In this paper, we describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads. On individual roads, we consider the standard Lighthill-Whitham-Richards model which is discretized using the discontinuous Galerkin method along with suitable limiters. In order to solve traffic flows on networks, we construct suitable numerical fluxes at junctions based on preferences of the drivers. We prove basic properties of the constructed numerical flux and the resulting scheme and present numerical experiments, including a junction with complicated traffic light patterns with multiple phases. Differences with the approach to numerical fluxes at junctions from \v{C}ani\'{c} et al., 2015, are discussed and demonstrated numerically on a simple network.

中文翻译：

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网络宏观交通流模型的非连续Galerkin方法

在本文中，我们描述了一种用于解决道路网络宏观交通流模型的数值技术。在个别道路上，我们考虑使用不连续Galerkin方法以及合适的限制器离散化的标准Lighthill-Whitham-Richards模型。为了解决网络上的流量，我们根据驾驶员的偏好在交汇处构造了合适的数值通量。我们证明了所构造的数值通量和所得方案的基本特性，并提出了数值实验，包括具有多相的复杂交通信号灯图案的路口。\ v {C} ani \'{c}等人（2015年）在结点处的数值通量方法的差异已被讨论并通过简单的网络进行了数值证明。