A kinetic scheme for the one-dimensional open channel flow equations with applications on networks

In this paper, a kinetic method to compute approximative solutions of the one-dimensional open channel flow equations with a varying cross-sectional area and a varying bottom profile is proposed. The scheme preserves the steady states at rest, keeps the water height non-negative and is able to handle dry channel beds. These three properties are essential indicators for the quality of a numerical scheme. The ability of the scheme to treat varying cross-sectional areas along the channel is an important advancement in comparison to previous papers. Further the same equations are considered on a network by coupling the equations at the nodes. The main difference to the majority of common numerical hydraulic models is the usage of the energy equality as coupling condition which seems to be more realistic than conditions based on the water height. Moreover, we set up a numerical method for computing subcritical flow on such networks. Several examples are treated to illustrate the results.