期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 467, 期 -, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2022.111465
关键词
TENO; THINC; WENO; Shock-capturing schemes; Hyperbolic conservation laws
资金
- Guangdong Basic and Applied Basic Research Foundation [2022A1515011779]
- Key Laboratory of Computational Aerodynamics, AVIC Aerodynamics Research Institute
- Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone [HZQB-KCZYB-2020083]
In this study, a new low-dissipation TENO scheme is proposed for compressible flow simulations, which enhances the capability of resolving discontinuities and suppresses numerical oscillations through an improved discontinuity-detecting criterion, a local interpolation-like strategy, and a two-steepness approximation.
For compressible flows characterized by a wide range of flow length scales and discontinuities, it is still an open challenge to design the optimal schemes, which resolve the small-scale flow structures with low numerical dissipation and capture the shock waves without artificial oscillations. In Takagi et al. [1], a novel TENO5-THINC scheme with the combination of classical TENO5 (fifth-order Targeted Essentially Non-Oscillatory) scheme and the non-polynomial THINC (Tangent of Hyperbola for INterface Capturing) reconstruction has been proposed. Building upon the strategy of isolating discontinuities from smooth and high-wavenumber regions, in the present work, a new very low-dissipation TENO scheme with discontinuity-resolving property is proposed for compressible flow simulations based on three new concepts: (1) an improved discontinuity-detecting criterion is devised based on the TENO weighting strategy, which significantly enhances the discontinuity-detecting accuracy compared to that in TENO5-THINC; (2) A local interpolation-like strategy is pro-posed to represent the detected discontinuity with subcell resolutions, and this strategy can minimize the numerical dissipation even when compared to the THINC reconstruction scheme; (3) According to the varying sharpness of the discontinuities separated by the discontinuity-detecting indicator, the local interpolation-like strategy is extended with a two-steepness approximation. Specifically, the discontinuities will be classified as genuinely sharp discontinuities and general ones. For the genuinely sharp discontinuities, the inter-face flux will be estimated by a steeper step-like function with even less numerical dissipation. The resulting scheme maintains the high-order and low-dissipation properties of the TENO scheme for smooth flow scales, while further improving the discontinuity-resolving capability and suppressing the numerical oscillations in the vicinity of discontinuities. A variety of benchmark cases with broadband length scales as well as discontinuities is presented to demonstrate the high wave-resolution property and the sharp shock-capturing capability of the proposed scheme. (C) 2022 Elsevier Inc. All rights reserved.
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