Comparison of numerical schemes for LWR model under heterogeneous traffic conditions

Abstract

First order macroscopic model like Lighthill-Whitham-Richards (LWR) has been extensively studied and applied for various homogeneous traffic problems. Applicability and adaptability of LWR models to various heterogeneous traffic conditions is still under exploration. Finding solutions for the macroscopic models using analytical methods is a complicated task, numerical approximations are used. The present study attempts to understand the suitability of different numerical schemes for a traffic conditions in detail. Various first order and second order numerical schemes were chosen for numerical integration. Derivation of the numerical scheme, several important issues like accuracy, stability and convergence of each scheme were discussed. Simulated variables like flow, density and speeds were compared with the original data collected from the two different urban arterials with and without bottlenecks in Delhi, India. The comparison of the results of various numerical schemes shows that Lax-Friedrichs and MacCormack schemes produced better results and more stable than the other schemes.