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.
- Crowd model
- Elliptic region
- Fully adaptive multiresolution
- Mixed hyperbolic-elliptic system
- Multiphase flow
- System of conservation laws