Comparison of Numerical Schemes for LWR Model under Heterogeneous Traffic Conditions
Comparison of Numerical Schemes for LWR Model under Heterogeneous Traffic Conditions
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异构交通条件下LWR模型数值方案比较
DOI：
10.3311/pptr.8297
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发表时间：
2016
影响因子：
--
通讯作者：
K. R. Rao
中科院分区：
文献类型：
--
作者：
H. Gaddam;Anjaneyulu Chinthireddy;K. R. Rao
Lighthill-WhithamRichards（LWR）等一阶宏观模型已被广泛研究并应用于各种齐次交通问题。LWR模型对各种异质交通条件的适用性和适应性仍在探索中。用解析方法求解宏观模型是一项复杂的任务，通常采用数值近似。本研究试图详细了解不同数值方案对交通状况的适用性。数值积分采用了不同的一阶和二阶数值格式。在数值格式的推导过程中，讨论了格式的精度、稳定性和收敛性等重要问题。模拟的变量，如流量，密度和速度进行了比较，从两个不同的城市干道，在印度德里，没有瓶颈收集的原始数据。通过对不同数值格式的比较，发现Lax-Friedrichs和MacCormack格式的计算结果更好，更稳定。
First order macroscopic model like Lighthill-WhithamRichards (LWR) has been extensively studied and applied for various homogeneous traffic problems. Applicability and adaptability of LWR models to various heterogeneous traffic conditions is still under exploration. Finding solutions for the macroscopic models using analytical methods is a complicated task, numerical approximations are used. The present study attempts to understand the suitability of different numerical schemes for a traffic conditions in detail. Various first order and second order numerical schemes were chosen for numerical integration. Derivation of the numerical scheme, several important issues like accuracy, stability and convergence of each scheme were discussed. Simulated variables like flow, density and speeds were compared with the original data collected from the two different urban arterials with and without bottlenecks in Delhi, India. The comparison of the results of various numerical schemes shows that Lax-Friedrichs and MacCormack schemes produced better results and more stable than the other schemes.