VISCOUS FLOWFIELD BASED ON DISCONTINUOUS BOUNDARY ELEMENT METHOD AND VORTEX METHOD

Ding Jinghu; Ye Jihong

doi:10.6052/0459-1879-12-171

Volume 45 Issue 2

Turn off MathJax

Article Contents

Abstract

References

Chinese Journal of Theoretical and Applied Mechanics > 2013 > 45(2): 202-213. > DOI: 10.6052/0459-1879-12-171 CSTR: 32045.14.0459-1879-12-171

Ding Jinghu, Ye Jihong. VISCOUS FLOWFIELD BASED ON DISCONTINUOUS BOUNDARY ELEMENT METHOD AND VORTEX METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(2): 202-213. DOI: 10.6052/0459-1879-12-171

Citation:

PDF (1694 KB)

VISCOUS FLOWFIELD BASED ON DISCONTINUOUS BOUNDARY ELEMENT METHOD AND VORTEX METHOD

Ding Jinghu,
Ye Jihong^,

Key laboratory for RC&PC Structures of China Ministry of Education, Southeast University, Nanjing 210018, China

Funds: The project was supported by the National Science fund for Distinguished Young Scholars (51125031) and Graduate Student Research and Innovation Program of Jiangsu Province (CXLX-0130).

Received Date: June 03, 2012
Revised Date: December 03, 2012

Graphical Abstract

Abstract

Abstract

The two-dimensional, three-dimensional viscosity and incompressible flow fields are simulated bases on a combination application of discontinuous boundary element method and vortex method in our present study. Discrete vortex elements are used to analogue the vorticity generation, accumulation and transport mechanisms of the unsteady separated flow fields. And it decomposes the computing domain into an interior domain of vortex blobs and a thin numerical boundary layer of vortex sheets. The convection and stretch of the vortical field is imitated by Lagrangian vortex method, and the random walk method is adopted to describe the diffusion process of the vortical field. Additionally, vortex element's vortical velocity is calculated by generalized Biot-Savart law, while discontinuous boundary element method is used to compute potential velocity. To avoid the discontinuous of normal velocity, all nodes of discontinuous boundary element are selected at smooth boundary. Since a large scale boundary element equation set with a nonsymmetrical coefficient matrix should be solved, the present study import a pre-conditioning the generalized minimum residual (GMRES) iterative algorithm, which takes full advantage of the boundary element method. Moreover, regularization algorithm that applies at interior points close to the boundary, which the nearly singular surface integrals are transformed into a series of line integrals along the contour of the element, help to eliminate the unacceptable results of potential velocity and velocity gradient in potential calculation. The accuracy of present method is verified in both examples of two-dimension and three-dimension flow field calculation, as well as the significant increased simulation precision and efficiency.
- vortex method,
- discontinuous boundary element method,
- GMRES iterative algorithm,
- regularization algorithm,
- viscous flow field

FullText(HTML)

References (21)

References

Chorin AJ. Numerical study of slightly viscous flow. J Fluid Mech, 1973, 57(4): 785-796

Chorin AJ. Vortex sheet approximation of boundary layers. J comput Phys, 1978, 27(3): 428-432

Nakanishi Y, Kamemoto K. Numerical simulation of flow around a sphere with vortex blobs. J wind Eng Ind Aero, 1992, 46-47(1): 363-381

Turkiyyah G, Reed G, Yang JY. Fast vortex methods for predicting wind-Induced pressures on buildings. J Wind Eng Ind Aerodyn, 1995, 58(1-2): 51-79

Gharakhani A, Ghoniem AF. Three-dimensional vortex simulation of time dependent incompressible internal viscous flows. J Comput Phys, 1997, 134(1): 75-95

Zhao LJ, Tsukamoto H. Hybrid vortex method for high Reynolds number flows around three-dimensional complex boundary. Comput Fluids, 2007, 36(7): 1213-1223

