New two-dimensional slope limiters for discontinuous Galerkin methods on arbitrary meshes

Hussein Hoteit, Ph Ackerer*, R. Mosé, J. Erhel, B. Philippe

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

65 Scopus citations

Abstract

In this paper, we introduce an extension of Van Leer's slope limiter for two-dimensional discontinuous Galerkin (DG) methods on arbitrary unstructured quadrangular or triangular grids. The aim is to construct a non-oscillatory shock capturing DG method for the approximation of hyperbolic conservative laws without adding excessive numerical dispersion. Unlike some splitting techniques that are limited to linear approximations on rectangular grids, in this work, the solution is approximated by means of piecewise quadratic functions. The main idea of this new reconstructing and limiting technique follows a well-known approach where local maximum principle regions are defined by enforcing some constraints on the reconstruction of the solution. Numerical comparisons with some existing slope limiters on structured as well as on unstructured meshes show a superior accuracy of our proposed slope limiters.

Original languageEnglish (US)
Pages (from-to)2566-2593
Number of pages28
JournalInternational Journal for Numerical Methods in Engineering
Volume61
Issue number14
DOIs
StatePublished - Dec 14 2004

Keywords

  • Discontinuous Galerkin methods
  • Hyperbolic conservative laws
  • Slope limiters
  • Upwind schemes

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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