WENO Interpolation-Based and Upwind-Biased Free-Stream Preserving Nonlinear Schemes
WENO Interpolation-Based and Upwind-Biased Free-Stream Preserving Nonlinear Schemes
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基于 WENO 插值和逆风偏向自由流保护非线性方案
DOI：
10.4208/aamm.oa-2020-0170
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发表时间：
2021-06
影响因子：
1.4
通讯作者：
Xu Fengyuan
中科院分区：
文献类型：
--
作者：
Li Qin;Sun Dong;Xu Fengyuan
对于具有复杂几何形状和结构化网格的流动模拟，优选高阶差分格式以实现高精度。为了实现这一目标，满足自由流保持是必要的，以减少数值计算网格度量的数值误差。对于带通量分裂的线性迎风格式，自由流保持性在早期的研究[Q。Li等人，Commun. Comput.物理、22（2017），pp. 64-94]。本文提出了一系列新的基于韦诺插值的非线性迎风偏置格式。新的非线性格式在变形网格上具有激波捕捉能力，这是线性迎风格式所不具备的。该格式通过在中间点引入通量，采用韦诺插值来实现格式的非线性，并通过选择相应的网格格式来实现迎风偏置结构。开发了新的三阶和五阶非线性格式并进行了试验。讨论了所提出的格式、韦诺格式和混合WCNS格式之间的关系，得到了具有中点和节点的中心格式的一般形式。通过数值试验，所提出的格式可以达到设计的精度和自由流保持性能。在一维Sod和ShuOsher问题中，计算结果与理论预测一致.在二维情况下，对涡的保持、M∞ = 4的超声速无粘绕流、Riemann问题和激波-涡干扰问题进行了试验。更具体地，采用两种类型的栅格，即，均匀/光滑网格和随机化/局部随机化网格。所有格式在均匀/光滑网格上都能得到满意的结果。在随机网格上，除了Riemann问题和激波-涡干扰问题中的一个三阶格式失败外，大多数格式都能达到合理的计算精度。总的来说，所提出的非线性格式具有求解严重变形网格上流动问题的能力，可以用于工程应用。* 通讯作者。电子邮件：qin-li@vip.tom.com（Q. Li）http://www.global-sci.org/aamm 1441 c ©2021 Global Science Press 1442 Q. Li，D. Sun和F.徐/高级应用数学机械，13（2021），pp. 1441-1484 AMS科目分类：65 M06
For flow simulations with complex geometries and structured grids, it is preferred for high-order difference schemes to achieve high accuracy. In order to achieve this goal, the satisfaction of free-stream preservation is necessary to reduce the numerical error in the numerical evaluation of grid metrics. For the linear upwind schemes with flux splitting the free-stream preserving property has been achieved in the early study [Q. Li et al., Commun. Comput. Phys., 22 (2017), pp. 64–94]. In the current paper, new series of nonlinear upwind-biased schemes through WENO interpolation will be proposed. In the new nonlinear schemes, the shock-capturing capability on distorted grids is achieved, which is unavailable for the aforementioned linear upwind schemes. By the inclusion of fluxes on the midpoints, the nonlinearity in the scheme is obtained through WENO interpolations, and the upwind-biased construction is acquired by choosing relevant grid stencils. New thirdand fifth-order nonlinear schemes are developed and tested. Discussions are made among proposed schemes, alternative formulations of WENO and hybrid WCNS, in which a general formulation of center scheme with midpoint and nodes employed is obtained as a byproduct. Through the numerical tests, the proposed schemes can achieve the designed orders of accuracy and free-stream preservation property. In 1-D Sod and ShuOsher problems, the results are consistent with the theoretical predictions. In 2-D cases, the vortex preservation, supersonic inviscid flow around cylinder at M∞ = 4, Riemann problem, and shock-vortex interaction problems have been tested. More specifically, two types of grids are employed, i.e., the uniform/smooth grids and the randomized/locally-randomized grids. All schemes can get satisfactory results in uniform/smooth grids. On the randomized grids, most schemes have accomplished computations with reasonable accuracy, except the failure of one third-order scheme in Riemann problem and shock-vortex interaction. Overall, the proposed nonlinear schemes have the capability to solve flow problems on badly deformed grids, and the schemes can be used in the engineering applications. ∗Corresponding author. Email: qin-li@vip.tom.com (Q. Li) http://www.global-sci.org/aamm 1441 c ©2021 Global Science Press 1442 Q. Li, D. Sun and F. Xu / Adv. Appl. Math. Mech., 13 (2021), pp. 1441-1484 AMS subject classifications: 65M06
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DOI：
10.2514/6.1978-1208
发表时间：
1978-07
期刊：
--
影响因子：
--
作者：
P. Thomas;C. Lombard
通讯作者：
P. Thomas;C. Lombard
固定网格磁通分裂线性迎风方案度量评价误差的进一步研究
影响因子：
3.7
作者：
Qin Li;Dong Sun;Pengxin Liu
通讯作者：
Pengxin Liu
DOI：
10.2514/6.1978-10
发表时间：
1978
期刊：
--
影响因子：
--
作者：
T. Pulliam;J. Steger
通讯作者：
T. Pulliam;J. Steger
影响因子：
4.1
作者：
Jiang, GS;Shu, CW
通讯作者：
Shu, CW
DOI：
10.1016/j.jcp.2006.07.009
发表时间：
2006-12
期刊：
J. Comput. Phys.
影响因子：
--
作者：
S. Pirozzoli
通讯作者：
S. Pirozzoli