期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 374, 期 -, 页码 724-751出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2018.07.043
关键词
TENO scheme; WENO scheme; Optimal finite difference scheme; High order scheme; Shock-turbulence interaction
资金
- China Scholarship Council [201206290022]
- National Natural Science Foundation of China [11628206]
In Fu et al. [23], a family of high-order targeted ENO (TENO) schemes with a new nonlinear weighting strategy has been proposed. Building upon this strategy, in the current paper, a new class of adaptive TENO schemes for hyperbolic conservation laws is proposed based on three new concepts: (1) a hierarchical voting strategy is proposed to improve the ENO-like stencil selection; (2) the TENO weighting strategy is extended to function as a built-in discontinuity-location detector. Since the reconstruction scheme must not cross any discontinuity, corresponding target schemes are selected from a set of predefined linear schemes which are optimized towards maximum accuracy order or spectral resolution; (3) based on the observation that the cut-off parameter C-T in the TENO weighting strategy determines nonlinear dissipation, a C-T adaptation strategy is developed to minimize numerical dissipation for high-wavenumber fluctuations while maintaining robustness for shock-capturing. Six-point and eight-point TENO schemes are constructed, and their spectral properties are analyzed by the ADR analysis. A set of benchmark cases is considered to demonstrate the performance of proposed adaptive TENO schemes. Numerical results suggest that the proposed TENO schemes preserve the accuracy order at first and second order critical points and show less numerical dissipation compared with typical WENO schemes. Moreover, the TENO8-NA scheme exhibits good results for both highly compressible flows and nearly incompressible turbulence. (C) 2018 Elsevier Inc. All rights reserved.
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