Numerical solution of kinematic wave equation using differential quadrature method

Kinematic wave equation is a simplification of the fully dynamic wave equation of the fluid flow in open channels. In this equation, the inertia and pressure forces are neglected compared to the gravity force and the friction. Due to the simplicity of kinematic wave, many researchers are still interested in this model in its range of applicability.Until now, various numerical methods such as Finite Difference (FD) and Finite Element (FE) have been used for solution of kinematic wave equation. Differential Quadrature Method (DQM) as an alternative numerical method has attracted the attention of some researchers because of its stability, accuracy and efficiency. In this study, the applicability of DQM for solution of the kinematic wave equation is investigated. For evaluation of this method, the results were compared with analytical solution and observed data.Results of this study show that the type of grid distribution affects the results significantly. The cosine grid distribution is better than uniform grid distribution as it was suggested by previous applications in the literature. DQM for simulating kinematic wave model is not sensitive to choice of the test functions. In general, DQM can be considered as another numerical method for kinematic wave equation using less number of grid points to achieve accurate results. It is also unconditionally stable. The main disadvantage of the kinematic wave equation is its failure to predict wave attenuation. This can be resolved by using diffusion wave model and the same numerical technique.