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On the Stability and Accuracy of the Spectral Difference Method

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Abstract

In this article, it is shown that under certain conditions, the spectral difference (SD) method is independent of the position of the solution points. This greatly simplifies the design of such schemes, and it also offers the possibility of a significant increase in the efficiency of the method. Furthermore, an accuracy and stability study, based on wave propagation analysis, is presented for several 1D and 2D SD schemes. It was found that higher than second-order 1D SD schemes using the Chebyshev–Gauss–Lobatto nodes as the flux points have a weak instability. New flux points were identified which produce accurate and stable SD schemes. In addition, a weak instability was also found in 2D third- and fourth-order SD schemes on triangular grids. Several numerical tests were performed to verify the analysis.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Fluid Dynamics and Thermodynamics Research Group, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium

    Kris Van den Abeele & Chris Lacor

  2. Department of Aerospace Engineering, Iowa State University, 2271 Howe Hall, Ames, IA, 50011, USA

    Z. J. Wang

Authors
  1. Kris Van den Abeele
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  2. Chris Lacor
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  3. Z. J. Wang
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Correspondence to Kris Van den Abeele.

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Van den Abeele, K., Lacor, C. & Wang, Z.J. On the Stability and Accuracy of the Spectral Difference Method. J Sci Comput 37, 162–188 (2008). https://doi.org/10.1007/s10915-008-9201-0

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  • DOI: https://doi.org/10.1007/s10915-008-9201-0

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