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, 2014)
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 reï¬nement indicatorin an adaptive ï¬nite volume method for solving SWE. This is the ï¬rst studyin implementing WLR into an adaptive ï¬nite 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 theeï¬€ectiveness of WLR as the reï¬nement indicator in the adaptive method.DOI :Â http://dx.doi.org/10.22342/jims.20.1.176.11-18