A simple finite-volume method on a cartesian mesh for pedestrian flows with obstacles

Cheng，Yuanzhen1; Chertock，Alina2; Kurganov，Alexander1,3

10.1007/978-3-319-57397-7_4

2017

2194-1009

2194-1017

Springer Proceedings in Mathematics and Statistics

199

43-55

Lille, France

Springer New York LLC

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.

Eikonal equation Fast sweeping method Finite-volume method Hyperbolic conservation laws Interface tracking method Pedestrian flow model

通讯

英语

EI ; CPCI-S

WOS:000435519100004

20172403766096

Differential equations ; Geometrical optics ; Numerical methods ; Physical properties

Light/Optics:741.1 ; Calculus:921.2 ; Numerical Methods:921.6 ; Physical Properties of Gases, Liquids and Solids:931.2

2-s2.0-85020417205

Scopus

1.Mathematics Department,Tulane University,New Orleans,70118,United States
2.Department of Mathematics,North Carolina State University,Raleigh,27695,United States
3.Department of Mathematics,Southern University of Science and Technology of China,Shenzhen,518055,China

Cheng，Yuanzhen,Chertock，Alina,Kurganov，Alexander. A simple finite-volume method on a cartesian mesh for pedestrian flows with obstacles[C]:Springer New York LLC,2017:43-55.