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.