气动弹性计算中网格变形方法研究进展
收稿日期: 2013-09-02
修回日期: 2013-10-10
网络出版日期: 2013-10-17
基金资助
国家自然科学基金（11072199，11172273）；航空科学基金（20121353014）
Research Progress on Mesh Deformation Method in Computational Aeroelasticity
Received date: 2013-09-02
Revised date: 2013-10-10
Online published: 2013-10-17
Supported by
National Natural Science Foundation of China (11072199, 11172273); Aeronautical Science Foundation of China (20121353014)
网格变形是气动弹性计算中实现计算网格随运动边界变形的主要方法。在总结目前网格变形方法发展现状的基础上，对近几年常用的网格变形方法，即弹簧法、弹性体法、超限插值法、Delaunay背景网格法、径向基函数插值法和温度体法等做了简要的总结。根据各方法构建模型的不同，将它们分成物理模型法、数学插值法和混合方法3类，简要介绍了各方法的基本思想和研究进展，重点比较了各方法的网格变形特性（变形能力、变形质量和变形效率）和优缺点。总结了当前流场边界与结构边界的数据传递方法，对当前气动弹性计算中遇到的网格变形的难点问题作了简要评述并对未来网格变形方法的发展方向进行了探讨。
张伟伟 , 高传强 , 叶正寅 . 气动弹性计算中网格变形方法研究进展[J]. 航空学报, 2014 , 35(2) : 303 -319 . DOI: 10.7527/S1000-6893.2013.0423
Mesh deformation is a main method to implement the computational mesh deformation with a moving boundary in computational aeroelasticity. First, an investigation of the status of the current advances in the researches on mesh deformation is presented in this paper, and some common mesh deformation approaches in recent years are reviewed in detail, which are spring analogy method, elastic solid method, transfinite interpolation method, Delaunay graph method, radial basis function method and temperature analogy method. Besides, based on the established models, the existing methods can be classified into physical model method, mathematical interpolation method and hybrid approach. A brief introduction of each method is made on theoretical method and research advance. The main emphasis is on the difference among the three methods of advantages and disadvantages as well as properties including deformation capability, deformation quality and efficiency. As an important aspect in computational aeroelasticity, the calculation data transformation between flow field boundary and structure boundary is summarized as well. At last, the present problems of mesh deformation which are frequently encountered in computational aeroelasticity are discussed, and in order to meet the needs of projects, possible prospects in future mesh deformation investigations are also proposed.
[1] Schuster D H, Liu D D, Huttsell L J. Computational aeroelasticity: success, progress, challenge[J]. Journal of Aircraft, 2003, 40(5): 843-856.
[2] Heathcote J. Flexible flapping airfoil propulsion at zero free-stream velocity[J]. AIAA Journal, 2004, 42(11): 2196-2204.
[3] Zhou X, Li S X, Sun S L, et al. Advances in the research on unstructured mesh deformation[J]. Advances in Mechanics, 2011, 41(5): 547-561. (in Chinese) 周璇, 李水乡, 孙树立, 等. 非结构网格变形方法研究进展[J]. 力学进展, 2011, 41(5): 547-561.
[4] Sudhakar Y, Vengadesan S. Flight force production by flapping insect wings in inclined stroke plane kinematics[J]. Computers & Fluids, 2010(39): 683-695.
[5] Shyy W, Aono H, Chimakurthi S K. Recent progress in flapping wing aerodynamics and aeroelasticity[J]. Progress in Aerospace Sciences, 2010, 46(7): 284-327.
[6] Gaitonde A L, Fiddes S P. A moving mesh system for the calculation of unsteady flows, AIAA-1993-0641[R]. Reston: AIAA, 1993.
[7] Banita J T. Unsteady Euler airfoil solutions using unstructured dynamic meshes[J].AIAA Journal, 1990, 28(8): 1381-1388.
[8] Tezduyar T E. Stabilized finite element formulations for incompressible flow computations[J]. Advances in Applied Mechanics, 1992, 28(1): 1-44.
