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Solitary wave solution to Aw-Rascle viscous model of traffic flow |
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| Authors: | Chun-xiu WU Peng ZHANG S.C.WONG Dian-liang QIAO Shi-qiang DAI |
| Affiliation: | 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University,Shanghai 200072, P.R.China; College of Mathematics and Computer Science, Quanzhou Normal University,Quanzhou 362000, Fujian Province, P.R.China 2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University,Shanghai 200072, P.R.China 3. Department of Civil Engineering, The University of Hong Kong, Hong Kong, P.R.China |
| Abstract: | A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries (KdV) equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution. |
| Keywords: | hyperbolic conservation law higher-order traffic flow model traveling wave solution conservative scheme |
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