Generalization of Runge-Kutta Discontinuous Galerkin Method to LWR Traffic Flow Model with Inhomogeneous Road Conditions Peng Zhang, Ru-Xun Liu Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China Received 13 March 2003; accepted 8 March 2004 Published online 18 May 2004 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.20023 The discussed model is characterized by changeable lane numbers and free flow velocities that give rise to the spatially varying flux function in conservation equation. Accordingly a new numerical flux and a new limiter for the Runge-Kutta Discontinuous Galerkin method are considered, which are compared with a natural but simple extension. It is verified that the new generalization is of high-resolution and has wider stable and convergent ranges. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 21: 80 – 88, 2005 Keywords: LWR model; spatially varying flux; numerical flux; limiter 1. INTRODUCTION Lighthill and Whitham [1] and Richards [2] developed a continuum traffic flow model that is known as the LWR theory. The theory has played an important role both for the traffic flow research [3, 4] and for the study of wave propagation [5], especially when taking into account the changeable lane number and free flow velocity. The consideration is significant in describing a traffic jam (a blow-up in solution) and its recovery, but from which some questions arise since this gives rise to a spatially varying (or discontinuous) flux. While the traditional up-winding schemes are applied, these spatially varying functions in the flux (a( x) and b( x) in our problem) must be continuous at the cell interface. This handling is inappropriate because the equation is hardly a strictly hyperbolic and its characteristics are no longer straight lines [6]. For more details in this study; also cf. [6 –12]. Correspondence to: Ru-Xin Liu, Department of Mathematics, University of Science and Technology of China, Hefel 230026, Anhul, PR China (e-mail: liurx@ustc.edu.cn), Peng Zhang (pengzhang@ustc.edu) Contract grant sponsor: China Postdoctoral Science Foundation; contract grant number: 2003034254 Contract grant sponsor: National Natural Science Foundation of China; contract grant number: 10371118. © 2004 Wiley Periodicals, Inc.