<abstract xmlns="http://www.w3.org/1999/xhtml"><p> A full dynamic model in the form of the shallow water equations (SWE) is often useful for reproducing the unsteady flow in open channels, as well as over a floodplain. However, most of the numerical algorithms applied to the solution of the SWE fail when flood wave propagation over an initially dry area is simulated. The main problems are related to the very small or negative values of water depths occurring in the vicinity of a moving wet-dry front, which lead to instability in numerical solutions. To overcome these difficulties, a simplified model in the form of a non-linear diffusive wave equation (DWE) can be used. The diffusive wave approach requires numerical algorithms that are much simpler, and consequently, the computational process is more effective than in the case of the SWE. In this paper, the numerical solution of the one-dimensional DWE based on the modified finite element method is verified in terms of accuracy. The resulting solutions of the DWE are compared with the corresponding benchmark solution of the one-dimensional SWE obtained by means of the finite volume methods. The results of numerical experiments show that the algorithm applied is capable of reproducing the reference solution with satisfactory accuracy even for a rapidly varied wave over a dry bottom.</p></abstract>

A full dynamic model in the form of the shallow water equations (SWE) is often useful for reproducing the unsteady flow in open channels, as well as over a floodplain. However, most of the numerical algorithms applied to the solution of the SWE fail when flood wave propagation over an initially dry area is simulated. The main problems are related to the very small or negative values of water depths occurring in the vicinity of a moving wet-dry front, which lead to instability in numerical solutions. To overcome these difficulties, a simplified model in the form of a non-linear diffusive wave equation (DWE) can be used. The diffusive wave approach requires numerical algorithms that are much simpler, and consequently, the computational process is more effective than in the case of the SWE. In this paper, the numerical solution of the one-dimensional DWE based on the modified finite element method is verified in terms of accuracy. The resulting solutions of the DWE are compared with the corresponding benchmark solution of the one-dimensional SWE obtained by means of the finite volume methods. The results of numerical experiments show that the algorithm applied is capable of reproducing the reference solution with satisfactory accuracy even for a rapidly varied wave over a dry bottom.

Modelling of Flood Wave Propagation with Wet-dry Front by One-dimensional Diffusive Wave Equation

Gdańsk University of Technology, Faculty of Civil and Environmental Engineering, ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland

Archives of Hydro-Engineering and Environmental Mechanics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A full dynamic model in the form of the shallow water equations (SWE) is often useful for reproducing the unsteady flow in open channels, as well as over a...

Modelling of Flood Wave Propagation with Wet-dry Front by One-dimensional Diffusive Wave Equation

Published Online: Oct 07, 2015

Page range: 111 - 125

Received: Oct 09, 2014

DOI: https://doi.org/10.1515/heem-2015-0007

Keywords
diffusive wave equation, shallow water equations, overland flow, floodplain inundation, finite element method

© by Dariusz Gąsiorowski

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Modelling of Flood Wave Propagation with Wet-dry Front by One-dimensional Diffusive Wave Equation

Published Online: Oct 07, 2015

Page range: 111 - 125

Received: Oct 09, 2014

DOI: https://doi.org/10.1515/heem-2015-0007

Keywordsdiffusive wave equation, shallow water equations, overland flow, floodplain inundation, finite element method

© by Dariusz Gąsiorowski

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
diffusive wave equation, shallow water equations, overland flow, floodplain inundation, finite element method