[9] Liu X Q, Qin N, Xia H. Fast dynamic grid deformation based on Delaunay graph mapping[J]. Journal of Computational Physics, 2006, 211(2): 405-423.
[10] Boer A, Schoot M S, Faculty H B. Mesh deformation based on radial basis function interpolation[J]. Computers and Structures, 2007, 85(11): 784-795.
[11] Chen Y, Cao S L, Liang K H, et al. Research on dynamic closing process of hollow-jet valve[J]. Fluid Machinery, 2009, 37(12): 9-14. (in Chinese) 陈炎, 曹树良, 梁开洪, 等. 射流放水阀动态关闭过程研究[J]. 流体机械, 2009, 37(12): 9-14.
[12] Yang Z, Mavriplis D J. Unstructured dynamic meshes with higher order time integration schemes for the unsteady Navier-Stokes equations, AIAA-2005-1222[R]. Reston: AIAA, 2005.
[13] McDaniel D R, Morton S A. Efficient mesh deformation for computational stability and control analyses on unstructured viscous meshes, AIAA-2009-1363[R]. Reston: AIAA, 2009.
[14] Yang G W. Recent progress on computational aeroelasticity[J]. Advances in Mechanics, 2009, 39(4): 406-420. (in Chinese) 杨国伟. 计算气动弹性若干研究进展[J]. 力学进展, 2009, 39(4): 406-420.
[15] Zhang L P, Deng X G, Zhang H X. Reviews of moving grid generation techniques and numerical methods for unsteady flow[J]. Advances in Mechanics, 2010, 40(4): 424-447. (in Chinese) 张来平, 邓小刚, 张涵信. 动网格生成技术及非定常计算方法进展综述[J]. 力学进展, 2010, 40(4): 424-447.
[16] Blom F J. Considerations on the spring analogy[J]. International Journal for Numerical Methods in Fluids, 2000, 32(6): 647-668.
[17] Guo Z, Liu J, Qu Z H. Dynamic unstructured grid method with applications to 3D unsteady flows involving boundaries[J]. Chinese Journal of Theoretical and Applied Mechanics, 2003, 35(2): 140-146. (in Chinese) 郭正, 刘君, 瞿章华. 非结构动网格在三维可动边界问题中的应用[J]. 力学学报, 2003, 35(2): 140-146.
[18] Farhat C, Degand C, Koobus B, et al. Torsional springs for two-dimensional dynamic unstructured fluid meshes[J]. Computer Methods in Applied Mechanics and Engineering, 1998, 163(4): 231-245.
[19] Huo S H, Wang F S, Yue Z F. Spring analogy method for generating of 2D unstructured dynamic meshes[J]. Journal of Vibration and Shock, 2011, 30(10): 177-182. (in Chinese) 霍世慧, 王富生, 岳珠峰. 弹簧近似法在二维非结构动网格生成技术中的应用[J]. 振动与冲击, 2011, 30(10): 177-182.
[20] Mitsuhiro M. Unstructured dynamic mesh for large movement and deformation, AIAA-2002-0122[R]. Reston: AIAA, 2002.
[21] Zeng D H, Ethier C R. A semi-torsional spring analogy model for updating unstructured meshes in 3D moving domains[J]. Finite Elements in Analysis and Design, 2005, 41(3): 1118-1139.
[22] Bottasso C L, Detomi D, Serra R. The ball-vertex method: a new simple spring analogy method for unstructured dynamic meshes[J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194(8): 4244-4264.
[23] Markou G A, Mouroutis Z S, Charmpis D C, et al. The ortho-semi-torsional (OST) spring analogy method for 3D mesh moving boundary problems[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196(4): 747-765.
[24] Mouroutis Z S, Markou G A, Papadrakakis M, et al. An efficient mesh updating technique for fluid structure interaction problems[J]. International Journal of Computational Methods, 2007, 4(2): 249-263.
