Generic macroscopic traffic flow models on junctions

This study is concerned with the higher order macroscopic traffic flow modeling and simulation of traffic flow on junctions. More precisely, we deal with a generic class of second order models, known in the literature as the GSOM family which embeds a large variety of traffic models. While classical approaches focus on the Eulerian point-of-view, here we recast the model using its Lagrangian coordinates and we treat the junction as a specific discontinuity in Lagrangian framework. We propose a complete numerical methodology based on a finite difference scheme for solving such a model which is compatible with micro and macro description, and satisfy the constraints of the invariance principle.