Existence result for the coupling of shallow water and Borda–Carnot equations with Riemann data

Abstract

We consider a subcritical flow in a sudden expansion canal. The flow is given by 1D Saint-Venant equations on each side of the expansion together with mass conservation and Borda–Carnot conditions at the expansion. We show, following the ideas of [M. S. Goudiaby and G. Kreiss, A Riemann problem at a junction of open canals, J. Hyp. Diff. Eq. 10(3) (2013) 431–460], that the linear Riemann problem always has a unique solution while for the nonlinear problem, a unique solution is obtained only under a certain condition.