Journal
NETWORKS AND HETEROGENEOUS MEDIA
Volume 6, Issue 3, Pages 401-423Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/nhm.2011.6.401
Keywords
Crowd model; Multiphase flow; System of conservation laws; Mixed hyperbolic-elliptic system; Elliptic region; Fully adaptive multiresolution
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Funding
- Conicyt (Chile) through the Fondecyt [11080253]
- European Research Council [ERC-2008-AdG 227058]
- postdoctoral program Becas Chile
- Deutsche Forschungsgemeinschaft (German Research Foundation) [SCHW548/5-1]
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A flow composed of two populations of pedestrians moving in different directions is modeled by a two-dimensional system of convection-diffusion 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 hyperbolic-elliptic 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.
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