publication . Doctoral thesis . 2016

Microscopic and macroscopic models for pedestrian crowds

Makmul, Juntima;
Open Access English
  • Published: 01 Jan 2016
  • Country: Germany
Abstract
This thesis is concerned with microscopic and macroscopic models for pedes- trian crowds. In the first chapter, we consider pedestrians exit choices and model human behaviour in an evacuation process. Two microscopic models, discrete and continuous, are studied in this chapter. The former is a cellular automaton model and the latter is a social force model. Different numerical test cases are investigated and their results are compared. In chapter 2, a hierarchy of models for pedestrian flows is derived. We examine a detailed microscopic social force model coupled to a local visibil- ity model on the one hand and macroscopic models including the interaction force...
Subjects
free text keywords: 510 Mathematik
Related Organizations
Download from
37 references, page 1 of 3

1 Exit Selection and Pedestrian Evacuation Models 9 1.1 Cellular Automata . . . . . . . . . . . . . . . . . . . . . . . . 9 1.1.1 Model Description . . . . . . . . . . . . . . . . . . . . 9 1.1.2 Exit Selection Model . . . . . . . . . . . . . . . . . . . 12 1.1.3 Extended Model . . . . . . . . . . . . . . . . . . . . . 19 1.2 Social Force Model . . . . . . . . . . . . . . . . . . . . . . . . 31 1.2.1 Model Description . . . . . . . . . . . . . . . . . . . . 32 1.2.2 Exit Selection Model . . . . . . . . . . . . . . . . . . . 34 1.2.3 Extended Model . . . . . . . . . . . . . . . . . . . . . 37 1.3 Numerical Method . . . . . . . . . . . . . . . . . . . . . . . . 40 1.3.1 The Eikonal Equation . . . . . . . . . . . . . . . . . . 40 1.3.2 The Advection-Diffusion Equation . . . . . . . . . . . . 47 1.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . 60 1.4.1 Unadventurous and Group Effects . . . . . . . . . . . . 61 1.4.2 Inertial Effect . . . . . . . . . . . . . . . . . . . . . . . 68 1.4.3 Smoke Spreading Effect . . . . . . . . . . . . . . . . . 69 1.4.4 Flow with the Stream Effect . . . . . . . . . . . . . . . 75 1.4.5 Obstacle Effect . . . . . . . . . . . . . . . . . . . . . . 77 1.4.6 No Effect . . . . . . . . . . . . . . . . . . . . . . . . . 91 1.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

2 Local visibility model for pedestrian flow: a hierarchy of models and particle methods 100 2.1 Microscopic social force model . . . . . . . . . . . . . . . . . . 100 2.2 Mean field and macroscopic limits . . . . . . . . . . . . . . . . 102 2.2.1 Mean field equation . . . . . . . . . . . . . . . . . . . . 102 2.2.2 Hydrodynamic model . . . . . . . . . . . . . . . . . . . 104 2.2.3 The Scalar Model . . . . . . . . . . . . . . . . . . . . . 106 2.3 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . 107

[1] K. Abe. Human science of panic. Brain Pub. Co., Tokyo, 1986.

[2] S. Ahmed, S. Bak, J. Mclaughlin, and D. Renzi. A third order accurate fast marching method for the eikonal equation in two dimensions. Society for Industrial and Applied Mathematics.SIAM J. SCI. COMPUT, 33(5), pages 2402-2420, 2011.

[3] L.E. Aik and T.W. Choon. Simulating evacuations with obstacles using a modified dynamic cellular automata model. Hindawi Publishing Corporation, 2012. [OpenAIRE]

[4] R. Alizadeh. A dynamic cellular automaton model for evacuation process with obstacles. Safety Science 49, pages 315-323, 2011.

[11] C. Burstedde, A. Kirchner, K. Klauck, A. Schadschneider, and J. Zittartz. Cellular automaton approach to pedestrian dynamics - applications. Pedestrian and Evacuation Dynamics (Springer 2001), page 87, 2001. [OpenAIRE]

[12] S.C. Cao, W.G. Song, X.D. Liu, and N. Mu. Simulation of pedestrian evacuation in a room under fire emergency. Procedia Engineering 71. Published by Elsevier Ltd., pages 403-409, 2014.

[13] J.A. Carrillo, M.R. D'Orsogna, and V. Panferov. Double milling in self-propelled swarms from kinetic theory. Kinetic and related models 2, pages 363-378, 2009. [OpenAIRE]

[14] T.F. Chan. Stability analysis of finite difference schemes for the advection diffusion equation. SIAM Journal of Numerical Analysis 21, pages 272-283, 1984.

[15] J.K. Chen, J.E. Beraun, and T.C. Carney. A corrective smoothed particle method for boundary value problems in heat conduction. Internat. J. Numer. Methods Engrg 46, pages 231-252, 1999.

[16] Y. Chuang, M.R. DOrsogna, D. Marthaler, A.L. Bertozzi, and L.S. Chayes. State transitions and the continuum limit for a 2d interacting, self-propelled particle system. Physica D 232, pages 33-47, 2007.

[17] V. Coscia and C. Canavesio. First-order macroscopic modelling of human crowd dynamics. Math. Mod. Meth. Appl. Sci. 18, pages 1217- 1247, 2008.

[18] M. Dehghan and R. Salehi. A boundary-only meshless method for numerical solution of the eikonal equation. Comput. Mech, pages 283- 294, 2011.

[19] T. Deschamps and L.D. Cohen. Fast extraction of tubular and tree 3d surfaces with front propagation methods. Pattern Recognition. 16th International Conference, pages 731-734, 2002.

37 references, page 1 of 3
Any information missing or wrong?Report an Issue