Discontinuous Galerkin method for macroscopic traffic flow models on networks

TL;DR

This paper develops a discontinuous Galerkin numerical method for macroscopic traffic flow models on road networks, incorporating driver preferences at junctions and analyzing flux properties through numerical experiments.

Contribution

It introduces a novel numerical flux construction at junctions based on driver preferences and proves its fundamental properties, advancing traffic flow modeling on networks.

Findings

Effective numerical fluxes at junctions are constructed and analyzed.

The method accurately captures complex traffic light patterns and junction behaviors.

Differences from previous flux approaches are demonstrated through simulations.

Abstract

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.