Description and WENO Numerical Approximation to Nonlinear Waves of a Multi-Class Traffic Flow LWR Model

ZHANG Peng; DAI Shi-qiang; LIU Ru-xun

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Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(6): 637-644

ZHANG Peng, DAI Shi-qiang, LIU Ru-xun. Description and WENO Numerical Approximation to Nonlinear Waves of a Multi-Class Traffic Flow LWR Model[J]. Applied Mathematics and Mechanics, 2005, 26(6): 637-644.

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Description and WENO Numerical Approximation to Nonlinear Waves of a Multi-Class Traffic Flow LWR Model

1.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;

Received Date: 2003-12-30
Rev Recd Date: 2005-02-05
Publish Date: 2005-06-15

Abstract

Abstract

A strict proof of the hyperbolicity of the multi-class LWR(Lighthill-Whitham-Richards) traffic flow model,as well as the descriptions on those nonlinear waves characterized in the traffic flow problems were given.They were mainly about the monotonicity of densities across shocks and in rarefactions.As the system had no characteristic decomposition explicitly,a high resolution and higher order accuracy WENO (weighted essentially non-oscillatory) scheme was introduced to the numerical simulation,which coincides with the analytical description.
- hyperbolicity,
- characteristic,
- traffic wave,
- WENO scheme

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References(15)

References

[1]	戴世强，冯苏苇，顾国庆.交通流动力学:它的内容、方法和意义[J].自然杂志，1997,11(4):196—201.
[2]	Helbing D.Traffic and related self-driven many-particle systems[J].Rev Mod Phys,2001,73(4)：1067—1141. doi: 10.1103/RevModPhys.73.1067
[3]	Lighthill M H,Whitham G B.On kinematics wave—Ⅱ a theory of traffic flow on long crowded roads[J].Proc Roy Soc London,Ser A,1955,22：317—345.
[4]	Richards P I.Shack waves on the highway[J].Operations Research,1956,4(2)：42—51. doi: 10.1287/opre.4.1.42
[5]	Wong G C K，Wong S C.a multi-class traffic flow model—an extension of LWR model with heterogeneous drivers[J].Transpn Res A,2002,36(9)：827—841.
[6]	Harten A,Engquish B，Osher S,et al.Uniformly high order essentially non-oscillatory schemes Ⅲ[J].J Comput Phys,1987,71(2)：231—303. doi: 10.1016/0021-9991(87)90031-3
[7]	Jiang G,Shu C -W.Efficient implementation of weighted ENO schemes[J].J Comput Phys,1996,126(1)：202—228. doi: 10.1006/jcph.1996.0130
[8]	Liu X -D,Osher S，Chan T.Weighted essentially nonoscillatory schemes[J].J Comput Phys,1994,115(1)：200—212. doi: 10.1006/jcph.1994.1187
[9]	Shu C -W.Lecture Notes in Mathematics-Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws[R]. 1697, Cetraro, Italy: Springe, 1997，329—432.
[10]	Whitham G B.Linear and Nonlinear Waves[M].NY: John Wiley and Sons, 1974.
[11]	Lax P D.Shock Waves and Entropy.In:Zarantonello E A Ed.Nonlinear Functional Analysis[M].New York:Academic Press, 1971.
[12]	Lax P D.Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves[M].Philadelphia:SIAM,1973.
[13]	Toro E F.Riemann Solvers and Numerical Methods for Fluid Dynamics[M].Berlin:Springer~Verlay,1999.
[14]	Shu C -W.TVB uniformly high order scheme for conservation laws[J].Mathematics of Computation,1987,49(179)：105—121. doi: 10.1090/S0025-5718-1987-0890256-5
[15]	Shu C -W.Total-variation-diminishing time discretizations[J].SIAM Journal on Scientific and Statistical Computation,1988，9(4)：1073—1084. doi: 10.1137/0909073