Upwind schemes with exact conservation property for one-dimensional open channel flow equations

In this paper we present an application and extension of the upwind schemes with source terms decomposed, developed by Bermudez, Vazquez, Hubbard, and Garcia-Navarro, to the one-dimensional open channel flow equations with general, i.e., nonprismatic and nonrectangular, geometries. Our specific numerical approximations for terms that appear in these equations and are related to the channel's geometrical properties are quite straightforward and natural, and at the same time respect the balancing of the flux gradient and the source term. As a consequence, the resulting upwind schemes have the exact conservation property. In several test problems we illustrate the achieved improvement, particularly significant for applications to natural watercourses due to their irregular riverbed geometries.