WEAK LOCAL RESIDUALS IN AN ADAPTIVE FINITE VOLUME METHOD FOR ONE-DIMENSIONAL SHALLOW WATER EQUATIONS

Sudi Mungkasi; Stephen Gwyn Roberts

doi:10.22342/jims.20.1.176.11-18

Sudi Mungkasi ⁽¹⁾ , Stephen Gwyn Roberts ⁽²⁾

(1) Department of Mathematics, Sanata Dharma University, Mrican, Tromol Pos 29, Yogyakarta 55002, Indonesia,

(2) Mathematical Sciences Institute, The Australian National University,, Australia

https://doi.org/10.22342/jims.20.1.176.11-18

Issue
Volume 20 Number 1 (April 2014)

Submitted
May 22, 2014

Accepted
May 23, 2014

Published
May 23, 2014

Keywords:

Finite volume methods, weak local residuals, reﬁnement indicator, adaptive mesh reﬁnement, shallow water equations

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Abstract

Weak local residual (WLR) detects the smoothness of numerical solutionsto conservation laws. In this paper we consider balance laws with a sourceterm, the shallow water equations (SWE). WLR is used as the reﬁnement indicatorin an adaptive ﬁnite volume method for solving SWE. This is the ﬁrst studyin implementing WLR into an adaptive ﬁnite volume method used to solve theSWE, where the adaptivity is with respect to its mesh or computational grids. Welimit our presentation to one-dimensional domain. Numerical simulations show theeﬀectiveness of WLR as the reﬁnement indicator in the adaptive method.

DOI : http://dx.doi.org/10.22342/jims.20.1.176.11-18

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Authors

Sudi Mungkasi

Department of Mathematics, Sanata Dharma University, Mrican, Tromol Pos 29, Yogyakarta 55002

penulis@jims-a.org (Primary Contact)

Stephen Gwyn Roberts

Mathematical Sciences Institute, The Australian National University,

Mungkasi, S., & Roberts, S. G. (2014). WEAK LOCAL RESIDUALS IN AN ADAPTIVE FINITE VOLUME METHOD FOR ONE-DIMENSIONAL SHALLOW WATER EQUATIONS. Journal of the Indonesian Mathematical Society, 20(1), 11–18. https://doi.org/10.22342/jims.20.1.176.11-18