Numerical Methods for Continuum Models

Abstract

Numerical methods are used to approximate the solution of traffic flow models. This is needed because in most realistic cases it is impossible to solve the problems analytically. When a macroscopic model is applied, usually the space and time domains are divided into intervals: road segments (grid cells) and time steps. For each time step and at each grid cell the model equations are solved approximately using numerical methods. The result is the density in each grid cell, at each time step. Alternative methods are based on moving coordinates and will also be discussed. In this chapter, the focus is on the numerical methods themselves, with the main purpose that the reader should be able to apply the methods. After reading this chapter the reader will understand the basics of applying numerical methods to macroscopic traffic flow models. They can apply those methods to the models and can argue about the impact of choices such as a fixed vs. moving coordinate system and grid cell and time step size.