[25] Wu Q, Zhong Y C, Yu S Z, et al. An iterative method for unstructured dynamic-grid using springs based on LU-SGS[J]. Chinese Journal of Computational Physics, 2009, 26(6): 806-812. (in Chinese) 吴晴, 钟易成, 余少志, 等. 基于LU-SGS 的非结构弹簧网格迭代算法[J]. 计算物理, 2009, 26(6): 806-812.
[26] Chu J. Research of the generation of dynamic unstructured meshes[D]. Nanjing: School of Energy and Power Engineering, Nanjing University of Science and Technology, 2006.(in Chinese) 褚江. 非结构动网格生成方法研究[D]. 南京: 南京理工大学能源与动力工程学院, 2006.
[27] Tezduyar T E, Behr M, Liou J. A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial domain/space-time procedure: I. the concept and the preliminary tests[J]. Computer Methods in Applied Mechanics and Engineering, 1992, 94(3): 339-351.
[28] Tezduyar T E, Behr M, Liou J. A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial domain/space-time procedure: Ⅱ. computation of free-surface flows, two-liquid flows, and flows with drifting cylinders[J]. Computer Methods in Applied Mechanics and Engineering, 1992, 94(3): 353-371.
[29] Tezduyar T E, Behr M, Mittal S, et al. A computation of unsteady incompressible flows with the finite element methods-space-time formulations, iterative strategies and massively parallel implementations[J]. ASME, 1992, 143: 7-24.
[30] Stein K, Tezduyar T E, Benney R. Mesh moving techniques for fluid-structure interactions with large displacements[J]. Journal of Applied Mechanics, 2003, 70(1): 58-63.
[31] Smith R W, Wright J A. A classical elasticity-based mesh update method for finite volume flow solvers, AIAA-2009-0771[R]. Reston: AIAA, 2009.
[32] Huo S H, Wang F S, Yan W Z, et al. Layered elastic solid method for the generation of unstructured dynamic mesh[J]. Finite Elements in Analysis and Design, 2010, 46(10): 949-955.
[33] Nielsen E J, Anderson W K. Recent improvements in aerodynamic design optimization on unstructured meshes[J]. AIAA Journal, 2002, 40(6): 1155-1163.
[34] Truong A H, Oldfield C A, Zingg D W. Mesh movement for a discrete-adjoint Newton-Krylov algorithm for aerodynamic optimization[J]. AIAA Journal, 2008, 46(7): 1695-1704.
[35] Chen Y, Cao S L, Liang K H, et al. A new dynamic grids based on temperature analogy and its application in vibration engineering with fluid-solid interaction[J]. Journal of Vibration and Shock, 2010, 29(4): 1-5. (in Chinese) 陈炎, 曹树良, 梁开洪, 等. 基于温度体模型的动网格生成方法及在流固耦合振动中的应用[J]. 振动与冲击, 2010, 29(4): 1-5.
[36] Chen Y, Cao S H, Zhu B S, et al. Vibration of thin cambered blade based on temperature analogy[J]. Journal of Mechanical Engineering, 2010, 46(10): 170-175. (in Chinese) 陈炎, 曹树良, 祝宝山, 等. 基于温度体动网格方法的微弯薄翼振动问题[J]. 机械工程学报, 2010, 46(10): 170-175.
[37] Chen Y, Cao S L, Liang K H, et al. Parameter control in temperature analogy method[J]. Chinese Journal of Computational Physics, 2010, 27(3): 396-406. (in Chinese) 陈炎, 曹树良, 梁开洪, 等. 温度体动网格模型中控制参数的研究[J]. 计算物理, 2010, 27(3): 396-406.
[38] Chen Y, Zhang Q Z, Cao S L, et al. A new method of dynamic grid generation based on reference temperature distribution[J]. Transactions of Beijing Institute of Technology, 2012, 32(9): 900-904. (in Chinese) 陈炎, 张勤昭, 曹树良, 等. 基准温度分布动网格生成方法的研究及应用[J]. 北京理工大学学报, 2012, 32(9): 900-904.
[39] Gaitonde A L. A dual-time method for the solution of the 2D unsteady Navier-stokes equations on structuredmoving meshes, AIAA-1995-1877-CR[R]. Reston: AIAA, 1995.
