On numerical modeling of overland flow

The reliability of several finite difference numerical formulations for solving one-dimensional kinematic and diffusion wave equations that describe overland flow is investigated. Particular emphasis is placed on two numerical schemes which are second order accurate in space and time, one each from the explicit and implicit families, respectively: the MacCormack and the 4-point implicit schemes. The end numerical solutions are compared to analytical solutions used as benchmark data, and to implicit and explicit schemes widely used to solve the overland flow governing equations. The magnitude of the time step was selected from the CFL stability condition. The algorithms are used to solve two examples, and the results are compared in terms of accuracy and required computational time. In both cases, the results indicate that the MacCormack and 4-point implicit methods are superior in terms of accuracy to the other widely used schemes. The MacCormack and 4-point implicit methods are comparable in accuracy, but the MacCormack algorithm is computationally more efficient.