Adaptive numerical simulation of traffic flow density

In this paper, we describe a one-dimensional adaptive moving mesh method and apply it to the traffic flow model introduced in 2006 by Sopasakis and Katsoulakis and its modified model proposed in 2009 by Kurganov and Polizzi. These models can be written as a scalar conservation law with a global flux. The proposed scheme is an extension of the moving non-oscillatory central scheme, which belongs to a class of moving finite volume methods.We also modify the model given by Kurganov and Polizzi to account for the driver’s reaction, i.e. delayed response. Finally, the moving finite volume method is extended accordingly.