Solving Lighthill-Whitham and Richards Traffic Flow Model using Discontinuous Galerkin Method

Abstract

Traffic congestion at junctions, particularly in urban areas, presents significant challenges in Malaysia. Addressing this issue, the study provides an efficient numerical approach for solving the Lighthill-Whitham and Richards (LWR) traffic flow model using the discontinuous Galerkin (DG) method. The scope of this study is limited to the LWR model at junctions with one incoming and two outgoing roads. The study aims to derive the numerical flux of the LWR model, especially focusing on junction scenario using the Lax-Friedrichs numerical flux and hence solve the LWR model numerically using the DG method. The results demonstrate the DG method’s ability to accurately capture sharp discontinuities and provide a reliable representation of traffic behaviours at junctions.