Flux limiters on clustered points for solving hyperbolic conservation laws

Javad Farzi (Department of Applied mathematics, Sahand University of Technology)

It is well known that the solutions of hyperbolic conservation laws have, in general, discontinuities and shocks in the domain of solution. To obtain non-oscillatory, entropy satisfying accurate solutions there are different approaches, which have been extensively studied in the literature. A well-known approach is to use the flux limiters to control the spurious oscillations and kill out the overshoots and undershoots in the vicinity of discontinuity or shock. In this paper we mainly study the effect of grid clustering to reduce the mentioned oscillations and provide sharp solutions.