Junction Riemann problem for one-dimensional shallow water equations with bottom discontinuities and channels width variations

We investigate the solution of the nonlinear junction Riemann problem for the one-dimensional shallow water equations (SWEs) in a simple star network made of three rectangular channels. We consider possible bottom discontinuities between the channels and possible differences in the channels width. In the literature, the solution of the Riemann problem at the junction is investigated for the symmetric case without bottom steps and channels width variations. Here, the solution is extended to a more general situation such that neither the equality of the channels width nor the symmetry of the flow are assumed in the downstream channels. The analysis is performed under sub-criticality conditions and the results are summarized in a main theorem, while a series of numerical examples are presented and support our conclusions.