全局方向模板对非结构有限体积梯度与高阶导数重构的影响

孔令发; 董义道; 刘伟

doi:10.6052/0459-1879-20-093

全局方向模板对非结构有限体积梯度与高阶导数重构的影响

国防科技大学空天科学学院, 长沙410073

基金项目: 1)国家重大资助项目(GJXM92579)

详细信息

通讯作者:
刘伟

中图分类号: V211.3
计量
- 文章访问数: 01445
- HTML全文浏览量: 0329
- PDF下载量: 096
出版历程
- 收稿日期: 2020-03-24
- 刊出日期: 2020-10-09

THE INFLUENCE OF GLOBAL-DIRECTION STENCIL ON GRADIENT AND HIGH-ORDER DERIVATIVES RECONSTRUCTION OF UNSTRUCTURED FINITE VOLUME METHODS

College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China

摘要

摘要: 模板选择方式对非结构有限体积方法的计算准确性会产生显著影响. 在之前的工作中, 基于局部方向模板存在的问题, 我们探索了一种更加简单有效的全局方向模板选择方法, 并将其应用于二阶精度非结构有限体积求解器. 基于该方法找到的模板单元均沿着壁面法向与流向, 可有效捕捉流场变化, 反映流动的各向异性, 并且模板选择过程脱离了对网格拓扑的依赖, 避免了局部方向模板选择方法中复杂的阵面推进与方向判断过程, 克服了在大压缩比三角形网格上模板单元偏离壁面法向的现象, 同时在二阶精度求解器上得到了较高的计算精度与计算准确性. 为了进一步验证全局方向模板在高阶精度非结构有限体积方法中应用的可行性, 本文初步测试了该模板对变量梯度及高阶导数重构的影响. 经检验, 在不同类型的网格上, 采用全局方向模板得到的变量梯度与高阶导数误差明显低于局部方向模板, 同时也低于共点模板的计算误差. 此外, 在高斯积分点处由全局方向模板得到的变量点值与导数误差同样在三种模板中最低. 因此该模板选择方法在非结构有限体积梯度与高阶导数重构方面具有较好的数值表现, 具备在高阶精度非结构有限体积求解器中应用并推广的可行性.
- 高阶精度非结构有限体积方法 /
- $k$-exact重构算法 /
- 模板选择方法 /
- 全局方向 /
- 局部方向
Abstract: The accuracy of unstructured finite volume methods is greatly influenced by different stencils. In previous work, based on the existing problems of local-direction stencil, we explored a more concise global-direction stencil selection method for the second-order unstructured finite volume solver, and stencil cells selected by this novel stencil selection method are always along the boundary normal and circumferential directions even on grids with high aspect ratio. As a result, the variation of flowfield is effectively captured, and flow anisotropy are well reflected. In addition, the novel method is topology-independent, since global directions are determined by the flowfield, while the local directions are strongly coupled with the grid. Therefore, the complex process of advancing front as well as local directions estimation are completely avoided in the novel stencil selection method, and the phenomenon that stencil cells deviate from the boundary normal vector is effectively eliminated on high-aspect-ratio triangular grids. What's more, a better computational accuracy and lower truncation errors on the second-order accurate finite volume solver are obtained by the employment of global-direction stencil. In order to further test the effectiveness of global-direction stencil on high-order unstructured finite volume methods, we will preliminarily utilize this stencil to test the effect of gradient and high-order derivatives reconstruction. After verification, computational errors of global-direction stencil are lower than that of local-direction stencil, and also lower than that of commonly used vertex-neighbor stencil on different grid types. Besides, errors of variable and derivatives at the Gauss point obtained by global-direction stencil are also the lowest among three methods we tested. Therefore, the global-direction stencil is well performed on gradient as well as high-order derivatives reconstruction, and it is feasible to extend this novel stencil selection method to high-order unstructured finite volume methods.
- high-order unstructured finite volume methods /
- $k$-exact reconstruction algorithm /
- stencil selection method /
- global direction /
- local direction

