The project concerns of a week of collaborative research on numerical simulations of macroscopic models for crowd dynamics. Understanding crowd dynamics is a question of interest, particularly regarding safety issues for the evacuation of large buildings, concert halls, festivals … ln the last decades, many math­ematical models have been proposed in order to allow numerical simulations of such phenomena. The goal of this project is to compare numerically several of these models. The first model we want to include in our comparison is the Hughes’ model [6] that couples two first order non-linear PDEs. We will also consider on a class of models based on the theory of Mean Field Garnes (some examples may be found in [7, 1, 2] for instance). The last class of model we want to include in our comparison are the modified versions of the Hughes’ model, either with non-local term [3, 4], or with regularized equations [5]. We want to determine whether the models can reproduce some well known phenomena, such as the « Faster is slower » effect and the Braess paradox. ln addition, we will also try to simulate the evacuation of realistic festival sites. Finally, we hope that this numerical study will also lead to improvements of existing models and lead to further theoretical investigations.
These questions arise directly when considering our three different fields of expertise (Mean Field Garnes for Jules, Hughes’ model for Théo and scalar conservation law and numerics for Florian).