Description and WENO Numerical Approximation to Nonlinear Waves of a Multi-Class Traffic Flow LWR Model
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摘要: 证明了交通流多等级LWR(Lighthill-Whitham-Richards)模型的双曲性质,并根据交通流的特征给出关于其非线性波的描述,主要包括车流通过激波和稀疏波时密度和速度的单调性变化.由于方程组没有显式的特征分解,所以引入具有高分辨和高精度的WENO(weighted essentially non~oscillatory)格式作数值模拟,得到与理论描述完全一致的数值结果.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.
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Key words:
- hyperbolicity /
- characteristic /
- traffic wave /
- WENO scheme
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[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
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