A comparative study of TVD-limiters-well-known limiters and an introduction of new ones

This paper gives a comparative study of TVD-limiters for standard explicit Finite Volume schemes. In contrast to older studies, it includes also unsymmetrical limiter functions that depend on the local CFL-number. We classify the limiters and show how to extend these families of limiters. We introduce a new member of the Superbee family, which is adapted to Roe's linear third-order scheme. Based on an idea by Serna and Marquina, new smooth limiters are introduced, which turn the van Leer and van Albada limiters into complete classes of limiters. The comparison of the limiters is done with some standard test cases. The results clarify the influence of the chosen limiter on the quality of the numerical results. Compared with ENO or WENO schemes, they also show the high resolution, which can be obtained by a CFL-number-dependent limiter when the grid is not highly refined. Copyright (C) 2010 John Wiley & Sons, Ltd.