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A two-dimensional finite element based overland flow model was developed and used to study the accuracy and stability of three numerical schemes and watershed parameter aggregation error. The conventional consistent finite element scheme results in oscillations for certain time step ranges. The lumped and the upwind finite element schemes are tested as alternatives to the consistent scheme. The upwind scheme did not improve on the stability or the accuracy of the solution, while the lumped scheme provided stable and accurate solutions for time steps twice the size of time steps needed for the consistent scheme. A new accuracy based dynamic time step estimate for the two-dimensional overland flow kinematic wave solution is developed for the lumped scheme. The newly developed dynamic time step estimates are functions of the mesh size, and time of concentration of the watershed hydrograph. Due to lack of analytical solutions, the time step was developed by comparing numerical solutions of various levels of discretization to a reference solution using a very fine mesh and a very small time step. The time step criteria were tested on a different set of problems and proved to be adequate for accurate and stable solutions. A sensitivity analysis for the watershed slope, Manning’s roughness coefficient and excess rainfall rate was conducted in order to test the effect of parameter aggregation on the stability and accuracy of the solution. The results of this analysis show that aggregation of the slope data resulted in the highest error. The roughness coefficient had a smaller effect on the solution while the rainfall intensity did not show any significant effect on the flow rate solution for the range of rainfall intensity used. This work pioneers the challenge of providing guidelines for accurate and stable numerical solutions of the two-dimensional kinematic wave equations for overland flow. [Copyright &y& Elsevier]

Solving the kinematic wave equations for overland flow using the conventional consistent Galerkin finite element scheme is known to result in numerical oscillations due to the non-symmetric first spatial derivative terms in the kinematic wave equations. In this paper the lumped and the upwind finite element schemes are evaluated as alternatives to the consistent Galerkin finite element scheme. Stability analysis of the upwind scheme shows that the damping effect, that could reduce the oscillations, is small for the high Courant numbers encountered in overland flow problems. The upwind scheme, using upwind factors of 0.1 and 1.0, did not provide any improvement to the stability of the lumped and the consistent schemes. The lumped scheme considerably reduces oscillations without significant reduction in the overall solution accuracy. No analytical guidelines for time-step criteria that will insure stability and accuracy were provided by the stability analysis performed for the three schemes. Problem specific accuracy-based dynamic time-step criteria was developed and evaluated for the lumped scheme. These time-steps were found to be on average, double the size of the dynamic time-steps for the consistent scheme. [Copyright &y& Elsevier]