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High-Order Methods for Simulations in Engineering

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Efficient High-Order Discretizations for Computational Fluid Dynamics

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 602))

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Abstract

Engineers create new things and hence always have to deal with incomplete information. A critical review is made of the accuracy of the available physical and modeling parameters. It shows that in many cases key physical and modeling parameters such as viscosities, boundary conditions, geometry, and even basic physics are not known to within 1%. This raises the question as to whether any numerical method needs to be of even higher quality than a fraction of this threshold. Thereafter work estimates for traditional high-order elements are derived. The comparison of error and work estimates shows that even for relative accuracy in the 0.1% range, which is one order below the typical accuracy of engineering interest (1% range), linear elements may outperform all higher order elements. The chapter concludes with some recent LES results that indicate that eight-order schemes on a grid of size 2h are similar to second-order schemes on a grid of size h, and some open questions.

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Acknowledgements

It is a pleasure to acknowledge many fruitful discussions on high-order methods with Profs. Ramon Codina (UPC, Barcelona), Antonio Huerta (UPC, Barcelona), Dominique Pelletier (Montreal), as well as Drs. Romain Aubry (GMU, NRL), Adrien Loseille (INRIA, Rocquencourt), Frederic Alauzet (INRIA, Rocquencourt) and Javier Principe (CIMNE, Barcelona) throughout the decades.

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  1. Center for Computational Fluid Dynamics, George Mason University, Fairfax, VA, 22030-4444, USA

    Rainald Löhner

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  1. Rainald Löhner
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Correspondence to Rainald Löhner .

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  1. Institute for Computational Mechanics, Technical University Munich, Garching bei München, Germany

    Martin Kronbichler

  2. Department of Mathematics, University of California, Berkeley, Berkeley, CA, USA

    Per-Olof Persson

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Löhner, R. (2021). High-Order Methods for Simulations in Engineering. In: Kronbichler, M., Persson, PO. (eds) Efficient High-Order Discretizations for Computational Fluid Dynamics. CISM International Centre for Mechanical Sciences, vol 602. Springer, Cham. https://doi.org/10.1007/978-3-030-60610-7_7

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  • DOI: https://doi.org/10.1007/978-3-030-60610-7_7

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