Kinematic wave computation using an efficient implicit method

The kinematic wave theorem is the simplest and widely employed distributed routing method used in practical applications for the computation of flood wave propagation in overland and open-channel flows with steep topography. In this paper, an efficient finite-difference implicit MacCormack scheme is developed for the simulation of one-dimensional kinematic wave flows. Simulated results are compared with two analytical solutions and one experimental measurement to assess the performance of an explicit MacCormack scheme, implicit nonlinear kinematic wave scheme and implicit MacCormack scheme. The computed results show that the proposed implicit MacCormack scheme is simple, accurate, highly stable and greatly efficient in solving kinematic wave problems.