一种基于求解椭圆型方程的结构动网格生成方法

doi:10.7527/S1000-6893.2016.0303

流体力学与飞行力学

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一种基于求解椭圆型方程的结构动网格生成方法

卢凤翎^1,2, 陈小前¹, 禹彩辉², 苗萌²

1. 国防科技大学航天科学与工程学院, 长沙 410073;
2. 空间物理重点实验室, 北京 100076

收稿日期:2016-07-21 修回日期:2016-11-20 出版日期:2017-03-15 发布日期:2016-11-24
通讯作者: 卢凤翎,E-mail:lufengling126@126.com E-mail:lufengling126@126.com

A dynamic structured grid generation method based on solving elliptic equations

LU Fengling^1,2, CHEN Xiaoqian¹, YU Caihui², MIAO Meng²

1. College of Aerospace Science and Engineering, National University of Defence Technology, Changsha 410073, China;
2. Science and Technology on Space Physics Laboratory, Beijing 100076, China

Received:2016-07-21 Revised:2016-11-20 Online:2017-03-15 Published:2016-11-24

摘要/Abstract

摘要：

基于椭圆型网格生成法，实现了一种简单高效的贴体结构动网格生成方法，可用于具有移动边界问题的非定常流动数值模拟。该方法提出，在网格变形过程中，Poisson方程需要的控制网格间距和正交性的源项可以通过提取已知的静态网格源项直接得到，并在整个动网格生成过程中保持不变。因此，在椭圆型网格生成中需要通过外迭代确定源项的过程可以得到省略，而且该方法不需要人工指定参数。这使得方法具有高效和易于嵌入到已有程序中的特点。数值模拟结果证明，采用这种方法获得的网格能够较好地保持静态网格原有的正交性和光滑性，在相同迭代步数约束下，网格求解效率低于传统弹簧模拟法，但鲁棒性优于弹簧模拟法。

关键词: 动网格生成, 椭圆型网格生成, 计算流体力学, 数值网格生成, 网格变形方法

Abstract:

A simple robust structured dynamic grid generation method based on the solution of elliptic partial differential equations is developed for computing the unsteady flows with moving boundaries. In the method, the source terms of the Poisson equation which can control the spacing and the orthogonality of the grid are inherited from the known static grid, and held fixed throughout the process of dynamic grid generation. With the process, the outer iterations for determining the source terms usually needed in the elliptic grid generation can thus be saved, and no adjustable parameters are required to be prescribed. This makes the method more efficient and easy to implement in an existing CFD code. The numerical results demonstrate that the proposed method can provide an efficient way of deforming the grid based on solving elliptic partial differential equations. The orthogonality and smoothness of original static grid can be maintained well by the proposed method. When the same number of iterations are given as the constraint condition, the grid generation efficiency of the method is lower than that of the spring analogy, but the robustness of the method is superior to the spring analogy.

Key words: dynamic grid generation, elliptic grid generation, computational fluid dynamics, numerical grid generation, grid deformation approach

中图分类号:

V211.3

卢凤翎, 陈小前, 禹彩辉, 苗萌. 一种基于求解椭圆型方程的结构动网格生成方法[J]. 航空学报, 2017, 38(3): 120632-120632.

LU Fengling, CHEN Xiaoqian, YU Caihui, MIAO Meng. A dynamic structured grid generation method based on solving elliptic equations[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(3): 120632-120632.

