ODE solution to the characteristic form of the Saint-Venant equations

An ordinary differential equation algorithm was formulated to approximate the solution to the characteristic form of the Saint-Venant equations for one-dimensional, gradually varied, unsteady open-channel flow in prismatic irrigation canals. The algorithm was applied by developing a network of characteristics using difference equations for randomly spaced intervals in the x − t (space–time) plane. Consistency, convergence and numerical stability of the equations are demonstrated, and a method to estimate the error of the predictor–corrector scheme is proposed. A mathematical model was developed to test the algorithm using a hypothetical case of unsteady flow, and it was compared to the results from two other mathematical simulation models, providing a high degree of agreement.