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

Sudi Mungkasi, Stephen Gwyn Roberts

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


Keywords


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

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

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Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
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p-ISSN: 2086-8952 | e-ISSN: 2460-0245


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