In this paper, we propose a macroscopic model that describes the influence of a slow moving large vehicle on road traffic. The model consists of a scalar conservation law with a nonlocal constraint on the flux. The constraint level depends on the trajectory of the slower vehicle which is given by an ODE depending on the downstream traffic density. After proving well-posedness, we first build a finite volume scheme and prove its convergence, and then investigate numerically this model by performing a series of tests. In particular, the link with the limit local problem of [M. L. Delle Monache and P. Goatin, J. Differ. Equ. 257 (2014), 4015-4029] is explored numerically.

We propose a model for self-organized trac ow at bottlenecks that consists of a scalar conservation law with a nonlocal constraint on the ux. The constraint is a function of an organization marker which evolves through an ODE depending on the upstream trac density and its variations. We prove well-posedness for the problem, construct and analyze a nite volume scheme, perform numerical simulations and discuss the model and related perspectives.

We propose a mathematical framework to the study of scalar conservation laws with moving interfaces. This framework is developed on a LWR model with constraint on the flux along these moving interfaces. Existence is proved by means of a finite volume scheme. The originality lies in the local modification of the mesh and in the treatment of the crossing points of the trajectories.