Abstract
Prediction-Correction algorithm is used to handle the congestion in some
pedestrian flow model (of second order). The idea consists in transporting the
population according to a spontaneous velocity field at a first step, and then
straighten up the density using some kind of projection. It was used first in a
pioneering work by B. Maury and al. where the projection is taken in -Wasserstein
space. In this talk, we’ll give an overview on this algorithm and we propose a new
manner to handle this kind of algorithms showing how these algorithms are
closely connected to nonlinear diffusion diffusion-transport equation of Hele-Shaw
type. We focus the conference on two types of strategy and we present the
main theoretical and numerical results that we obtain on these models.