Improving simple explicit methods for unsteady open channel and river flow. (English) Zbl 1079.76594
Summary: A rigorous study of the explicit Lax-Friedrichs scheme for its application to one-dimensional shallow water flows is presented. The deficiencies of this method are identified and the way to overcome them are presented. It is compared to the explicit first order upwind scheme and to the explicit second order Lax-Wendroff scheme by means of the simulation of several test cases with exact solution. All three schemes in their best balanced version are applied to the simulation of a real river flood wave leading to very satisfactory results.
MSC:
76M20 | Finite difference methods applied to problems in fluid mechanics |
76B10 | Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing |
86A05 | Hydrology, hydrography, oceanography |