Open canals flow with fluvial to torrential phase transitions on networks

Network flows and specifically open canal flows can be modeled by systems of balance laws defined on topological graphs. The shallow water or Saint-Venant system of balance laws is one of the most used model and present two phases: fluvial or sub-critical and torrential or super critical. Phase transitions may occur within the same canal but transitions related to networks are less investigated. In this paper we provide a complete characterization of possible phase transitions for a simple network with two canals and one junction. Our analysis allows the study of more complicate scenarios. Moreover, we provide some numerical simulations to show the theory at work.