A flow composed of two populations of pedestrians moving in different directions is modeled by a two-dimen\-sional system ofconvection-diffusion equations. An efficient simulation of the two-dimensional model is obtained by a finite-volume scheme combinedwith a fully adaptive multiresolution strategy. Numerical tests showthe flow behavior in various settings of initial and boundaryconditions, where different species move in countercurrent orperpendicular directions.The equations are characterized ashyperbolic-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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Berres et al. (2011) studied this question.
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