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 language | English (US) |
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Pages (from-to) | 2566-2593 |
Number of pages | 28 |
Journal | International Journal for Numerical Methods in Engineering |
Volume | 61 |
Issue number | 14 |
DOIs | |
State | Published - Dec 14 2004 |
Externally published | Yes |
Keywords
- Discontinuous Galerkin methods
- Hyperbolic conservative laws
- Slope limiters
- Upwind schemes
ASJC Scopus subject areas
- Numerical Analysis
- General Engineering
- Applied Mathematics