HTML全文

参考文献(1)

[1]	Mavriplis DJ. Unstructured grid techniques. Annual Review of Fluid Mechanics, 1997,29:473-547
[2]	曾扬兵, 沈孟育, 王保国等. N-S方程在非结构网格下的求解. 力学学报, 1996,28(6):641-650
[2]	( Zeng Yangbing, Shen Mengyu, Wang Baoguo, et al. Solution of N-S equations on unstructured grid. Chinese Journal of Theoretical and Applied Mechanics, 1996,28(6):641-650 (in Chinese))
[3]	王年华, 李明, 张来平. 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. 力学学报, 2018,50(3):527-537
[3]	( Wang Nianhua, Li Ming, Zhang Laiping. Accuracy analysis and improvement of viscous flux schemes in unstructured second-order finite-volume discretization. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(3):527-537 (in Chinese))
[4]	Dufresne Y, Moureau V, Lartigue G, et al. A massively parallel CFD/DEM approach for reactive gas-solid flows in complex geometries using unstructured meshes. Computers & Fluids, 2020,198:104402
[5]	王年华, 常兴华, 马戎等. HyperFlow软件非结构网格亚跨声速湍流模拟的验证与确认. 力学学报, 2019,51(3):813-825
[5]	( Wang Nianhua, Chang Xinghua, Ma Rong, et al. Verification and validation of HyperFlow solver for subsonic and transonic turbulent flow simulations on unstructured/hybrid grids. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(3):813-825 (in Chinese))
[6]	Park MA, Balan A, Anderson WK, et al. Verification of unstructured grid adaptation components// AIAA Scitech 2019 Forum, San Diego, 2019-1-7-11, 2019: 1723
[7]	邵帅, 李明, 王年华等. 基于非结构/混合网格模拟黏性流的高阶精度DDG/FV 混合方法. 力学学报, 2018,50(6):1470-1482
[7]	( Shao Shuai, Li Ming, Wang Nianhua, et al. High-order DDG/FV hybrid method for viscous flow simulation based on unstructured / hybrid grid. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(6):1470-1482 (in Chinese))
[8]	Diskin B, Thomas JL, Nielsen EJ, et al. Comparison of node-centered and cell-centered unstructured finite-volume discretizations: Viscous fluxes. AIAA Journal, 2010,48:1326-1338
[9]	Diskin B, Thomas JL. Comparison of node-centered and cell-centered unstructured finite-volume discretizations: Inviscid fluxes. AIAA Journal, 2011,49:836-854
[10]	Jameson A, Mavriplis DJ. Finite volume solution of the two-dimensional Euler equations on a regular triangular mesh. AIAA Journal, 1986,24:611-618
[11]	Caraeni D, Hill DC. Unstructured-grid third-order finite volume discretization using a multistep quadratic data-reconstruction method. AIAA Journal, 2010,48:808-817
[12]	Schwoppe A, Diskin B. Accuracy of the cell-centered grid metric in the DLR TAU-Code. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 2013,121:429-437
[13]	贺立新, 张来平, 张涵信. 间断Galerkin有限元和有限体积. 力学学报, 2007,23(1):15-22
[13]	( He Lixin, Zhang Laiping, Zhang Hanxin. Discontinuous Galerkin finite element and finite volume. Chinese Journal of Theoretical and Applied Mechanics, 2007,23(1):15-22 (in Chinese))
[14]	Mavriplis DJ. Multigrid solution of the two-dimensional Euler equations on unstructured triangular meshes. AIAA Journal, 1988,26:824-831
[15]	赵辉, 张耀冰, 陈江涛等. 非结构网格体心梯度求解方法的精度分析. 空气动力学学报, 2019,37(5):844-854
[15]	( Zhao Hui, Zhang Yaobing, Chen Jiangtao, et al. Accuracy analysis of the method for solving the cell-centered gradient on unstructured grid. Acta Aerodynamica Sinica, 2019,37(5):844-854 (in Chinese))
[16]	Shima E, Kitamura K, Haga T. Green-gauss/weighted-least-squares hybrid gradient reconstruction for arbitrary polyhedra unstructured grids. AIAA Journal, 2013,51:2740-2747
[17]	王亚辉, 刘伟, 袁礼等. 求解二维Euler方程有限单元边插值的降维重构算法. 气体物理, 2019,3:34-41
[17]	( Wang Yahui, Liu Wei, Yuan Li, et al. A dimension reduction reconstruction algorithm for solving two-dimensional Euler equations with finite element edge interpolation. Physics of Gases, 2019,3:34-41 (in Chinese))
