Macroscopic First Order Models of Multicomponent Human Crowds with Behavioral Dynamics
This paper presents a new approach to the behavioral dynamics of human crowds. Macroscopic first order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional process by
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Abstract This paper presents a new approach to the behavioral dynamics of human crowds. Macroscopic first order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional process by which walkers select their velocity direction. The present approach is applied to describe the dynamics of a homogeneous crowd in venues with complex geometries. Numerical results are obtained using a finite volume method on unstructured grids. Our results visualize the predictive ability of the model. Solutions for heterogeneous crowd can be obtained by the same technique where crowd heterogeneity is modeled by dividing the whole system into subsystems identified by different features.
1 Plan of the Paper The modeling of crowd dynamics can be developed, at the three scales, namely microscopic (individual based), macroscopic (corresponding to the dynamics of mean averaged quantities), and to the intermediate mesoscopic (corresponding to the dynamics of a probability distribution function over the microscopic scale state of individuals), see the book [11]. The latter approach is such that interactions are modeled at the micro-scale, while mean quantities, such as local number density and linear momentum, are obtained by velocity weighted moments of the aforesaid probability distribution. A critical analysis of the advantages and drawbacks of the different scales selected for the modeling approach is discussed in various papers, [3, 7, 9] where it is stated that the present state of the art does not yet allow well-defined hallmarks
N. Bellomo () King Abdulaziz University, Jeddah, Saudi Arabia Politecnico di Torino, Torino, Italy e-mail: [email protected] S. Berrone • L. Gibelli • A.B. Pieri Department of Mathematical Sciences, Politecnico di Torino, Torino, Italy e-mail: [email protected]; [email protected]; [email protected] © Springer International Publishing Switzerland 2016 Y. Bazilevs, K. Takizawa (eds.), Advances in Computational Fluid-Structure Interaction and Flow Simulation, Modeling and Simulation in Science, Engineering and Technology, DOI 10.1007/978-3-319-40827-9_23
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to support an optimal choice. A detailed investigation has been carried out to understand the complex dynamics at the microscopic scale, see, among others, [13] and [15]. These models can contribute to implement both meso-scale models [5] and hybrid models [1], where the state of the system is defined in probability over the velocity direction and deterministically over the velocity. Macroscopic, hydrodynamic, models are of great interest in that they are far less computationally demanding than those at the other two scales. This requirement is particularly important when dealing with complex flows such as coupling pedestrian flows to vehicular traffic networks [10]. However, macroscopic models suffer a number of drawbacks. Firstly, the heterogeneous behavior of walkers gets lost in the averaging process needed by their d
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