求解复杂交通流模型的低耗散中心迎风格式  

Low Dissipation Central-Upwind Scheme for Solving Complex Traffic Flow Model

作　　者：杨苗苗 封建湖[1] 程晓晗[1] 冯娟娟 YANG Miaomiao;FENG Jianhu;CHENG Xiaohan;FENG Juanjuan(School of Science,Chang’an University,Xi’an 710064,China)

机构地区：[1]长安大学理学院

出　　处：《计算机工程》2019年第6期37-44,共8页Computer Engineering

基　　金：国家自然科学基金(11601037);陕西省自然科学基金(2018JQ1027);中央高校基本科研业务费专项资金(310812171002)

摘　　要：针对非均匀道路上的多车种LWR交通流模型,提出一种低耗散中心迎风格式。以4阶中心加权基本无震荡重构和低耗散中心迎风数值通量为基础,通过构造不同形式的全局光滑因子及增大非光滑模板对应的非线性权重优化数值格式的耗散特性,并采用Runge-Kutta方法对半离散数值格式在时间方向上进行离散使其保持4阶精度。对非均匀道路上多车种LWR交通流模型的车道数变化和交通信号灯控制问题进行数值模拟,结果表明该格式具有4阶求解精度,且分辨率高。To address the multi-class Lightill-Whitham-Richards(LWR) traffic flow model on non-uniform roads,a low-dissipation central-upwind scheme is proposed.Based on the 4th-order Central Weighted Essentially Non-Oscillatory(CWENO) reconstruction and the low dissipation central-upwind numerical flux,the dissipative characteristics of the numerical format are optimized by constructing different forms of global smoothing factors and increasing the nonlinear weights corresponding to non-smooth templates.The Runge-Kutta method discretizes the semi-discrete numerical scheme in the time direction to maintain 4th-order precision.The numerical simulation of the lane number change and traffic signal control problem of multi-class LWR traffic flow model on non-uniform roads shows that the scheme has 4th-order solving accuracy and high resolution.

关 键 词：交通流 低耗散 中心迎风格式 中心加权基本无震荡 激波 稀疏波 

分 类 号：O242.1[理学—计算数学]