Non-oscillatory Spectral Element Chebyshev Method for Shock Wave Calculations

✍ Scribed by David Sidilkover; George Em Karniadakis

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 462 KB
• Volume: 107
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1993.1121

✦ Synopsis

A new algorithm based on spectral element discretization and nonoscillatory ideas is developed for the solution of hyperbolic partial differential equations. A conservative formulation is proposed based on cell averaging and reconstruction procedures, that employs a staggered grid of Gauss Cliebyshev and Gauss - Lobatto Chebyshev discretizations. The non-oscillatory reconstruction procedure is based on ideas similar to those proposed by Cai et al. (Math. Comput. 52, 389 (1989)) 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 through model problems of linear advection, inviscid Burgers equation, and one-dimensional Euler system that the proposed aigorithm leads to stable, non-oscillatory accurate results. Exponential accuracy away from the discontinuity is realized for the inviscid Burgers equation example. (c) 1993 Academic Press, Inc.