Implicit high-resolution methods for modelling one-dimensional open channel flow

Three implicit high-resolution total variation diminishing (TVD) schemes are presented for solving the Saint-Venant equations. The applicability, performance and validity of these methods are investigated. Recently created benchmark solutions are reproduced for a wide range of cases, which include friction, nonuniform bed slopes, transitions between subcritical and supercritical flow, nonprismatic cross sections and hydraulic jumps. The tests produce satisfactory results without resorting to excessively fine grids. All the methods also produce satisfactory results for an idealized dambreak problem.