An Accurate Smoothness Indicator for Shallow Water Flows along Channels with Varying Width

Abstract:

We extend the application of numerical entropy production, as a smoothness indicator, from conservation laws to balance laws. We aim to indicate the smoothness of solutions to the shallow water equations involving varying width, which are a system of balance laws. The numerical entropy production appears to be accurate to detect discontinuities. As a numerical test, a radial dam break is considered. We assume that there is a higher level of water inside a radial dam than water outside the dam wall. If the radial dam is totally broken, then water flows from inside to outside. The flow results in a solution having shock discontinuities. Finding the positions of the discontinuities is our interest. They are the positions where numerical solutions, such as those generated by a finite volume method, decrease their accuracy. Detecting the position of the discontinuity can help in the improvement of the numerical solution in terms of its accuracy. We obtain that the numerical entropy production is simple to implement but give an accurate detection. The discontinuity of the stage (free water surface) is clearly detected by large values of the numerical entropy production as the smoothness indicator.

• Periodical: Applied Mechanics and Materials (Volume 771)
• Pages: 157-160
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.771.157
• Online since: July 2015
• Authors: Sudi Mungkasi*
• Keywords: Finite Volume Method (FVM), Numerical Entropy Production, Shallow Water Equations, Smoothness Indicator, Varying Width

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