A comparative study of TVD-limiters—well-known limiters and an introduction of new ones
Article first published online: 28 MAY 2010
Copyright © 2010 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids
Volume 67, Issue 4, pages 404–440, 10 October 2011
How to Cite
Kemm, F. (2011), A comparative study of TVD-limiters—well-known limiters and an introduction of new ones. Int. J. Numer. Meth. Fluids, 67: 404–440. doi: 10.1002/fld.2357
- Issue published online: 1 SEP 2011
- Article first published online: 28 MAY 2010
- Manuscript Accepted: 15 APR 2010
- Manuscript Revised: 2 MAR 2010
- Manuscript Received: 23 APR 2009
- total variation diminishing;
- finite volumes;
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 © 2010 John Wiley & Sons, Ltd.