非结构网格二阶有限体积法中黏性通量离散格式精度分析与改进

王年华; 李明; 张来平

doi:10.6052/0459-1879-18-037

非结构网格二阶有限体积法中黏性通量离散格式精度分析与改进

doi: 10.6052/0459-1879-18-037

王年华^1,*, ,,
李明¹,
张来平^1,2

1 中国空气动力研究与发展中心计算空气动力研究所,四川绵阳 621000
2 中国空气动力研究与发展中心空气动力学国家重点实验室,四川绵阳 621000

基金项目: 国家重点研发计划(2016YFB0200701)和国家自然科学基金(11532016, 91530325)资助项目.

详细信息

作者简介:
通讯作者:王年华,研究实习员,主要研究方向: 计算流体力学, 有限体积离散方法. E-mail：nianhuawong@126.com

通讯作者:
王年华

中图分类号: V211.3;
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出版历程
- 收稿日期: 2018-02-08
- 刊出日期: 2018-05-18

ACCURACY ANALYSIS AND IMPROVEMENT OF VISCOUS FLUX SCHEMES IN UNSTRUCTURED SECOND-ORDER FINITE-VOLUME DISCRETIZATION

Wang Nianhua^{1,*
, ,},
Li Ming¹,
Zhang Laiping^1,2

1 Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan, China
2 State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan, China

摘要

摘要: 非结构网格二阶有限体积离散方法广泛应用于计算流体力学工程实践中,研究非结构网格二阶精度有限体积离散方法的计算精度具有现实意义. 计算精度主要受到网格和计算方法的影响,本文从单元梯度重构方法、黏性通量中的界面梯度计算方法两个方面考察黏性流动模拟精度的影响因素. 首先从理论上分析了黏性通量离散中的“奇偶失联”问题,并通过基于标量扩散方程的制造解方法验证了“奇偶失联”导致的精度下降现象,进一步通过引入差分修正项消除了“奇偶失联”并提高了扩散方程计算精度;其次,在不同类型、不同质量的网格上进行基于扩散方程的制造解精度测试,考察单元梯度重构方法、界面梯度计算方法对扩散方程计算精度的影响,结果显示,单元梯度重构精度和界面梯度计算方法均对扩散方程计算精度起重要作用;最后对三个黏性流动算例(二维层流平板、二维湍流平板和二维翼型近尾迹流动)进行网格收敛性研究,初步验证了本文的结论,得到了计算精度和网格收敛性均较好的黏性通量计算格式.
- 非结构网格 /
- 有限体积方法 /
- 黏性通量 /
- 计算精度 /
- 网格收敛性研究 /
- 制造解方法
Abstract: Due to the widespread applications of unstructured second-order finite volume schemes in computational fluid dynamics (CFD) simulations, studying the discretization accuracy of second-order finite volume schemes is of practical value. Two primary factors that affecting accuracy of viscous flow simulation, including cell gradient reconstruction and interface gradient calculation method, are considered in this paper. Firstly, the odd-even decoupling problem in the discretization of viscous flux is analyzed theoretically and verified by the method of manufactured solutions (MMS) based on the scalar diffusion equation. Modification of interface gradient is proposed to eliminate the decoupling problem and the computational accuracy of the diffusion equation is improved greatly as a result. Then, the effects of cell gradient reconstruction and interface gradient method on the accuracy of viscous flow simulation are studied by the MMS method based on the diffusion equation. Results of MMS grid convergence tests show that cell gradient reconstruction and interface gradient method determine the accuracy of viscous flow simulation together. Finally, grid convergence tests are carried out for three realistic viscous flow cases, i.e., the laminar flat plate, the turbulent flat plate and the 2D airfoil near wake in NASA Turbulence Modeling Resource website. The numerical results verify the conclusions obtained by MMS tests, and the viscous flux discretization schemes are obtained with better performance in accuracy and grid convergence property.
- unstructured grids /
- finite volume schemes /
- viscous fluxes /
- numerical accuracy /
- grid convergence study /
- the method of manufactured solutions

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参考文献(1)

