An adaptive finite-volume method for a model of two-phase pedestrian flow | Zendy

Stefan Berres | Zendy; Ricardo Ruíz-Baier | Zendy; Hartmut Schwandt | Zendy; Elmer M. Tory | Zendy

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An adaptive finite-volume method for a model of two-phase pedestrian flow

Author(s) -

Stefan Berres,

Ricardo Ruíz-Baier,

Hartmut Schwandt,

Elmer M. Tory

Publication year - 2011

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2011.6.401

Subject(s) - finite volume method , degenerate energy levels , flow (mathematics) , mathematical analysis , phase space , space (punctuation) , diffusion , stability (learning theory) , mathematics , countercurrent exchange , dimension (graph theory) , mechanics , physics , geometry , computer science , quantum mechanics , thermodynamics , machine learning , pure mathematics , operating system

A flow composed of two populations of pedestrians moving in different directions is modeled by a two-dimensional system of convectiondiff usion equations. An efficient simulation of the two-dimensional model is obtained by a finite-volume scheme combined with a fully adaptive multiresolution strategy. Numerical tests show the flow behavior in various settings of initial and boundary conditions, where different species move in countercurrent or perpendicular directions. The equations are characterized as hyperbolicelliptic degenerate, with an elliptic region in the phase space, which in one space dimension is known to produce oscillation waves. When the initial data are chosen inside the elliptic region, a spatial segregation of the populations leads to pattern formation. The entries of the diffusion-matrix determine the stability of the model and the shape of the patterns. © American Institute of Mathematical Sciences

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