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CLC number: O354.4; O354.5

On-line Access: 2020-06-11

Received: 2020-01-19

Revision Accepted: 2020-06-22

Crosschecked: 2020-07-15

Cited: 0

Clicked: 2005

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Liang Li

https://orcid.org/0000-0002-8116-0668

Hong-bo Wang

https://orcid.org/0000-0002-9177-0582

Guo-yan Zhao

https://orcid.org/0000-0001-7831-7049

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Journal of Zhejiang University SCIENCE A 2020 Vol.21 No.9 P.695-720

http://doi.org/10.1631/jzus.A2000006


Efficient WENOCU4 scheme with three different adaptive switches


Author(s):  Liang Li, Hong-bo Wang, Guo-yan Zhao, Ming-bo Sun, Da-peng Xiong, Tao Tang

Affiliation(s):  Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha 410073, China

Corresponding email(s):   whbwatch@nudt.edu.cn, zhaoguoyan09@nudt.edu.cn

Key Words:  WENOCU4, Shock-capturing schemes, Adaptive switch, Numerical robustness, Dissipation


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Liang Li, Hong-bo Wang, Guo-yan Zhao, Ming-bo Sun, Da-peng Xiong, Tao Tang. Efficient WENOCU4 scheme with three different adaptive switches[J]. Journal of Zhejiang University Science A, 2020, 21(9): 695-720.

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Abstract: 
Although classical WENOCU schemes can achieve high-order accuracy by introducing a moderate constant parameter C to increase the contribution of optimal weights, they exhibit distinct numerical dissipation in smooth regions. This study presents an extension of our previous research which confirmed that adaptively adjusting parameter C can indeed overcome the inadequacy of the usage of a constant small value. Cmin is applied near a discontinuity while Cmax is used elsewhere and they are switched according to the variation of the local flow-field property. This study provides the reference values of the adaptive parameter C of WENOCU4 and systematically evaluates the comprehensive performance of three different switches (labeled as the binary, continuous, and hyperbolic tangent switches, respectively) based on an optimized efficient WENOCU4 scheme (labeled as EWENOCU4). Varieties of 1D scalar equations, empirical dispersion relation analysis, and multi-dimensional benchmark cases of Euler equations are analyzed. Generally, the dissipation and dispersion properties of these three switches are similar. Especially, employing the binary switch, EWENOCU4 achieves the best comprehensive properties. Specifically, the binary switch can efficiently filter more misidentifications in smooth regions than others do, particularly for the cases of 1D scalar equations and Euler equations. Also, the computational efficiency of the binary switch is superior to that of the hyperbolic tangent switch. Moreover, the optimized scheme exhibits high-resolution spectral properties in the wavenumber space. Therefore, employing the binary switch is a more cost-effective improvement for schemes and is particularly suitable for the simulation of complex shock/turbulence interaction. This study provides useful guidance for the reference values of parameter C and the evaluation of adaptive switches.

三种不同自适应开关的高效WENOCU4格式研究

目的:现有研究尚未提供WENOCU4格式中参数C的建议值.本文旨在根据流场特性自适应地调节参数C的量级从而提高格式的数值表现. 为此,通过广泛的数值模拟以提供自适应参数C的参考值,并系统地评估三种能够自适应调节参数C的开关的性能,测得综合表现最佳的开关,进而为获得高阶WENO改进型格式提供参考.
创新点:1. 提供了高效WENOCU4格式的自适应参数C的参考值; 2. 系统地评估了三种自适应开关(二进制型、连续型和双曲正切型)的性能,并证实了二进制型开关的最佳表现.
方法:1. 通过理论分析,系统研究三种自适应开关的原理和性能特点; 2. 通过广泛的数值模拟(包括一维标量方程、经验色散关系和多维欧拉方程的标准算例),获得自适应参数C的参考值并验证其合理性; 3. 通过广泛的数值模拟,系统评估三种自适应开关的综合表现(包括数值色散和耗散特性以及计算效率),并获得综合性能最佳的自适应开关.
结论:1. 对于高效WENOCU4格式而言,本研究证实了Cmin=40和Cmax=400是合理的自适应参数C的参考值,因此不应该直接采用WENOCU6的原始建议值. 2. 根据流场的连续性,采用自适应的参数C可以在保证数值稳定性的同时,有效地抑制WENOCU4的数值耗散. 3. 相比于其它开关,二进制型开关的综合表现最佳;其能够过滤激波感知器在光滑区域的一些误判,构造简单,且计算效率较高. 4. 本研究对三种自适应开关的评估具有一般性,因此易于拓展到其它高阶WENO格式的改进工作中.

关键词:WENOCU4; 激波捕捉格式; 自适应开关; 数值鲁棒性; 耗散性

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