Alexander Kurganov
Title: Numerical
Methods for Modern Traffic Flow Models
Abstract: I
will describe two different traffic flow models. The first model is a
scalar conservation law with Arrhenius look-ahead dynamics. It is a
modification of the classical fluid dynamics model by Lighthill and
Whitham. The modification is based on an assumption that unlike
the fluid particles, drivers can see the traffic dynamics ahead of
their cars and adjust the speeds of their cars correspondingly. This
factor results in a global dependence of the flux on the solution,
which makes it challenging to develop numerical methods for the
studied scalar conservation law.
The second model is a
modification of the Aw-Rascle system, designed to describe the
formation and dynamics of traffic jams. The model consists of a
constrained pressureless gas dynamics system, which is extremely
stiff. The stiffness makes it difficult to develop robust and
accurate explicit numerical schemes for this model.
I will
present several numerical methods for the above two models and
demonstrate their superb performance on a number of numerical
examples.