Unsteady Free-Surface Flow Computations

The solutions of the free-surface equations for subcritical unsteady one-dimensional flow are solved by four different formulations, each based on the method of characteristics. Advantages and disadvantages of each procedure are given. Examples emphasize the important features and corroborate a stability criteria that is presented. The implicit characteristics grid approach is the most accurate for overland flow situations or analysis of single channels; however, it is not useful for complex systems. The explicit rectangular grid is the simplest to program but may lead to instabilities if very large time increments are used. The latter method is also comparatively expensive for long duration transients.