This paper deals with the construction of a discontinuous Galerkin scheme for the solution of Lighthill-Whitham-Richards traffic flows on networks. The focus of the paper is the construction of two new numerical fluxes at junctions, which are based on the Godunov numerical flux. We analyze the basic properties of the two Godunov-based fluxes and the resulting scheme, namely conservativity and the traffic distribution property. We prove that if the junction is not congested, the traffic flows according to predetermined preferences of the drivers. Otherwise a small traffic distribution error is present, which we interpret as either the existence of dedicated turning lanes, or factoring of human behavior into the model. We compare our approach to that of \v{C}ani\'c et al. (J. Sci. Comput., 2015). Numerical experiments are provided.
翻译：本文涉及一个不连续的Galerkin计划, 以解决Lighthill- Whitham-Richards在网络上的交通流量。 本文的重点是根据Godunov 数字通量在交界处建造两个新的数字通量。 我们分析了两个基于Godunov 的通量的基本特性以及由此产生的计划, 即保守性和交通分配属性。 我们证明, 如果连接点不凝固, 交通流量会按照司机的预定偏好进行。 否则, 就会出现一个小的交通分配错误, 我们把它解释为存在专用的转弯道, 或者将人类行为因素纳入模型。 我们比较了我们的方法与“ v{C}ani\c et al.” (J. Sci. Comput, 2015) 的方法。 我们提供了数字实验。
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