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Skew-symmetric splitting of high-order central schemes with nonlinear filters for computational aeroacoustics turbulence with shocks

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Abstract

A class of high-order nonlinear filter schemes by Yee et al. (J Comput Phys 150:199–238, 1999), Sjögreen and Yee (J Comput Phys 225:910–934, 2007), and Kotov et al. (Commun Comput Phys 19:273–300, 2016; J Comput Phys 307:189–202, 2016) is examined for long-time integrations of computational aeroacoustics (CAA) turbulence applications. This class of schemes was designed for an improved nonlinear stability and accuracy for long-time integration of compressible direct numerical simulation and large eddy simulation computations for both shock-free turbulence and turbulence with shocks. They are based on the skew-symmetric splitting version of the high-order central base scheme in conjunction with adaptive low-dissipation control via a nonlinear filter step to help with stability and accuracy capturing at shock-free regions as well as in the vicinity of discontinuities. The central dispersion-relation-preserving schemes as well as classical central schemes of arbitrary orders fit into the framework of skew-symmetric splitting of the inviscid flux derivatives. Numerical experiments on CAA turbulence test cases are validated.

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Acknowledgements

Funding was provided by Ames Research Center (Grant No. 1009492.02.01.01.05.02).

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Authors and Affiliations

  1. Multid Analyses AB, Gothenburg, Sweden

    B. Sjögreen

  2. NASA Ames Research Center, Mountain View, USA

    H. C. Yee & A. A. Wray

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  1. B. Sjögreen
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  2. H. C. Yee
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  3. A. A. Wray
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Correspondence to H. C. Yee.

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Communicated by C.-H. Chang.

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Sjögreen, B., Yee, H.C. & Wray, A.A. Skew-symmetric splitting of high-order central schemes with nonlinear filters for computational aeroacoustics turbulence with shocks. Shock Waves 29, 1117–1132 (2019). https://doi.org/10.1007/s00193-019-00925-z

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