Numerical Simulation of Macroscopic Traffic Equations

Details Numerical Simulation of Macroscopic Traffic Equations Numerical Simulation of Macroscopic Traffic Equations

1999-09-02

arxiv.org/abs/cond-mat/9909033v1

Computing in Science & Engineering 1, 89-99 (Sep./Oct. 1999)

Physics

Condensed Matter

Soft Condensed Matter

For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.html and http://www.theo2.physik.uni-stuttgart.de/trei

Scientific paper

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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