Paola Goatin, Daniel Inzunza, Luis M. Villada:
Nonlocal macroscopic models of multi-population pedestrian flows for walking facilities optimization
We propose a nonlocal macroscopic pedestrian flow model for two populations with different destinations trying to avoid each other in a confined environment, where the nonlocal term accounts for anisotropic interactions, mimicking the effect of different cones of view, and the presence of walls or other obstacles in the domain. In particular, obstacles can be incorporated in the density variable, thus avoiding to include them in the vector field of preferred directions. In order to compute the solution, we propose a Finite Difference scheme that couples highorder WENO approximations for spatial discretization, a multi-step TVD method for temporal discretization, and a high-order numerical derivative formula to approximate the derivatives of nonlocal terms, and in this way avoid excessive calculations. Numerical tests confirm that each population manages to evade both the presence of the obstacles and the other population. The evacuation time problem is studied, in particular, the optimal position of the obstacles is obtained using a total travel time optimization processes.