract

We consider a two-dimensional pedestrian flow model with obstacles governed by scalar hyperbolic conservation laws, in which the flux is implicitly dependent on the density through the Eikonal equation. We propose a simple second-order finite-volume method, which is applicable to the case of obstacles of arbitrary shapes. Though the method is only first-order accurate near the obstacles, it is robust and provides sharp resolution of discontinuities as illustrated in a number of numerical experiments.

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previous chapter Some Discrete Functional Analysis Tools
next chapter Benchmark Proposal for the FVCA8 Conference: Finite Volume Methods for the Stokes and Navier–Stokes Equations
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Metadata
Title
A Simple Finite-Volume Method on a Cartesian Mesh for Pedestrian Flows with Obstacles
Authors
Yuanzhen Cheng
Alina Chertock
Alexander Kurganov
Copyright Year
2017
Book
Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects

Print ISBN: 978-3-319-57396-0

Electronic ISBN: 978-3-319-57397-7

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-57397-7_4

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