Numerical Solutions of Traffic Flow on Networks: Using the LWR-Model and the Godunov Scheme

This paper shows how to create a simulationtool for traffic flow in a network using the Lighthill--Witham--Richards model and the Godunov scheme. First some basic rules about conservation laws are described and how to solve them using the method characteristics. This leads to the notion of weak solutions which can be solved by shock- and rarefractions-solutions. This is then used to describe how traffic behaves on a single road by using the LWR-model. The behavior of traffic at junctions is discussed, more specifically how to find the maximum flux through a junction when we deal with different amount of incoming and outgoing roads. The paper gives different examples of numerical solution methods to conservation laws, which gives motivation for the Godunov scheme. A numerical scheme using the LWR-model and the Godunov scheme is tested on different traffic models. The main test is a simplified model of Trondheim, Norway. The results are presented in videos, as well as graphs and tables that show the duration of the driving time through different routes of the model