An improved solution for diffusion waves to overland flow

Diffusion wave equation describes the flood wave propagation which is used in solving overland and open channel flow problems. Therefore, it is important to understand and solve the diffusion wave equations accurately. For this purpose, researchers have previously developed several analytical and numerical methods for the solution of the partial differential equation of diffusion waves. The solution derived by Kazezyılmaz-Alhan and Medina (2007) [12] can be used to solve overland flow problems during rainfall events with both constant and variable rainfall intensity, and with constant hydraulic diffusivity and wave celerity. In this paper, this method is improved by employing the De Hoog algorithm instead of Stehfest algorithm for Laplace inversion and adapting the solution to variable hydraulic diffusivity and wave celerity. In addition, the performances of the Stehfest and the De Hoog algorithms are compared. Synthetic examples are solved by using both Stehfest and De Hoog algorithms incorporated into the existing analytical solution to present the accuracy of the De Hoog algorithm over the Stehfest algorithm. The examples are also solved by using the new method in order to demonstrate the improvement over the existing method.