A note on the weighted essentially non-oscillatory numerical scheme for a multi-class Lighthill-Whitham-Richards traffic flow model

• Published in: Communications in numerical methods in engineering Vol. 25; no. 11; pp. 1120 - 1126
• Main Authors: Zhang, Peng, Wong, S. C., Dai, Shi-Qiang
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.11.2009; Wiley
• Subjects: Applied sciences; characteristic speed; Eigenvalues; Exact sciences and technology; Flux; Ground, air and sea transportation, marine construction; hyperbolic conservation laws; Inequalities; Mathematical models; Numerical analysis; numerical stability; Road transportation and traffic; Splitting; Traffic flow; J integral; Conservation law; Flow models; hyperbolic conservation laws; Traffic management; Hyperbolic equation; characteristic speed; Eigenvalue problem; Modeling; Weight; Numerical stability
• ISSN: 1069-8299; 2040-7947; 2040-7939; 1099-0887; 2040-7947
• DOI: 10.1002/cnm.1277

In a recent paper, the weighted essentially non‐oscillatory (WENO) numerical scheme was applied to solve a multi‐class Lighthill–Whitham–Richards (MCLWR) traffic flow model (J. Comput. Phys. 2003; 191:639–659). We discuss and present an enhanced WENO scheme with Lax–Friedrichs flux splitting by improving the estimation of the minimal characteristic speed of the MCLWR model, which is based on a set of inequalities of eigenvalues. Copyright © 2009 John Wiley & Sons, Ltd.