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首页> 外文期刊>Transportation Research Part B: Methodological >Explicit construction of entropy solutions for the Lighthill-Whitham-Richards traffic flow model with a piecewise quadratic flow-density relationship
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Explicit construction of entropy solutions for the Lighthill-Whitham-Richards traffic flow model with a piecewise quadratic flow-density relationship

机译：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

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摘要

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.
机译：在本文中，我们明确构造了Lighthill-Whitham-Richards（LWR）交通流模型的熵解，该模型的流量密度关系是分段二次的，连续的，凹的，但在两个二次多项式相交的交点处是不可微的，并具有分段线性初始条件和分段恒定边界条件。所提出的模型是LWR模型中众所周知的分段线性流动密度关系的一般化。由于观察到的交通流量数据可以很好地与此类连续的分段二次函数拟合，因此，显式构造的解决方案提供了一种快速而准确的解决方案工具，可用于预测交通流量或作为诊断工具来测试数值方案的性能。我们为两个典型的交通流情况实现了这些显式熵解，并将它们与通过高阶加权基本非振荡（WENO）方案获得的数值解进行了比较。

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