A Conserved HighOrder Traffic Flow Model With Discontinuous Flux and Its Numerical Simulation

QIAO Dianliang; LI Xiaoyang; GUO Mingmin; ZHANG Peng

doi:10.21656/1000-0887.390277

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QIAO Dianliang, LI Xiaoyang, GUO Mingmin, ZHANG Peng. A Conserved HighOrder Traffic Flow Model With Discontinuous Flux and Its Numerical Simulation[J]. Applied Mathematics and Mechanics, 2019, 40(5): 546-561. doi: 10.21656/1000-0887.390277

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A Conserved HighOrder Traffic Flow Model With Discontinuous Flux and Its Numerical Simulation

doi: 10.21656/1000-0887.390277

¹Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R.China;²Department of Aeronautics and Astronautics,Fudan University, Shanghai 200433, P.R.China;³Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai 200072, P.R.China

Funds: The National Natural Science Foundation of China（General Program)(11672348;11272199);The National Key R&D Program of China(2018YFB1600900);The National Basic Research Program of China(973 Program)(2012CB725404)

Received Date: 2018-11-01
Rev Recd Date: 2019-01-02
Publish Date: 2019-05-01

Abstract

Abstract

Under inhomogeneous road conditions, a conserved high-order (CHO) anisotropic traffic flow model was extended to obtain a CHO model with discontinuous fluxes. Based on the property of the Riemann invariant for the CHO model with discontinuous fluxes, the first-order Godunov, EO (Engquist-Osher) and LF (Lax-Friedrichs) numerical schemes for this model were designed with the local simplification method and the δ mapping algorithm. The numerical simulations show that, the CHO model with discontinuous fluxes is reasonable and effective. It can describe equilibrium and non-equilibrium traffic flows, and can better describe the actual traffic phenomena compared with the LWR (Lighthill-Whitham-Richards) model with a discontinuous flux.
- CHO model with discontinuous fluxes,
- Riemann invariant,
- local simplification,
- δ mapping

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References(40)

References

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