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Abstract

Numerical entropy production can be used as a smoothness indicator of solutions to conservation laws. By definition the entropy production is non-positive. However some authors, using a finite volume method framework, showed that positive overshoots of the numerical entropy production were possible for conservation laws (no source terms involved). Note that the one-and-a-half-dimensional shallow water equations without source terms are conservation laws. A report has been published regarding the behaviour of the numerical entropy production of the one-and-a-half-dimensional shallow water equations without source terms. The main result of that report was that positive overshoots of the numerical entropy production were avoided by use of a modified entropy flux which satisfies a discrete numerical entropy inequality. In the present article we consider an extension problem of the previous report. We take the one-and-a-half-dimensional shallow water equations involving topography. The topography is a source term in the considered system of equations. Our results confirm that a modified entropy flux which satisfies a discrete numerical entropy inequality is indeed required to have no positive overshoots of the entropy production.

DOI : http://dx.doi.org/10.22342/jims.21.1.198.35-43

Keywords

Numerical entropy production shallow water equations smoothness indicator finite volume method

Article Details

Author Biography

Sudi Mungkasi, Sanata Dharma University

Lecturer at the Department of Mathematics
How to Cite
Mungkasi, S. (2015). NUMERICAL ENTROPY PRODUCTION OF THE ONE-AND-A-HALF-DIMENSIONAL SHALLOW WATER EQUATIONS WITH TOPOGRAPHY. Journal of the Indonesian Mathematical Society, 21(1), 35–43. https://doi.org/10.22342/jims.21.1.198.35-43

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