Modeling of urban traffic networks with lattice Boltzmann modelJian-ping Meng1, 2, Yue-hong Qian1 and Shi-qiang Dai1
1 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University - Shanghai, 200072, China
2 College of Mathematics, Physics and Information Engineering, Zhejiang Normal University - Jinhua 321004, China
received 17 July 2007; accepted in final form 21 December 2007; published February 2008
published online 28 January 2008
It is of great importance to uncover the characteristics of traffic networks. However, there have been few researches concerning kinetics models for urban traffic networks. In this work, a lattice Boltzmann model (LBM) for urban traffic networks is proposed by incorporating the ideas of the Biham-Middleton-Levine (BML) model into the LBM for road traffic. In the present model, situations at intersections with the red and green traffic signals are treated as a kind of boundary conditions varying with time. Thus, the urban traffic network could be described in the mesoscopic level. By performing numerical simulations under the periodic boundary conditions, the behavior of average velocity is investigated in detail. The numerical results agree quite well with those given by the Chowdhury-Schadschneider (ChSch) model (CHOWDHURY D. and SCHADSCHNEIDER A., Phys. Rev. E, 59 (1999) R1311). Furthermore, the statistical noise is reduced in this discrete kinetics model, thus, the present model has considerably high computational efficiency.
47.11.-j - Computational methods in fluid dynamics.
05.20.Dd - Kinetic theory.
45.70.Vn - Granular models of complex systems; traffic flow.
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