一种基于增量径向基函数插值的流场重构方法

刘溢浪; 张伟伟; 蒋跃文; 叶正寅

doi:10.6052/0459-1879-14-028

一种基于增量径向基函数插值的流场重构方法

doi: 10.6052/0459-1879-14-028

1.
西北工业大学航空学院, 西安 710072
2. 牛津大学工学院, 牛津 OX1 3PJ, 英国

基金项目: 国家自然科学基金（11172237），教育部“新世纪优秀人才支持计划”（NCET-13-0478）和陕西省“青年科技新星”计划等资助项目.

详细信息

作者简介:
张伟伟，教授，主要研究方向：非定常空气动力学、气动弹性力学及流动控制.E-mail：aeroelastic@nwpu.edu.cn

中图分类号: V211.3
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出版历程
- 收稿日期: 2014-01-21
- 修回日期: 2014-03-17
- 刊出日期: 2014-09-18

A RECONSTRUCTION METHOD FOR FINITE VOLUME FLOW FIELD SOLVING BASED ON INCREMENTAL RADIAL BASIS FUNCTIONS

1.
College of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China
2. Department of Engineering Science University of Oxford, Oxford, OX1 3PJ, UK

Funds: The project was supported by the National Natural Science Foundation of China (11172237), Program for New Century Excellent Talents in University (NCET-13-0478) and the Youth Nova of Science and Technology of Shanxi Province.

摘要

摘要: 由于流场参数重构中，用于重构的基网格单元的物理参数波动量相对于均值较小，径向基函数（RBF）直接插值方法重构会产生较大的数值振荡，论文提出了一种增量RBF 插值方法，并用于有限体积的流场重构步，明显改善了插值格式的收敛性和稳定性. 算例首先通过简单的一维模型说明该方法的有效性，当目标函数波动量相对于均值为小量时，增量RBF 插值能够抑制数值振荡；进一步通过二维亚音速、跨音速定常无黏算例、静止圆柱绕流非定常算例以及超音速前台阶算例来说明该方法在典型流场数值求解中的通用性和有效性. 研究表明增量RBF 重构方法可陡峭地捕捉激波间断，可有效改善流场求解的收敛性和稳定性，数值耗散小，计算效率高.
- 有限体积法 /
- 增量RBF插值 /
- 流场重构 /
- 稳定性
Abstract: A reconstruction method of flow field solving, based on incremental RBF (Radial Basis Functions) interpolation, has been developed in the paper. Since the fluctuation of flow parameters in the stencil cells used to reconstruct is small compared with the mean value in flow field reconstruction, direct RBF reconstruction will bring large numerical oscillations. The incremental RBF reconstruction developed in this paper effectively improves convergence and stability of the interpolation scheme. In first example, a simple one-dimensional model is used to illustrate the effective of this method when the fluctuation of the objective function is much smaller than the mean value. Furthermore, applicability and effectiveness of incremental RBF reconstruction method is proved by using four typical flow fields, namely, two-dimensional subsonic, transonic inviscid steady flow fields around NACA0012, the viscid unsteady flow around a stationary cylinder and a Mach 3 wind tunnel case with a step problem. Research shows that incremental RBF reconstruction method can smoothly capture steep shock and effectively improve the convergence and stability of flow solver with small numerical dissipation and high computational efficiency.
- finite volume /
- incremental RBF interpolation /
- reconstruction /
- stability

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参考文献(26)

李荫藩, 宋松和, 周铁. 双曲型守恒律的高阶、高分辨率有限体积法. 力学进展, 2001, 31(2): 245-263 (Li Yinfan, Song Songhe, Zhou Tie. High order, high resolution finite volume methods for hyperbolic conservation laws. Advances in Mechanics, 2001, 31(2): 245-263 (in Chinese))

张来平, 贺立新, 刘伟等. 基于非结构/混合网格的高阶精度格式研究进展. 力学进展, 2013, 43(2):202-236 (Zhang Laiping, He Lixin, Liu Wei, et al. Reviews of high-order methods on unstructured and hybrid grid. Advances in Mechanics, 2013, 43(2): 202-236 (in Chinese))

Barth TJ, Jespersen DC. The design and application of upwind schemes on unstructured meshes. AIAA 89-0366, 1989