[40] Gaitonde A L, Fiddes S P. Three-dimensional moving mesh method for the calculation of unsteady transonic flows[J]. Aeronautical Journal, 1995, 99(4): 150-160.
[41] Byun C, Guruswamy G P. A parallel multi-block moving grid method for aeroelastic applications on full aircraft, AIAA-1998-4782[R]. Reston: AIAA, 1998.
[42] Dong L L. The application of transfinite interpolation to numerical simulation of control surface oscillating deflection[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2011, 31(4): 207-209. (in Chinese) 董琳琳. 超限插值法在舵面振荡偏转数值模拟中的应用[J]. 弹箭与制导学报, 2011, 31(4): 207-209.
[43] Yuan X X, Zhang H X, Xie Y F, et al. The development of an unsteady numerical methods and its application on dynamic vehicle flows[J]. Acta Aerodynamica Sinica, 2004, 22(4): 432-438. (in Chinese) 袁先旭, 张涵信, 谢昱飞, 等. 非定常数值模拟方法的发展及其在动态绕流中的应用[J]. 空气动力学学报, 2004, 22(4): 432-438.
[44] Liu X Q, Li Q, Chai J H, et al. A new dynamic grid algrithm and its application[J]. Acta Areonautica et Astronautica Sinica, 2008, 29(4): 817-822. (in Chinese) 刘学强, 李青, 柴建忠, 等. 一种新的动网格方法及其应用[J]. 航空学报, 2008, 29(4): 817-822.
[45] Zhang L P, Chang X H, Duan X P, et al. A block LU-SGS implicit unsteady incompressible flow solver on hybrid dynamic grids for 2D external bio-fluid simulations[J]. Computers & Fluids, 2008, 38(2): 290-308.
[46] Lv C. Study of dynamic grid deformationical algorithm and its application[D]. Changsha: Graduate School, National University of Defense Technology, 2010. (in Chinese) 吕超. 变形网格计算方法研究及其应用[D]. 长沙:国防科技大学研究生院, 2010.
[47] Xiao T H. A numerical method for unsteady low Reynolds number flows and application to micro air vehicles[D]. Nanjing: College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 2009. (in Chinese) 肖天航. 低雷诺数非定常流场的数值方法及其在微型飞行器上的应用[D]. 南京: 南京航空航天大学航空宇航学院, 2009.
[48] Xiao T H, Ang H S, Tong C. A new dynamic mesh generation method for large movements of flapping-wings with complex geometries[J]. Acta Areonautica et Astronautica Sinica, 2008, 29(1): 405-423. (in Chinese) 肖天航, 昂海松, 仝超. 大幅运动复杂构形扑翼动态网格生成的一种新方法[J]. 航空学报, 2008, 29(1): 405-423.
[49] Lin Y Z, Chen B, Xu X. Radial basis function interpolation in moving mesh technique[J]. Chinese Journal of Computational Physics, 2012, 29(2): 191-197. (in Chinese) 林言中, 陈兵, 徐旭. 径向基函数插值方法在动网格技术中的应用[J]. 计算物理, 2012, 29(2): 191-197.
[50] Jakobsson S, Amoignon O. Mesh deformation using radial basis functions for gradient-based aerodynamic shape optimization[J]. Computers & Fluids, 2007, 36 (11): 1119-1136.
[51] Botsch M, Kobbelt L. Real-time shape editing using radial basis functions[J]. Computer Graphics Forum, 2005, 24(3): 611-621.
[52] Rendall T C S, Allen C B. Unified fluid-structure interpolation and mesh motion using radial basis functions[J]. International Journal for Numerical Methods in Engineering, 2008, 74(10): 1519-1559.
[53] Rendall T C S, Allen C B. Efficient mesh motion using radial basis functions with data reduction algorithms[J]. Journal of Computational Physics, 2009, 228(5): 6231-6249.
[54] Rendall T C S, Allen C B. Reduced surface point selection options for efficient mesh deformation using radial basis functions[J]. Journal of Computational Physics, 2010, 229(1): 2810-2820.
