Modeling of moving bottlenecks in traffic flow: a PDE-ODE model with moving density constraints

In this article we study a strongly coupled PDE-ODE problem from an analytical and numerical point of view. This model describes a moving bottleneck that can be produced by the presence of a bus on a road network. The PDE is a scalar hyperbolic conservation law describing the traffic flow while the ODE, that describes the bus trajectory, is intended in Carathéodory sense. The moving constraint is given by an inequality on the flux which accounts for the bottleneck created by the bus on the road. We give an existence result and introduce a finite volume scheme. The algorithm uses a locally non-uniform moving mesh which tracks the bus position. Some numerical tests are presented, in order to describe the behavior of the solution