多等级交通流LWR模型中的非线性波描述与WENO数值逼近  

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

作　　者：张鹏[1] 戴世强[1] 刘儒勋[2] 

机构地区：[1]上海大学上海市应用数学和力学研究所,上海200072 [2]中国科学技术大学数学系,合肥230026

出　　处：《应用数学和力学》2005年第6期637-644,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10472064;10371118);中国博士后科学基金资助项目(2003034254);国家教育部博士点专项基金资助项目(20040280014)

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(weightedessentiallynon oscillatory)格式作数值模拟。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.

关 键 词：双曲性 特征线 交通波 WENO格式 

分 类 号：TB126[理学—工程力学]