A problem-independent limiter for high-order Runge-Kutta discontinuous Galerkin methods
type: Item
instance of: scholarly article
title: A problem-independent limiter for high-order Runge-Kutta discontinuous Galerkin methods
zbMATH Open document ID: 0979.65081
author: A. Burbeau
author: P. Sagaut
author: Charles-Henri Bruneau
published in: Journal of Computational Physics
publication date: 2002-02-10T00:00:00Z
review text: In the field of high-order discontinuous methods for convection dominated problems on unstructured meshes, Runge-Kutta discontinuous Galerkin methods have attracted great interest during the last two decades. The aim of the present paper is to propose a new slope limiter for discontinuous Galerkin methods of any order of accuracy which satisfies certain properties [cf. \textit{B. Cockburn} and \textit{C. W. Shu}, J. Comput. Phys. 141, No. 2, 199-224 (1998; Zbl 0920.65059) and \textit{R. Biswas, K. D. Devine} and \textit{J. E. Flaherty}, Appl. Numer. Math. 14, No. 1-3, 255-283 (1994; Zbl 0826.65084)]. Numerical results illustrate here good behaviour of the proposed limiter, for any kind of solutions (regular or with discontinuities). Extension of the new limiting procedure to triangular meshes, for the set of basis functions of Dubiner and in case of \(P^1\) and \(P^2\) approximations is presented.
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 1610379
zbMATH Keywords: Runge-Kutta discontinuous Galerkin methods
zbMATH Keywords: slope limiter
zbMATH Keywords: Euler equations
zbMATH Keywords: method of IMAS
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: jcph.2001.6718
OpenAlex ID: W2070854540
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DOI: 10.1006/JCPH.2001.6718
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description: scientific article; zbMATH DE number 1610379