Impact of diffusion coefficient averaging on solution accuracy of the 2D nonlinear diffusive wave equation for floodplain inundation

•We consider the averaging methods of coefficients in the 2D diffusive wave equation.•For solution the splitting method and the modified finite element method are used.•The numerical tests were carried out for the flows over dry floodplain with obstacles.•The averaging technique based on the arithmetic mean provides the best results.

SummaryIn the study, the averaging technique of diffusion coefficients in the two-dimensional nonlinear diffusive wave equation applied to the floodplain inundation is presented. As a method of solution, the splitting technique and the modified finite element method with linear shape functions are used. On the stage of spatial integration, it is often assumed that diffusion coefficient is constant over element and equal to its average value. However, the numerical experiments indicate that in the case of the flow over the dry floodplain with sudden changes in depths an inadequate averaging of these coefficients can lead to a non-physical solution or even to its instability. In the paper, the averaging techniques for estimation of diffusion coefficients were examined using the arithmetic, geometric, harmonic and the direction dependent means. The numerical tests were carried out for the flows over initially dry floodplain with varied elevation of bottom. It was shown that the averaging method based on the arithmetic mean with respect to the diffusion coefficients provides the satisfactory results in comparison to other techniques.