Non-oscillatory spectral element Chebyshev method for shock wave calculations
type: Item
instance of: scholarly article
title: Non-oscillatory spectral element Chebyshev method for shock wave calculations
zbMATH Open document ID: 0781.65083
author: David Sidilkover
author: George Em Karniadakis
published in: Journal of Computational Physics
publication date: 1994-02-17T00:00:00Z
review text: A new algorithm on a non-oscillatory spectral element discretization is developed for the solution of hyperbolic partial differential equations. A conservative formulation is proposed based on cell averaging and reconstruction procedures, that employ a staggered grid of Gauss- Chebyshev and Gauss-Lobatto-Chebyshev discretizations. The non-oscillatory reconstruction procedure is based on ideas similar to those proposed by \textit{W. Cai, D. Gottlieb} and \textit{C.-W. Shu} [Math. Comput. 52, No. 186, 389-410 (1989; Zbl 0666.65067)] but employs a modified technique which is more robust and simpler in terms of determining the location and strength of a discontinuity. It is demonstrated by model problems of linear advection, the inviscid Burgers equation and a one-dimensional Euler system that the proposed algorithm leads to stable, non-oscillatory results. Exponential accuracy away from the discontinuity is realized for the inviscid Burgers' equation example.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 76L05
zbMATH DE Number: 404846
zbMATH Keywords: non-oscillatory spectral element Chebyshev method
zbMATH Keywords: shock wave
zbMATH Keywords: cell averaging
zbMATH Keywords: Gauss-Lobatto-Chebyshev discretizations
zbMATH Keywords: linear advection
zbMATH Keywords: inviscid Burgers' equation
zbMATH Keywords: Euler system
reviewed by: Roumen Anguelov
MaRDI profile type: Publication
full work available at URL: jcph.1993.1121
OpenAlex ID: W1998740995
DOI: 10.1006/JCPH.1993.1121
description: scientific article; zbMATH DE number 404846