OJFD  Vol.6 No.4 , December 2016
Numerical Simulation of the Flow of Crowds at the Jamarat Bridge during the Annual Hajj Event
Abstract: The huge number of pilgrims to the holy Mecca in the Hajj needs high awareness of crowd safety management. The stoning of the Jamarat, which is one of the rituals of the Hajj, undergoes the most dangerous crowd movements where fatal accidents occurred. This work investigates some problems related with the crowd dynamics when stoning the Jamarat pillars and gives some solutions. The main idea of this research is to suppose that the crowd dynamics is assimilated to fluid movement under certain conditions. Numerical simulation using a computational fluid dynamics program is used to solve Navier-Stokes equations governing the mechanics of homogeneous and incompressible fluid in a domain similar to the Jamarat Bridge from the entrance to the middle Jamarah. Some solutions are proposed inspired by the flow solutions to better manage crowd movements in the Jamarat Bridge and eventually in other similar dynamics events like sporting events.
Cite this paper: Mnasri, C. and Farhat, A. (2016) Numerical Simulation of the Flow of Crowds at the Jamarat Bridge during the Annual Hajj Event. Open Journal of Fluid Dynamics, 6, 321-331. doi: 10.4236/ojfd.2016.64024.

[1]   Zheng, X.P., Zhong, T.K. and Liu, M.T. (2009) Modeling Crowd Evacuation of a Building Based on Seven Methodological Approaches. Building and Environment, 44, 437-445.

[2]   Bellomo, N. and Dogbe, C. (2011) On The Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives. SIAM Review, 53, 409-463.

[3]   Hughes, R.L. (2003) The Flow of Human Crowds. Annual Review of Fluid Mechanics, 35, 169-182.

[4]   Cusack, M.A. (2002) Modelling Aggregate-Level Entities as a Continuum. Mathematical and Computer Modelling of Dynamical Systems, 8, 33-48.

[5]   Helbing, D.A. (1992) Fluid Dynamic Model for the Movement of Pedestrians. Complex Systems, 6, 391-415.

[6]   Hughes, R.L. (2000) The Flow Of Large Crowds Of Pedestrians. Mathematics and Computers in Simulation, 53, 367-370.

[7]   Hughes, R.L. (2002) A Continuum Theory for the Flow of Pedestrians. Transportation Research Part B, 36, 507-535.

[8]   Smith, R.A. (1995) Density, Velocity and Flow Relationships for Closely Packed Crowds. Safety Science, 18, 321-327.

[9]   Henderson, L.F. (1974) On the Fluid Mechanics of Human Crowd Motion. Transportation Research, 8, 509-515.

[10]   Helbing D., Johansson A. and Al-Abideen H.Z. (2007) The Dynamics of Crowd Disasters: An Empirical Study. Physical Review E, 75, 046109.

[11]   Al-Haboubi, M.H. (2003) A New Layout Design for the Jamarat Area (Stoning the Devil), Arabian Journal for Science and Engineering, 28, 131-142.

[12]   Payne, H.J. (1971) Models of Freeway Traffic and Control. In: Bekey, G.A., Ed., Mathematical Models of Public Systems, Simulation Council, La Jolla, Vol. 1, 51-61.

[13]   Whitham, G.B. (1999) Linear and Nonlinear Waves. Wiley, New York. (reprint of the 1974 original, a Wiley-Interscience publication)

[14]   Karamouzas, L., Skinner, B. and Guy, S.J. (2014) A Universal Power Law Governing Pedestrian Interactions. Physical Review Letters, 113, Article ID: 238701.