Numerical entropy production as smoothness indicator for shallow water equations


  • Sudi Mungkasi Sanata Dharma University
  • Stephen Gwyn Roberts Australian National University



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


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

Author Biographies

Sudi Mungkasi, Sanata Dharma University

Associate Professor & Dean of Faculty of Science and Technology, Department of Mathematics, Faculty of Science and Technology, Sanata Dharma University, Yogyakarta, Indonesia.

Stephen Gwyn Roberts, Australian National University

Professor & Undergraduate Convenor of Mathematics, Mathematical Sciences Institute, College of Physical and Mathematical Sciences, Australian National University, Canberra.





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