Conservation Form of Helbing’s Fluid Dynamic Traffic Flow Model

LI Shu-feng; ZHANG Peng; Wong S C

doi:10.3879/j.issn.1000-0887.2011.09.003

Volume 32 Issue 9

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LI Shu-feng, ZHANG Peng, Wong S C. Conservation Form of Helbing’s Fluid Dynamic Traffic Flow Model[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1037-1045. doi: 10.3879/j.issn.1000-0887.2011.09.003

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Conservation Form of Helbing’s Fluid Dynamic Traffic Flow Model

doi: 10.3879/j.issn.1000-0887.2011.09.003

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;
Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, P. R. China;
Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, P. R. China

Received Date: 2011-03-23
Rev Recd Date: 2011-06-20
Publish Date: 2011-09-15

Abstract

Abstract

A standard conservation form was derived,the hyperbolicity of Helbing's fluid dynamic traffic flow model was proved,which was essential for general analytical and numerical study of this model.On the basis of this conservation form,a local discontinuous Galerkin scheme is designed to solve the resulting model efficiently.The evolution of an unstable equilibrium traffic state leading to a stable stop-and-go traveling wave was simulated.This simulation also verifies that the model has been truly improved through the introduction of modified diffusion coefficients,thereby helping to protect vehicles from collisions and avoiding the appearance of extremely large density.
- conservation form,
- hyperbolicity,
- local discontinuous Galerkin method,
- stop-and-go wave

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References(25)

References

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