[55] Rendall T C S, Allen C B. Improved radial basis function fluid-structure coupling via efficient localized implementation[J]. International Journal for Numerical Methods in Engineering, 2009, 78(10): 1188-1208.
[56] Sheng C H, Allen C B. Efficient mesh deformation using radial basis functions on unstructured meshes[J]. AIAA Journal, 2013, 51(3): 707-720.
[57] Wang G, Lei B Q, Ye Z Y. An efficient deformation technique for hybrid unstructured grid using radial basis functions[J]. Journal of Northwestern Polytechnical University, 2011, 29(5): 783-788. (in Chinese) 王刚, 雷博琪, 叶正寅. 一种基于径向基函数的非结构混合网格变形技术[J]. 西北工业大学学报, 2011, 29(5): 783-788.
[58] Wang G, Mian H H, Ye Z Y. An improved point selection method for hybrid-unstructured mesh deformation using radial basis functions, AIAA-2013-3076[R]. Reston: AIAA, 2013.
[59] Xie L, Xu M, An X M, et al. Research of mesh deforming method based on radial basis functions and nonlinear aeroelastic simulation[J]. Acat Aeronautica et Astronautica Sinica, 2013, 34(7): 1501-1511. (in Chinese) 谢亮, 徐敏, 安效民, 等. 基于径向基函数的网格变形及非线性气动弹性时域仿真研究[J]. 航空学报, 2013, 34(7): 1501-1511.
[60] Tsai H M, Wong A S F. Unsteady flow calculations with a parallel multiblock moving mesh algorithm[J]. AIAA Journal, 2001, 39(6): 1021-1020.
[61] Zhang B, Han J L. Spring-TFI hybrid dynamic mesh method with rotation correction[J]. Acta Areonautica et Astronautica Sinica, 2011, 32(10): 1815-1823. (in Chinese) 张兵, 韩景龙. 带旋转修正的弹簧-TFI混合动网格方法[J]. 航空学报, 2011, 32(10): 1815-1823.
[62] Huang L k, Gao Z Z, Zuo Y T. A fast and robust parallelizable moving mesh algorithm for multi-block structured grids[J]. Chinese Journal of Computational Mechanics, 2012, 29(3): 363-368. (in Chinese) 黄礼铿, 高正红, 左英桃. 一种快速稳健的并行多块结构动网格方法[J]. 计算力学学报, 2012, 29(3): 363-638.
[63] Zhou X, Li S X, Chen B. Spring-interpolation approach for generating unstructured dynamic meshes[J]. Acta Areonautica et Astronautica Sinica, 2010, 31(7): 1389-1395. (in Chinese) 周璇, 李水乡, 陈斌. 非结构动网格生成的弹簧-插值联合方法[J]. 航空学报, 2010, 31(7): 1389-1395.
[64] Lin T J, Guan Z Q. Fast dynamic mesh moving based on background grid morphing[J]. Chinese Journal of Computational Mechanics, 2012, 29(1): 105-110. (in Chinese) 林天军, 关振群. 基于背景网格变形的动态网格移动方法[J]. 计算力学学报, 2012, 29(1): 105-110.
[65] Zhang J L, Chen H Q. Research on dynamic mesh method based on unstructure background mesh[J]. Aeronautical Computing Technique, 2012, 42(2): 95-99. (in Chinese) 张加乐, 陈红全. 基于非结构背景网格的动网格方法研究[J]. 航空计算技术, 2012, 42(2): 95-99.
[66] Zheng G N, Yang G W. Hybrid grid deformation method based on background grid[J]. Journal of Vibration Engineering, 2011, 24(5): 473-481. (in Chinese) 郑冠男, 杨国伟. 基于背景网格的混合网格变形方法[J]. 振动工程学报, 2011, 24(5): 473-481.
