Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 349, Issue -, Pages 97-121Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2017.07.054
Keywords
TENO; WENO; LES; DNS; Spectral property; High-order scheme
Funding
- China Scholarship Council [201206290022]
- National Natural Science Foundation of China [11628206]
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In this paper, we extend the range of targeted ENO (TENO) schemes (Fu etal. (2016) [18]) by proposing an eighth-order TENO8 scheme. Ageneral formulation to construct the high-order undivided difference tau(K) within the weighting strategy is proposed. With the underlying scale-separation strategy, sixth-order accuracy for tau(K) in the smooth solution regions is designed for good performance and robustness. Furthermore, a unified framework to optimize independently the dispersion and dissipation properties of high-order finite-difference schemes is proposed. The new framework enables tailoring of dispersion and dissipation as function of wavenumber. The optimal linear scheme has minimum dispersion error and a dissipation error that satisfies a dispersion-dissipation relation. Employing the optimal linear scheme, a sixth-order TENO8-opt scheme is constructed. A set of benchmark cases involving strong discontinuities and broadband fluctuations is computed to demonstrate the high-resolution properties of the new schemes. (C) 2017 Elsevier Inc. All rights reserved.
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