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Pedestrian Flow Models

  • There have been many crowd disasters because of poor planning of the events. Pedestrian models are useful in analysing the behavior of pedestrians in advance to the events so that no pedestrians will be harmed during the event. This thesis deals with pedestrian flow models on microscopic, hydrodynamic and scalar scales. By following the Hughes' approach, who describes the crowd as a thinking fluid, we use the solution of the Eikonal equation to compute the optimal path for pedestrians. We start with the microscopic model for pedestrian flow and then derive the hydrodynamic and scalar models from it. We use particle methods to solve the governing equations. Moreover, we have coupled a mesh free particle method to the fixed grid for solving the Eikonal equation. We consider an example with a large number of pedestrians to investigate our models for different settings of obstacles and for different parameters. We also consider the pedestrian flow in a straight corridor and through T-junction and compare our numerical results with the experiments. A part of this work is devoted for finding a mesh free method to solve the Eikonal equation. Most of the available methods to solve the Eikonal equation are restricted to either cartesian grid or triangulated grid. In this context, we propose a mesh free method to solve the Eikonal equation, which can be applicable to any arbitrary grid and useful for the complex geometries.

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Author:Raghavender Etikyala
URN (permanent link):urn:nbn:de:hbz:386-kluedo-38031
Advisor:Axel Klar
Document Type:Doctoral Thesis
Language of publication:English
Publication Date:2014/05/16
Year of Publication:2014
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2014/05/13
Date of the Publication (Server):2014/05/16
Tag:Eikonal equation; Pedestrian FLow
Number of page:109
Faculties / Organisational entities:Fachbereich Mathematik
CCS-Classification (computer science):G. Mathematics of Computing
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):35-XX PARTIAL DIFFERENTIAL EQUATIONS
65-XX NUMERICAL ANALYSIS
76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX)
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 10.09.2012