Macroscopic models of traffic flow
Event details
| Date | 04.04.2014 |
| Hour | 12:15 › 13:15 |
| Speaker | Dr. Paola Goatin, INRIA, Sophia Antipolis, France |
| Location | |
| Category | Conferences - Seminars |
Macroscopic traffic flow models derived from fluid dynamics are very popular nowadays both for vehicular and pedestrian flows.
They offer a sound mathematical basis relying on well posedness results for hyperbolic non-linear conservation laws,
as well as fast and efficient numerical tools consisting of finite volume schemes.
I will present some recent results concerning models with phase transitions, flux constraints and non-local velocities, that can be used to describe some particular characteristics of traffic flow. In particular, I will show how phase transitions models allow for a better matching with experimental data, and are able to describe forward moving discontinuities in the congested phase. Conservation laws with flux constraints have been introduced to efficiently model toll-gates, constructions sites and also moving bottlenecks created by slow-moving large vehicles. Finally, models consisting of conservation laws with non-local flux have recently being introduced to capture the reaction of drivers to the downstream traffic.This approach could address the bounded acceleration issue of classical macroscopic models (which account for unrealistic infinite acceleration across shock discontinuities).
Bio: Paola Goatin holds a PhD in Functional Analysis from the International School for Advanced Studies in Trieste (Italy),
and a Habilitation (HDR) in Mathematics from Toulon University (France).
She has been assistant professor at Toulon University, before joining INRIA as a research scientist in 2010.
Her research activity focuses mainly on the analysis and numerical approximation of systems of partial differential equations of hyperbolic type.
Targeted applications include traffic flow modeling and management.
In particular, she currently holds an ERC Starting Grant for the project "Traffic Management by Macroscopic Models - TRAM3".
They offer a sound mathematical basis relying on well posedness results for hyperbolic non-linear conservation laws,
as well as fast and efficient numerical tools consisting of finite volume schemes.
I will present some recent results concerning models with phase transitions, flux constraints and non-local velocities, that can be used to describe some particular characteristics of traffic flow. In particular, I will show how phase transitions models allow for a better matching with experimental data, and are able to describe forward moving discontinuities in the congested phase. Conservation laws with flux constraints have been introduced to efficiently model toll-gates, constructions sites and also moving bottlenecks created by slow-moving large vehicles. Finally, models consisting of conservation laws with non-local flux have recently being introduced to capture the reaction of drivers to the downstream traffic.This approach could address the bounded acceleration issue of classical macroscopic models (which account for unrealistic infinite acceleration across shock discontinuities).
Bio: Paola Goatin holds a PhD in Functional Analysis from the International School for Advanced Studies in Trieste (Italy),
and a Habilitation (HDR) in Mathematics from Toulon University (France).
She has been assistant professor at Toulon University, before joining INRIA as a research scientist in 2010.
Her research activity focuses mainly on the analysis and numerical approximation of systems of partial differential equations of hyperbolic type.
Targeted applications include traffic flow modeling and management.
In particular, she currently holds an ERC Starting Grant for the project "Traffic Management by Macroscopic Models - TRAM3".
Practical information
- General public
- Free
Organizer
- Nikolas Geroliminis & Katrin Beyer
Contact
- Prof. Nikolas Geroliminis