A discrete contact model for crowd motion
A discrete contact model for crowd motion
复制标题
人群运动的离散接触模型
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Juliette Venel
中科院分区：
文献类型：
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作者：
B. Maury;Juliette Venel
本文的目的是开发一种人群运动模型，旨在处理高度拥挤的情况。我们提出的模型基于两个原则：我们首先定义一个自发速度，它对应于每个人在没有其他人的情况下希望拥有的速度。然后将实际速度计算为自发速度在允许速度集（即不违反非重叠约束的速度）上的投影。我们在这里描述了底层的数学框架，并解释了 J.F. Edmond 和 L. Thibault 在一致近正则集的扫掠过程上的最新结果如何能够适应于在适定性方面处理这种情况。我们基于预测校正算法提出了该接触动力学模型的数值方案。最后给出并讨论了数值例证。
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.