[18]	Moukalled F, Mangani L, Darwish M. The Finite Volume Method in Computational Fluid Dynamics. Berlin: Springer, 2016: 46-49
[19]	张帆. 非结构网格有限体积法的空间离散算法研究. [博士论文]. 大连: 大连理工大学, 2017
[19]	( Zhang Fan. Research on spatial discretization algorithm of unstructured mesh finite volume method. [PhD Thesis]. Dalian: Dalian University of Technology, 2017 (in Chinese))
[20]	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
[20]	( 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))
[21]	Sokolova I, Bastisya MG, Hajibeygi H. Multiscale finite volume method for finite-volume-based simulation of poroelasticity. Journal of Computational Physics, 2019,379:309-324.
[22]	White JA, Nishikawa H, Baurle RA. Weighted least-squares cell-average gradient construction methods for The VULCAN-CFD second-order accurate unstructured grid cell-centered finite-volume solver// AIAA Scitech 2019 Forum, San Diego, 2019-1-7-11, 2019: 0127
[23]	Nishikawa H, White JA. Face-and cell-averaged nodal-gradient approach to cell-centered finite-volume method on mixed grids// AIAA Scitech 2020 Forum, Orlando, 2020-1-6-10, 2020: 1787
[24]	Nishikawa H. Efficient gradient stencils for robust implicit finite-volume solver convergence on distorted grids. Journal of Computational Physics, 2019,386:486-501
[25]	Barth TJ, Jaespersen DC. The design and application of upwind schemes on unstructured meshes// 27th Aerospace Sciences Meeting, Nevada, 1989-1-9-12, 1989: 0366
[26]	Barth TJ. A 3-D upwind Euler solver for unstructured meshes// 10th Computational Fluid Dynamics Conference. Hawaii, 1991-1-24-27, 1991: 1548
[27]	Jalali A, Ollivier-Gooch CF. Higher-order unstructured finite volume RANS solution of turbulent compressible flows. Computers & Fluids, 2017,143:32-47
[28]	Ollivier-Gooch CF. Analysis of unstructured meshes from GMGW-1/HiLiftPW-3//2018 AIAA Aerospace Sciences Meeting, Florida. 2018-1-8-10, 2018: 0132
[29]	Jalali A, Ollivier-Gooch CF. Higher-order unstructured finite volume methods for turbulent aerodynamic flows// 22nd AIAA Computational Fluid Dynamics Conference, Dallas, 2015-1-22-26, 2015: 2284
[30]	Jalali A, Ollivier-Gooch CF. Higher-order least-squares reconstruction for turbulent aerodynamic flows// 11th World Congress on Computational Mechanics, Spain, 2014-7-20-25, 2014: 20-25
[31]	Zangeneh R, Ollivier-Gooch CF. Stability analysis and improvement of the solution reconstruction for cell-centered finite volume methods on unstructured meshes. Journal of Computational Physics, 2019,393:375-405
[32]	Ollivier-Gooch CF, Nejat A, Michalak K. Obtaining and verifying high-order unstructured finite volume solutions to the euler equations. AIAA Journal, 2009,47:2105-2120
[33]	Jalali A, Ollivier-Gooch CF. Higher-order finite volume solution reconstruction on highly anisotropic meshes// 21st AIAA Computational Fluid Dynamics Conference, California, 2013-6-24-27, 2013: 2565
[34]	Sozer E, Brehm C, Kiris CC. Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers// 52nd Aerospace Science Meeting, Washington DC, 2014-1-13-17, 2014: 1440
[35]	Xiong M, Deng XG, Gao X, et al. A novel stencil selection method for the gradient reconstruction on unstructured grid based on OpenFOAM. Computers & Fluids, 2018,172:426-442
[36]	Mavriplis DJ. An advancing front Delaunay triangulation algorithm designed for robustness. Journal of Computational Physics, 1995,117:90-101
[37]	Luo SH. A new mesh generation scheme for arbitrary planar domains. International Journal for Numerical Methods in Engineering, 1985,21:1403-1426
[38]	Li XS, Ren XD, Gu CW, et al. Shock-stable roe scheme combining entropy fix and rotated Riemann solver. AIAA Journal, 2020,58:779-786
[39]	Roe PL. Characteristic-based schemes for the Euler equations. Annual Review of Fluid Mechanics, 1986,18:337-365

