Christian Claudel University of Texas at Austin The Lighthill-Whitham-Richards (LWR) traffic flow model is commonly used to describe traffic flow on networks. A major issue of this model is however the lack of realistic description of traffic at a microscopic model. In this talk, we introduce a new exact and grid-free numerical scheme for computing solutions associated with an hybrid traffic flow model based on the LWR partial differential equation, for a class of fundamental diagrams. In this hybrid flow model, the vehicles satisfy the LWR equation whenever possible, and have a constant acceleration otherwise. We also show that the proposed computational method can handle both fixed or moving bottlenecks.