A Characteristics-Based Finite Element Method for Simulating Two-Dimensional Overland Flow Problems

The method of characteristics (MOC) in the context of finite element method was applied to simulate two-dimensional (2D) shallow water equations for overland flows. Many researchers have pointed out the advantage of MOC in solving two-dimensional shallow water hyperbolic equations having wave-like solutions. At the same time, they considered MOC for two-dimensional overland flow being non-tractable on complex topography and boundaries. For two-dimensional overland flows, finite element methods are very flexible in dealing with complex boundaries. The intrinsic difficulty in implementing MOC for 2D overland flows is that there are infinite numbers of wave characteristics in 2D problems, although only two independent wave directions are needed for a well-posed solution to the characteristic equations. We have implemented a numerical scheme that attempts to diagonalize the characteristic equations based on pressure and velocity gradient relationship. This diagonalization scheme was evaluated by comparison with other choice of wave characteristic directions in the literature. The circular dam break problem was solved with different selections of wave characteristic directions and the performance of each selection was evaluated based on accuracy and numerical stability. Finally, a 2D overland flow problem over complex topography in a wetland setting with very mild slope was solved with the diagonalization scheme along with other wave-selection directions to demonstrate its applicability.