施引文献(22)

期刊类型引用(14)

1.	刘加利，于梦阁，陈大伟，杨志刚. 考虑四极子声源的高速磁浮列车气动噪声数值模拟方法. 西南交通大学学报. 2024(01): 54-61 . 百度学术
2.	陈羽，柳壹明，毛懋，李启良，王毅刚，杨志刚. 高速列车底部结构参数对气动噪声影响规律. 西南交通大学学报. 2023(05): 1171-1179 . 百度学术
3.	宋军浩，刘加利，姚拴宝，陈大伟. 城际动车组隧道压力波及车内压力波动研究. 机车电传动. 2022(06): 44-50 . 百度学术
4.	丁叁叁，陈大伟，刘加利. 中国高速列车研发与展望. 力学学报. 2021(01): 35-50 . 本站查看
5.	郭易，郭迪龙，杨国伟，刘雯. 长编组高速列车的列车风动模型实验研究. 力学学报. 2021(01): 105-114 . 本站查看
6.	朱剑月，张清，徐凡斐，刘林芽，圣小珍. 高速列车气动噪声研究综述. 交通运输工程学报. 2021(03): 39-56 . 百度学术
7.	刘松，吴先梅，彭修乾，陈家熠，王聪. 基于双向流固耦合的输流圆管应力应变响应分析. 振动与冲击. 2021(20): 73-79 . 百度学术
8.	李青，邢立坤，柏江，邹元杰. 航天器噪声试验中结构振动响应预示方法研究. 力学学报. 2019(02): 569-576 . 本站查看
9.	时北极，何国威，王士召. 基于滑移速度壁模型的复杂边界湍流大涡模拟. 力学学报. 2019(03): 754-766 . 本站查看
10.	莫晃锐，安翼，刘青泉. 高速列车车体长度对气动噪声影响的数值研究. 力学学报. 2019(05): 1310-1320 . 本站查看
11.	潘永琛，姚建伟，刘涛，李昌烽. 基于涡旋识别方法的高速列车尾涡结构的讨论. 力学学报. 2018(03): 667-676 . 本站查看
12.	吴霆，时北极，王士召，张星，何国威. 大涡模拟的壁模型及其应用. 力学学报. 2018(03): 453-466 . 本站查看
13.	岳思. 磁悬浮列车噪声及控制措施研究. 通信电源技术. 2018(03): 48-50 . 百度学术
17.	朱雷威，郭建强，赵艳菊，宋雷鸣. 高速列车转向架区气动噪声分离研究. 振动.测试与诊断. 2020(03): 489-493+624 . 百度学术