参考文献

[1] STEGER J L, DOUGHERTY F C, BENEK J A. A chimera grid scheme[C]//Mini Symposium on Advances in Grid Generation, 1982.
[2] CHAN W M, PANDYAY S A, ROGERS S E. Effcient creation of overset grid hole boundaries and effects of their locations on aerodynamic loads[C]//21st AIAA Computational Fluid Dynamics Conference. Reston:AIAA, 2013.
[3] KIM N, CHAN W M. Automation of hole-cutting for overset grids using the x-rays approach:AIAA-2011-3052[R]. Reston:AIAA, 2011.
[4] 王文, 阎超. 新型重叠网格洞面优化方法及其应用[J]. 航空学报, 2016, 37(3):826-835. WANG W, YAN C. Novel overlapping optimization algorithm of overlapping grid and its applications[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(3):826-835(in Chinese).
[5] 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. ZHANG W W, GAO C Q, YE Z Y. Reseach progress on mesh deformation in computational aeroelasticity[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(3):303-319(in Chinese).
[6] FOSTER N F. Accuracy of high-order cfd and overset interpolation in finite volumee/difference codes[C]//22nd AIAA Computational Fluid Dynamics Conference. Reston:AIAA, 2015.
[7] UCHIDA Y, KANDA H. Spacing control of 3-D transfinite interpolation grid generation:AIAA-2005-5243[R]. Reston:AIAA, 2005.
[8] BATINA J T. Unsteady Euler airfoil solutions using unstructured dynamic meshes[J]. AIAA Journal, 1990, 28(8):1381-1388.
[9] BLOM F J. Considerations on the spring analogy[J]. International Journal of Numerical Methods in Fluid, 2000, 32(6):647-668.
[10] CANTARITI D L, GRIBBEN W M, BADCOCK K J, et al. A grid deformation technique for unsteady flow computations[J]. International Journal of Numerical Methods in Fluids, 2000, 32(3):285-311.
[11] 刘枫. 动网格技术研究及其在高超声速流动中的应用[D]. 长沙:国防科学技术大学, 2009:54-55. LIU F. Investigations of dynamic grid generation and its applications for supersonic flow[D]. Changsha:National University of Defense Technology, 2009:54-55(in Chinese).
[12] 郭正, 刘君, 翟章华. 用非结构动网格方法模拟有相对运动的多体绕流[J]. 空气动力学学报, 2001, 19(3):310-316. GUO Z, LIU J, ZHAI Z H. Simulation of flows past multi-body in relative motion with dynamic unstructured method[J]. Acta Aerodynamic Sinica, 2001, 19(3):310-316(in Chinese).
[13] TEZDUYAR T E. Stability finite element formulations for incompressible flow computations[J]. Advances in Applied Mechanics, 1992, 28(1):1-44.
[14] LIU X, QIN N, XIA H. Fast dynamic grid deformation based on delaunay graph mapping[J]. Journal of Computational Physics, 2006, 211(2):405-423.
[15] BORE A, SCHOOT M S, FACULTY S H. Mesh deformation based on radial basis function interpolation[J]. Computers and Structures, 2007, 85(11):784-795.
[16] RENDALL T C S, ALLEN C B. Efficient mesh motion using radial basis functions with data reduction algorithms[J]. Journal of Computational Physics, 2010, 229(8):2810-2820.
[17] WANG G, HARIS H M, YE Z Y. An improved point selection method for hybrid unstructured mesh deformation using radial basis functions:AIAA-2013-3076[R]. Reston:AIAA, 2013.
[18] 魏其, 李春娜, 谷良贤, 等. 一种基于径向函数和峰值选择法的高效网格变形技术[J]. 航空学报, 2016, 37(7):1401-1414. WEI Q, LI C N, GU L X, et al. An efficient mesh deformation method based on radial basis functions and peak-selection method[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(7):1401-1414(in Chinese).
[19] 孙岩, 邓小刚, 王光学, 等. 基于径向基函数改进的Delaunay图映射动网格方法[J]. 航空学报, 2014, 35(3):727-735. SUN Y, DENG X G, WANG G X, et al. An improvement on Delaunay graph mapping dynamic grid method based on radial basis functions[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(3):727-735(in Chinese).
[20] JOHNSON A A, TEZDUYAR T E. Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces[J]. Computer Methods in Applied Mechanics and Engineering, 1994, 119(1-2):73-94.
[21] USHIJIMA S. Three-dimensional arbitrary Lagrangian-Eulerian numerical prediction method for non-linear free surface oscillation[J]. International Journal for Numerical Methods in Fluids, 1998, 26(5):605-623.
[22] GRVBER B, CARTENS V. Computation of the unsteady transonic flow in harmonically oscillating turbine cascades taking into account viscous effects[J]. Journal of Turbomachinery, 1998, 120(1):104-111.
[23] THOMAS P D, MIDDLECOFF J F. Direct control of the grid point distribution in meshes generated by elliptic equations[J]. AIAA Journal, 1979, 18(6):652-656.
[24] SORENSON R L, STEGER J L. Numerical generation of 2D grids by the use of poisson equations with grids control:N81-14722[R]. 1981.
[25] SORENSON R L. A computer program to generate 2D grids about airfoil and other shapes by the use of poisson's equation:N80-26266[R]. 1980.
[26] HILGENSTOCK A. A fast method for the elliptic generation of three-dimensional grids with full boundary control[C]//Numerical Grid Generation in Computational Fluid Mechanics, 1988:137-146.
[27] SONAR T. Grid generation using elliptic partial differential equations:DFVLR-FB89-15[R]. 1989.
[28] GAITONDE A L, FIDDES S P. A moving mesh system for the calculation of unsteady flows:AIAA-1993-0641[R]. Reston:AIAA, 1993.
[29] LI J, HUANG S. Unsteady viscous flow simulations by a fully implicit method with deforming grid:AIAA-2005-1221[R]. Reston:AIAA, 2005.
[30] UNMEEL B M. Synthesis of contributed simulations for OREX test cases:NASA/TM-1998-112238[R]. Washington, D.C.:NASA, 1998.
[31] YOSHINAGA T, TATE A, WATANABE M. Dynamic test of the orbital reentry vehicle (OREX) in a transonic wind tunnel with comparison to flight data:AIAA-1995-1901-CP[R]. Reston:AIAA, 1995.
[32] THOMPSON J F. Numerical grid generation-foundations and applications[M]. North Holland:Amsterdam, 1985.
[33] SLATER J W. RAE2822 transonic airfoil:Study #1[EB/OL]. (2015-01-22)[2016-07-17]. http://www.grc.nasa.gov/WWW/wind/valid/raetaf/raetaf.html.

E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

一种基于求解椭圆型方程的结构动网格生成方法

A dynamic structured grid generation method based on solving elliptic equations

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