Numerical Simulation of Macroscopic Traffic Equations

1999/09/02 by Dirk Helbing, Martin Treiber
Physics and Astronomy · #cond-mat.soft

paper · pdf

published as Computing in Science & Engineering 1, 89-99 (Sep./Oct. 1999) · For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.html and http://www.theo2.physik.uni-stuttgart.de/treiber.html

arxiv created 1999/09/02 · arxiv updated 2009/11/30

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.

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