Frink NT, Parikh P, Pirzadeh S. A fast upwind solver for the Euler equations on three-dimensional unstructured meshes. AIAA 91-0102, 1991

Barth TJ. A 3-D upwind Euler solver for unstructured meshes. AIAA 91-1548, 1991

Barth TJ. Aspects of unstructured grids and finite-volume solvers for the Euler and Navier-Stokes equations. AGARD R-787, Special Course on Unstructured Grid Methods for Advection Dominated Flows, Brussels, Belgium, 18-22 May, 1992, 6.1-6.61

蒋跃文, 叶正寅. 适用于任意网格类型的格心有限体积法. 力学学报, 2010, 42(5): 830-837 (Jiang Yuewen, Ye Zhengyin. A cell-centered finite volume method for arbitrary grid type. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(5): 830-837 (in Chinese))

Hardy RL. Multiquadric equations of topography and other irregular surfaces. Journal of Geophysical Research, 1971, 76(8):1905-1915

Carr JC, Beatson RK, Cherrie JB, et al. Reconstruction and representation of 3D objects with radial basis functions. Computer Graphics. 2001, 103(1): 67-76

Morig S, Sgallari F. The partition of unity method for high-order finite volume schemes using radial basis functions reconstruction. Numerical Mathematics, 2009, 2(2):153-179

Estruch O, Lehmkuhl O, Borrell R, et al. A parallel radial basis function interpolation method for unstructured dynamic meshes.Computers & Fluids, 2013, 80(10): 44-54

Moroney TJ, Turner IW. A three-dimensional finite volume method based on radial basis functions for the accurate computational modelling of nonlinear diffusion equations. Journal of Computational Physics, 2007, 225(2): 1409-1426

Stevens D, Power H, Lees M, et al. The use of PDE centres in the local RBF Hermitian method for 3D convective-diffusion problems. Journal of Computational Physics, 2009, 228(12): 4606-4624

Stevens D, Power H. A scalable and implicit meshless RBF method for the 3D unsteady nonlinear Richards equation with single and multi-zone domains. Numerical Methods in Engineering, 2011, 85(2): 135-163

Stevens D, Power H, Meng CY, et al. An alternative local collocation strategy for high-convergence meshless PDE solutions, using radial basis functions. Journal of Computational Physics, 2013, 254(1): 52-75

Shu C, Ding H, Yeo KS. Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, 2003, 192(7): 941-954

Yong YS, Chang S, Ning Q. Multiquadric finite difference (MQ-FD) method and its application. Advances in Applied Mathematics and Mechanics, 2009, 1(5): 615-638

Sonar T. Optimal recovery using thin plate splines in finite volume methods for the numerical solution of hyperbolic conservation laws. Journal of Numerical Analysis, 1996, 16(4): 549-581

Iske A, Sonar T. On the structure of function spaces in optimal recovery of point functionals for ENO-schemes by radial basis functions. Numerische Mathematik, 1996, 74(2): 177-201

钱旭, 宋松和. 径向基函数在三维Euler方程数值计算中的应用. 空气动力学学报, 2011, 29(2): 231-234 (Qian Xu, Song Songhe. Rasial basis functions with applications to numerical calculations of 3-D Euler equations. Acta Aerodynamic Sinica, 2011, 29(2): 231-234 (in Chinese))

Li C, Ye Z, Wang G. Simulation of flow separation at the wing-body junction with different fairings. Journal of Aircraft, 2008, 45(1): 258-266

Buhmann MD, Radial Basis Functions: Theory and Implementations. Cambridge University Press, Cambridge, 2009, 11-23

Tritton DJ. Experiments on the flow past a circular cylinder at low Reynolds numbers. Journal of Fluid Mechanics, 1959, 6(4): 547-560

Lu L, Qin JM, Teng B, et al. Numerical investigations of lift suppression by feedback rotary oscillation of circular cylinder at low Reynolds number. Physics of Fluids, 2011, 23(3): 033601

Su MD, Kang QJ. Large eddy simulation of the turbulence flow around a circular cylinder at sub-critical Reynolds numbers. Journal of Mechanics, 1999, 31 (1): 100-105

Woodward P, Colella P. The numerical simulation of two-dimensional fluid flow with strong shocks. Journal of Computational Physics, 1984, 54(1):115-173

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