Abstract

Two new ways to couple scalar conservation laws on networks are presented. We first discuss a numerically motivated approach, in which a new scheme is derived using a relaxation system and taking the relaxation limit also at the nodes of the network. The scheme is mass conservative, allows for a second order extension and yields well defined and easy-to-compute coupling conditions for general networks. The second approach focuses on the traffic flow model by Lighthill, Witham and Richards in a network setting. The choice of coupling condition at the junction has been a major modeling challenge. Using car trajectory data obtained from drone photography over a German motorway we develop new data-driven coupling conditions, which we compare to classical approaches from literature.