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

Suncica Canic, Benedetto Piccoli, Jing Mei Qiu, Tan Ren

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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.

Original languageAmerican English
Pages (from-to)233-255
Number of pages23
JournalJournal of Scientific Computing
Issue number1
StatePublished - Apr 2015

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


  • Bound preserving
  • Discontinuous Galerkin
  • Hyperbolic network
  • Scalar conservation laws
  • Traffic flow


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