Numerical Errors in Diffusion Wave Models When Simulating Kinematic Flow

Diffusion wave models have been used successfully to simulate both canal flow and overland flow in hydrologic systems. When implicit numerical methods are used to solve diffusion wave models, it becomes easy to use very large time steps and a wide range of spatial grid resolutions. However, when the flow condition becomes kinematic instead of diffusive, numerical methods developed for solving diffusion wave models fail to give accurate and robust solutions. In this paper, numerical error behavior of two different implicit diffusion wave models are investigated under kinematic and near-kinematic flow conditions. Results of experiments show that both the fully implicit method (Akan and Yen, 1977) and the linearized implicit method (Lal, 1989) produce similar errors when the flow is diffusive. Results show that the numerical error is large with both methods when the flow is kinematic. In the case of the fully implicit method, the solution is excessively diffused until it disappears, and in the case of the linearized implicit method, the solution is amplified and sometimes oscillatory.