Numerical entropy production as smoothness indicator for shallow water equations

Sudi Mungkasi, Stephen Gwyn Roberts

Abstract


The numerical entropy production (NEP) for shallow water equations (SWE) is discussed and implemented as a smoothness indicator. We consider SWE in three different dimensions, namely, one-dimensional, one-and-a-half-dimensional, and two-dimensional SWE. An existing numerical entropy scheme is reviewed and an alternative scheme is provided. We prove the properties of these two numerical entropy schemes relating to the entropy steady state and consistency with the entropy equality on smooth regions. Simulation results show that both schemes produce NEP with the same behaviour for detecting discontinuities of solutions and perform similarly as smoothness indicators. An implementation of the NEP for an adaptive numerical method is also demonstrated.

doi:10.1017/S1446181119000154

Keywords


smoothness indicator, shock detector, numerical entropy production, finite volume method, shallow water equations.



DOI: https://doi.org/10.21914/anziamj.v61i0.14423



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.