Fluid Mathematical Models of Traffic Flow

  • Date: 10/19/2006

Michel Rascle (University of Nice)


University of British Columbia


I will start with a few basic facts on other types of description
(microscopic, kinetic ...) Then I will talk about fluid models, of
'first order': Lighthill-Whitham-Richards (LWR) , i.e. a scalar
conservation law, robust and (too ?) simple. The first type of "second
order models" (Payne-Whitham) was based on the gas dynamics system and
had severe drawbacks, like predicting sometimes cars moving backwards
(!). After the classical paper of Daganzo ('Requiem ...', 95), we
introduced with Aw ('Resurrection ...', 2000) a very simple fixing of
this PW model, which definitely cures these inconsistencies. I will
show the (rigorous) relations between this class of models and the
microscopic 'Follow the Leader' models. Finally, if time allows, I will
describe some apllications to flows on a network, and related issues,
like homgenization problems, or hybrid schemes.

Other Information: 

DG-MP-PDE Seminar 2006