[1]	Roe PL. Error estimates for cell-vertex solution of compressible Euler equations. NASA Contract Report 178235, 1987
[2]	Giles MB.Accuracy of node-based solutions on irregular meshes// 11th International Conference on Numerical Methods in Fluid Dynamics, 1989, 323: 369-373
[3]	Aftosmis M, Gaitonde D, Tavares TS.Behavior of linear reconstruction techniques on unstructured meshes.AIAA Journal, 1995, 33(11): 2038-2049
[4]	Sozer E, Brehm C, Kiris CC. Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered CFD solvers. AIAA Paper 2014-1440, 2014
[5]	Smith TM, Barone MF, Bond RB, et al. Comparison of reconstruction techniques for unstructured mesh vertex centered finite volume schemes. AIAA Paper 2007-3958, 2007
[6]	Mavriplis DJ. Revisiting the least-squares procedure for gradient reconstruction on unstructured meshes. AIAA Paper 2003-3986, 2003
[7]	Diskin B, Thomas JL. Accuracy of gradient reconstruction on grids with high aspect ratio. NIA Report No.2008-12
[8]	王年华, 张来平, 马戎等. 非结构网格质量对梯度重构及无黏流动模拟精度的影响. 计算力学学报, 2017, 34(5): 555-563
[8]	(Wang Nianhua, Zhang Laiping, Ma Rong, et al.Mesh quality effects on the accuracy of gradient reconstruction and inviscid flow simulation on isotropic unstructured grids.Chinese Journal of Computational Mechanics, 2017, 34(5): 555-563 (in Chinese))
[9]	Diskin B, Thomas JL. Comparison of node-centered and cell-centered unstructured finite-volume discretizations: Inviscid fluxes. AIAA Paper 2010-1079, 2010
[10]	Diskin B, Thomas JL, Nielsen EJ, et al. Comparison of node-centered and cell-centered unstructured finite-volume discretizations: Viscous fluxes. AIAA Paper 2009-0597, 2009
[11]	Jalali A, Ollivier-Gooch C. Accuracy assessment of finite volume discretizations of convective fluxes on unstructured meshes. AIAA Paper 2013-0705, 2013
[12]	Jalali A, Ollivier-Gooch C. Accuracy assessment of finite volume discretizations of diffusive fluxes on unstructured meshes. AIAA Paper 2012-0606, 2012
[13]	Jalali A, Sharbatdar M, Ollivier GC.Accuracy analysis of unstructured finite volume discretization schemes for diffusive fluxes. Computers and Fluids, 2014, 101: 220-232
[14]	Haselbacher A, Blazek J.On the accurate and efficient discretization of the Navier-Stokes equations on mixed grids.AIAA Journal, 2000, 38(11): 2094-2102
[15]	Nishikawa H. Beyond interface gradient: A general principle for constructing diffusion schemes.AIAA Paper 2010-5093, 2010
[16]	Sejekan CB, Ollivier-Gooch C.Improving finite-volume diffusive fluxes through better reconstruction.Computers and Fluids, 2016, 139: 216-232
[17]	Katz A, Sankaran V.Mesh quality effects on the accuracy of CFD solutions on unstructured meshes.Journal of Computational Physics, 2011, 230(20): 7670-7686
[18]	Katz A, Sankaran V.High aspect ratio grid effects on the accuracy of Navier-Stokes solutions on unstructured meshes.Computers and Fluids, 2012, 65: 66-79
[19]	Betchen LJ, Staatman AG.An accurate gradient and Hessian reconstruction method for cell-centered finite volume discretizations on general unstructured grids.International Journal for Numerical Methods in Fluids, 2010, 62(9): 945-962
[20]	Karimian S, Straatman AG.Discretization and parallel performance of an unstructured Navier-Stokes solver.International Journal for Numerical Methods in Fluids, 2006, 52(6): 591-615
[21]	Moukalled F, Mangani L, Darwish M.The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM and Matlab. Springer, 2016
[22]	Holmes DG, Connell SD. Solution of the 2D Navier-Stokes equations on unstructured adaptive grids. AIAA Paper 89-1932, 1989
[23]	Kim SE, Makarov B, Caraeni D. A multi-dimensional linear reconstruction scheme for arbitrary unstructured grids. AIAA Paper 2003-3990, 2003
[24]	Jalali A, Ollivier-Gooch C.High-order unstructured finite volume RANS solution of turbulent compressible flows.Computers and Fluids, 2017, 143: 32-47
[25]	NASA Turbulence Modeling Resources,
[26]	Rumsey CL. Recent developments on the Turbulence Modeling Resource website. AIAA Paper 2015-2927, 2015
[27]	Childs ML, Pulliam TH, Jespersen DC. OVERFLOW, Turbulence Modeling Resource verification results. NAS Technical Report: NAS-2014-03
[28]	The Drag Prediction Workshop.
[29]	Roy CJ, Tinoco EN. Summary of Data from the Sixth AIAA CFD Drag Prediction Workshop: Case 1 Code Verification. AIAA Paper 2017-1206, 2017
[30]	Tinoco EN, Brodersen OP, Keye S, et.al. Summary of Data from the Sixth AIAA CFD Drag Prediction Workshop: CRM Cases 2 to 5. AIAA Paper 2017-1208, 2017
[31]	The High Lift Prediction Workshop.
[32]	Rumsey CL, Slotnick JP. Overview and summary of the Second AIAA High-Lift Prediction Workshop. AIAA Paper 2014-0747, 2014
[33]	Blazek J.Computational Fluid Dynamics: Principles and Application. Elsevier, 2001
[34]	王年华, 张来平, 赵钟等. 基于制造解的非结构二阶有限体积离散格式的精度测试与验证. 力学学报, 2017, 49(3): 627-637
[34]	(Wang Nianhua, Zhang Laiping, Zhao Zhong, et al.Accuracy verification of unstructured second-order finite volume discretization schemes based on the method of manufactured solutions.Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 627-637 (in Chinese))
[35]	徐明海. 非结构化网格的扩散通量计算方法评价. 工程热物理学报, 2005, 26(2): 313-315
[35]	(Xu Minghai.Comparison of methods for diffusion flux calculation on unstructured grids.Journal of Engineering Thermophysics, 2005, 26(2): 313-315 (in Chinese))
[36]	Roache PJ, Steinburg S.Symbolic manipulation and computational fluid dynamics.AIAA Journal, 1984, 22(10): 1390-1394
[37]	Roache PJ.Code verification by method of manufactured solutions.Transactions of ASME, 2002, 124: 4-10
[38]	He X, Zhao Z, Ma R, et al.Validation of HyperFLOW in subsonic and transonic flow.Acta Aerodynamical Sinica, 2016, 34(2): 267-275
[39]	He X, He XY, He L, et al.HyperFLOW: A structured/unstructured hybrid integrated computational environment for multi-purpose fluid simulation.Procedia Engineering, 2015, 126: 645-649