Numerical Simulation of Macroscopic Traffic Equations

TL;DR

This paper evaluates explicit numerical schemes for simulating macroscopic traffic flow equations, analyzing their robustness, accuracy, and boundary condition handling through theoretical discussion and simulation examples.

Contribution

It introduces a comparative analysis of explicit integration schemes and boundary treatments for macroscopic traffic models, highlighting their advantages and limitations.

Findings

Explicit schemes vary in robustness and accuracy.

Diffusion and nonlocal terms influence simulation stability.

Effective boundary condition treatments improve model realism.

Abstract

Macroscopic traffic simulations are based on coupled non-linear partial differential equations, the solutions of which are either shock-like or inhomogeneous with steep gradients, at least in the interesting density regime. We discuss several suitable explicit integration schemes, including their advantages and disadvantages, their numerical robustness and errors. We compare the effects of diffusion with that of nonlocal terms. In addition, we investigate different possibilities of treating realistic open boundary conditions. The theoretical considerations are illuminated by many examples of simulation results.