The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: We first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people; The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here the underlying mathematical framework, and we explain how recent results by J.F. Edmond and L. Thibault on the sweeping process by uniformly prox-regular sets can be adapted to handle this situation in terms of well-posedness. We propose a numerical scheme for this contact dynamics model, based on a prediction-correction algorithm. Numerical illustrations are finally presented and discussed.
Laboratoire de Mathématiques d’Orsay, Université Paris-Sud（巴黎南大学奥赛数学实验室）；LAMAV, Université de Valenciennes et du Hainaut-Cambrésis（瓦朗谢纳及埃诺-卡姆布雷大学LAMAV）
A structure--preserving ALE--BGN--MDR method for Navier--Stokes free boundary problems with moving contact lines and gravity
Universität Regensburg（雷根斯堡大学）；The Hong Kong Polytechnic University（香港理工大学）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
Numerical analysis of the Biot equations coupled to frictional contact mechanics
Department of Mathematics, University of Bergen（卑尔根大学数学系）；Center for Modeling of Coupled Subsurface Dynamics, Department of Mathematics, University of Bergen（卑尔根大学耦合地下动力学建模中心）
