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Advances in Mathematical Physics
Volume 2016, Article ID 7528625, 7 pages
Research Article

Adaptive Finite Volume Method for the Shallow Water Equations on Triangular Grids

Department of Mathematics, Faculty of Science and Technology, Sanata Dharma University, Mrican, Tromol Pos 29, Yogyakarta 55002, Indonesia

Received 31 March 2016; Revised 21 August 2016; Accepted 5 September 2016

Academic Editor: Soheil Salahshour

Copyright © 2016 Sudi Mungkasi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a numerical entropy production (NEP) scheme for two-dimensional shallow water equations on unstructured triangular grids. We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a finite volume method. Numerical simulations show that NEP is successful to be a refinement/coarsening indicator in the adaptive mesh finite volume method, as the method refines the mesh or grids around nonsmooth regions and coarsens them around smooth regions.