Journal of Scientific Computing

, Volume 63, Issue 1, pp 233–255 | Cite as

Runge–Kutta Discontinuous Galerkin Method for Traffic Flow Model on Networks

  • Suncica Canic
  • Benedetto Piccoli
  • Jing-Mei Qiu
  • Tan Ren
Article

Abstract

We propose a bound-preserving Runge–Kutta (RK) discontinuous Galerkin (DG) method as an efficient, effective and compact numerical approach for numerical simulation of traffic flow problems on networks, with arbitrary high order accuracy. Road networks are modeled by graphs, composed of a finite number of roads that meet at junctions. On each road, a scalar conservation law describes the dynamics, while coupling conditions are specified at junctions to define flow separation or convergence at the points where roads meet. We incorporate such coupling conditions in the RK DG framework, and apply an arbitrary high order bound preserving limiter to the RK DG method to preserve the physical bounds on the network solutions (car density). We showcase the proposed algorithm on several benchmark test cases from the literature, as well as several new challenging examples with rich solution structures. Modeling and simulation of Cauchy problems for traffic flows on networks is notorious for lack of uniqueness or (Lipschitz) continuous dependence. The discontinuous Galerkin method proposed here deals elegantly with these problems, and is perhaps the only realistic and efficient high-order method for network problems.

Keywords

Scalar conservation laws Traffic flow Hyperbolic network Discontinuous Galerkin Bound preserving 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Suncica Canic
    • 1
  • Benedetto Piccoli
    • 2
  • Jing-Mei Qiu
    • 1
  • Tan Ren
    • 3
  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Department of Mathematical SciencesRutgers University - CamdenCamdenUSA
  3. 3.School of Aerospace EngineeringBeijing Institute of TechnologyBeijingChina

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