[67] Zhang L P, Duan X P, Chang X H, et al. A hybrid dynamic grid generation technique for morphing bodies based on Delaunay graph and local remeshing[J]. Acta Aerodynamica Sinica, 2009, 27(1): 32-40. (in Chinese) 张来平, 段旭鹏, 常兴华, 等. 基于Delaunay背景网格插值和局部网格重构的变形体动态混合网格生成技术[J]. 空气动力学学报, 2009, 27(1): 32-40.
[68] Xu M, Chen S L. Study of date exchange method for coupling computational CFD/CSD[J]. Chinese Journal of Applied Mechanics, 2004, 21(2): 33-37. (in Chinese) 徐敏, 陈士橹. CFD/CSD耦合计算研究[J]. 应用力学学报, 2004, 21(2): 33-37.
[69] Su B, Qian R J, Yuan X F. Advances in research on theory and method of data exchange on coupling interface for FSI analysis[J]. Spatial Structures, 2010, 16(1): 3-10. (in Chinese) 苏波, 钱若军, 袁行飞. 流固耦合界面信息传递理论和方法研究进展[J]. 空间结构, 2010, 16(1): 3-10.
[70] Stein K, Benney R, Kalro V, et al. Parachute fluid-structure interactions: 3-D computation[J]. Computer Methods in Applied Mechanics and Engineering, 2000, 190(2): 373-386.
[71] Boer A D, Zuijlen A H, Bijl H. Review of coupling methods for non-matching meshes[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196(8): 1515-1525.
[72] Goura G S, Badcock K J, Woodgate M A, et al. A data exchange method for fluid-structure interaction problems[J]. The Aeronautical Journal, 2001, 105(1): 215-221.
[73] Bathe K J, Zhang H, Shan J. Finite element analysis of fluid flows fully coupled with structural interactions[J]. Computers & Structures, 1999, 72 (1): 1-16.
[74] Harder R L, Desmarais R N. Interpolation using surface splines[J]. Journal of Aircraft, 1972, 9(2): 189-191.
[75] Smith M J, Hodges D H, Cesnik C E. Evaluation of computational algorithms suitable for fluid-structure interactions[J]. Journal of Aircraft, 2000, 37(2): 282-294.
[76] Yu Z W. Surface interpolation from irregularly distributed points using surface splines, with Fortran program[J]. Computers & Geosciences, 2001, 27(5): 877-882.
[77] Becker A, Wendland H. Multivariate interpolation for fluid-structure problems using radial basis functions[J]. Aerospace Science and Technology, 2001, 5(2): 125-134.
[78] Han X K, Qian R J, Su B, et al. Data exchange method for fluid-structure interaction based on interpolation algorithm adopting compactly supported radial based function[J]. Journal of Tongji University: Natural Science, 2011, 39(1): 48-52. (in Chinese) 韩向科, 钱若军, 苏波, 等. 基于紧支径向基函数的流固交互作用数据传递[J]. 同济大学学报: 自然科学版, 2011, 39(1): 48-52.
[79] Wang G. New type of grid generation technique together with the high efficiency and high accuracy scheme researches for complex flow simulation[D]. Xi'an: School of Aeronautics, Northwestern Polytechnical University, 2006. (in Chinese) 王刚. 复杂流动的网格技术及高效、高精度算法研究[D]. 西安: 西北工业大学航空学院, 2006.
[80] Zhang W W, Wang B B, Ye Z Y. High efficient numerical method for LCO analysis in transonic flows[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 42(6): 1023-1033. (in Chinese) 张伟伟, 王博斌, 叶正寅. 跨音速极限环型颤振的高效数值分析方法[J]. 力学学报, 2011, 42(6): 1023-1033.
[81] Zhang W W, Wang B B, Ye Z Y, et al. Efficient method for limit cycle flutter analysis based on nonlinear aerodynamic reduced-order models[J]. AIAA Journal, 2012, 50(5): 1019-1028.
[82] Zhang W, Zhang W W, Quan J G, et al. Gust alleviation of transonic wing[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(6): 962-969. (in Chinese) 张慰, 张伟伟, 全景阁, 等. 跨音速机翼阵风减缓研究[J]. 力学学报, 2012, 44(6): 962-969.
/
| 〈 |
|
〉 |
CJA