This paper extends the Wave Tracking resolution of the traffic LWR model to situations where boundary conditions are to be considered: variable input demand of traffic, variable output supply, discontinuity of the road profile, traffic signals, incidents It is mainly based on the notion of the Extended Riemann Problem and it demonstrates that, in a practical point of view, it can be solved by splitting into simple Riemann Problem since waves always drive away from the boundary. It is further shown how this practical result can be directly implemented in a wave tracking procedure, resulting in a comprehensive numerical scheme. In such a scheme waves are explicitly considered in their moving and when they collide. There may be collisions between two shock waves or between a shock wave and a stationary special wave representing the boundary condition. It is shown that each collision can be solved by a Riemann problem or a Riemann extended problem, resulting in the generation of one of several waves. A simple theoretical example is given in order to illustrate the potentiality of the resolution method to capture the LWR features as well as its computational efficiency. (A) Reprinted with permission from Elsevier. For the covering abstract see ITRD E134766.
Abstract