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High-Order Methods for Computational Physics pp 225–324Cite as

Adaptive Spectral Element Methods for Turbulence and Transition

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 9))

Abstract

These notes present an introduction to the spectral element method with applications to fluid dynamics. The method is introduced for one-dimensional problems, followed by the discretization of the advection and diffusion operators in multi-dimensions, and efficient ways of dealing with these operators numerically. We also discuss the mortar element method, a technique for incorporating local mesh refinement using nonconforming elements; this is the foundation for adaptive methods. An adaptive strategy based on analyzing the local polynomial spectrum is presented and shown to give accurate solutions even for problems with weak singularities. Finally we describe techniques for integrating the incompressible Navier-Stokes equations, including methods for performing computational linear and nonlinear stability analysis of non-parallel and time-periodic flows.

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  1. Aeronautics & Applied Mathematics, California Institute of Technology, Pasadena, California, 91125, USA

    Ronald D. Henderson

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  1. Ronald D. Henderson
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  1. Information Sciences Directorate, NASA Ames Research Center, 94035, Moffett Field, CA, USA

    Timothy J. Barth

  2. Karman Institute for Fluid Dynamics, Waterloosesteenweg, 72, 1640, Sint-Genesius-Rode, Belgium

    Herman Deconinck

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Henderson, R.D. (1999). Adaptive Spectral Element Methods for Turbulence and Transition. In: Barth, T.J., Deconinck, H. (eds) High-Order Methods for Computational Physics. Lecture Notes in Computational Science and Engineering, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03882-6_3

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  • DOI: https://doi.org/10.1007/978-3-662-03882-6_3

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