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Stephen Gwyn Roberts
Mathematical Sciences Institute, The Australian National University,
Mathematics

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WEAK LOCAL RESIDUALS IN AN ADAPTIVE FINITE VOLUME METHOD FOR ONE-DIMENSIONAL SHALLOW WATER EQUATIONS Mungkasi, Sudi; Roberts, Stephen Gwyn
Journal of the Indonesian Mathematical Society Volume 20 Number 1 (April 2014)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.20.1.176.11-18

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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