Explicit construction of entropy solutions for the Lighthill-Whitham-Richards traffic flow model with a piecewise quadratic flow-density relationship
Explicit construction of entropy solutions for the Lighthill-Whitham-Richards traffic flow model with a piecewise quadratic flow-density relationship
复制标题
具有分段二次流密度关系的 Lighthill-Whitham-Richards 交通流模型的熵解的显式构造
DOI：
10.1016/j.trb.2007.08.004
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发表时间：
2008-05
影响因子：
6.8
通讯作者：
Shu, Chi-Wang
中科院分区：
文献类型：
--
作者：
Wong, S. C.;Chen, Wenqln;Lu, Yadong;Zhang, Mengping;Shu, Chi-Wang
本文明确地构造了具有分段线性初始条件和分段常数边界条件的车流密度关系为分段二次、连续、凹但在两个二次多项式相交处不可导的lighhill - whitham - richards （LWR）交通流模型的熵解。所提出的模型是对LWR模型中众所周知的分段线性流密度关系的推广。由于观测到的交通流数据可以很好地与这种连续分段二次函数拟合，因此显式构造的解提供了一种快速准确的求解工具，可用于预测交通或作为诊断工具来测试数值方案的性能。我们实现了两种典型交通流的显式熵解，并将其与由高阶加权本质非振荡（WENO）格式得到的数值解进行了比较。
In this paper we explicitly construct the entropy solutions for the Lighthill–Whitham–Richards (LWR) traffic flow model with a flow–density relationship which is piecewise quadratic, continuous, concave, but not differentiable at the junction points where two quadratic polynomials meet, and with piecewise linear initial condition and piecewise constant boundary conditions. The proposed model is a generalization of the well-known piecewise linear flow–density relationship in the LWR model. As observed traffic flow data can be well fitted with such continuous piecewise quadratic functions, the explicitly constructed solutions provide a fast and accurate solution tool which may be used for predicting traffic or as a diagnosing tool to test the performance of numerical schemes. We implement these explicit entropy solutions for two representative traffic flow cases and also compare them with numerical solutions obtained by a high order weighted essentially non-oscillatory (WENO) scheme.
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DOI：
10.1016/s0191-2615(01)00011-x
发表时间：
2002-06-01
影响因子：
6.8
作者：
Lo, HK;Szeto, WY
通讯作者：
Szeto, WY
影响因子：
4.1
作者：
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通讯作者：
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DOI：
10.2307/3621729
发表时间：
2000-07
期刊：
The Mathematical Gazette
影响因子：
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作者：
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通讯作者：
L. Chambers
DOI：
10.1080/1061856031000104851
发表时间：
2003-03
影响因子：
1.3
作者：
Chi-Wang Shu
通讯作者：
Chi-Wang Shu
DOI：
10.1016/0022-247x(72)90114-x
发表时间：
1972-04
影响因子：
1.3
作者：
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通讯作者：
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