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Stability and accuracy of kinematic wave overland flow modeling

Purdue University
Publication Date
  • Hydrology|Engineering
  • Agricultural
  • Earth Science
  • Geography
  • Physics


Kinematic wave theory is widely used in modeling a variety of hydrologic processes. There is limited research on time steps ensuring stability and accuracy of finite element solutions for overland flow problems. In this study, new accuracy-based dynamic time step criteria for the one-dimensional and two-dimensional overland flow kinematic wave solution are developed. The newly developed dynamic time step estimates are functions of the mesh size, and time of concentration of the hydrograph. The new criteria were developed by comparing a numerical solution of the kinematic wave equation to analytical solutions for the 1-D problems and to a reference numerical solution obtained by using a very fine mesh and a small time step for 2-D problems. 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. The lumped and the upwind finite element schemes are evaluated as alternatives to the consistent Galerkin finite element scheme for one- and two-dimensional problems. The upwind scheme 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. The dynamic time step criteria can be integrated in flow routing models to choose the optimal time step with minimal user input. An interface to the FORTRAN finite element model with ArcView GIS is developed and tested. This interface simplified the input data file management and allowed for the use of raster data for running the model. A sensitivity analysis was also performed for the resolution of the soil characteristic data and the rainfall rate for 2-D problems. Several runs were performed using different scales of slope, roughness and excess rainfall rates and the output flow rates were compared to the reference solution. Watershed slope proved to be the most sensitive to data aggregation. Manning's roughness was sensitive to a lesser degree. No significant effect was noticed due to the aggregation of rainfall rates. ^

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