Xu W, Ye JH, Shan J. The application of BEM in the membrane structures interaction with simplified wind. Structural Engineering and Mechanics, 2009, 31(3): 349-365

Li Y, Ye JH. The interaction between membrane structure and wind based on the discontinuous boundary element. Sci China Ser E-Tech Sci, 2010, 53(2): 486-501

Jun L, Beer G, Meek JL. Efficient evaluation of integrals of order l/r, l/r², l/r³ using Gauss quadrature. Engineering Analysis, 1985, 2(3): 118-123

Milinzaao F, Saffman PG. The calculation of large Reynolds number fluid flow suing discrete vortices with random walk. J Comput Phys, 1977, 23(4): 380-392

Roberts SG. Accuracy of the random vortex method for a problem with non-smooth initial conditions. J Comput Phys, 1985, 58(1): 29-43

Nagarajan A, Mukherjee S. A mapping method for numerical evaluation of two-dimensional integrals with l/r singularity. Computational Mechanics, 1993, 12(1-2): 19-26

Phongtinnaboot W, Rungamornrat J, Chintanapakdee C. Modeling of cracks in 3D piezoelectric finite media by weakly singular SGBEM. Engineering Analysis with Boundary Elements, 2011, 35(3): 319-329

Maatouk K. Estimating quadrature errors for an efficient method for quasi-singular boundary integral. Applied Mathematics and Computation, 2012, 218(9): 4658-4670

牛忠荣, 王秀喜, 周焕林. 三维边界元法中几乎奇异积分的正则化算法. 力学学报, 2004, 36(1): 49-56 (Niu Zhongrong, Wang Xiuxi, Zhou Huanlin. A regularization algorithm for the nearly singular integrals in 3-D BEM. Acta Mechanica Sinica, 2004, 36: 49-56 (in Chinese))

周焕林, 牛忠荣, 王秀喜. 三维位势问题边界元法中几乎奇异积分的正则化. 计算物理, 2005, 22(6): 501-506 (Zhou Huanlin, Niu Zhongrong, Wang Xiuxi. Regularization of nearly singular integrals in the boundary element method for 3-D potential problems. Chinese Journal of Computational Physics, 2005, 22(6): 501-506 (in Chinese))

周焕林, 王秀喜, 牛忠荣. 位势问题边界元方法中几乎奇异积分的完全解析算法. 中国科学技术大学学报, 2003, 33(4): 431-437 (Zhou Huanlin, Wang Xiuxi, Niu Zhongrong. Completely analytical algorithm of nearly singular integrals in the boundary element method of potential problems. Journal of University of Science and Technology of China, 2003, 33(4): 431-437 (in Chinese))

Levitan ML, Mehta KC, Vann WP. Field measurements of pressures on the Texas Tech Building. J Wind Eng Ind Aerodyn, 1991, 38(2-3): 227-234

Levitan ML, Mehta KC. Texas tech field experiments for wind loads, Part II: meteorological instrumentation and terrain parameters. J Wind Eng Ind Aerodyn, 1992, 41-44(1-3): 1577-1588

Fishelov D. Vortex methods for slightly viscous three-dimensional flow. SIAM J Sci Stat Comput, 1990, 11(3): 399-424

Rouse H. Advanced Mechanics of Fluids. New York: John Wiley&Sons Inc, 1965. 120-126

[1]	Li Shuai, Peng Jun, Luo Changtong, Hu Zongmin. PREDICTION OF SHOCK INTERFERENCE FLOW FIELD STRUCTURE BASED ON THE MULTI-LEVEL BLOCK BUILDING ALGORITHM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(12): 3284-3297. DOI: 10.6052/0459-1879-21-385
[2]	Shao Shuai, Li Ming, Wang Nianhua, Zhang Laiping. HIGH-ORDER DDG/FV HYBRID METHOD FOR VISCOUS FLOW SIMULATION ON UNSTRUCTURED/HYBRID GRIDS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1470-1482. DOI: 10.6052/0459-1879-18-199
[3]	Shi Dongyan, Wang Zhikai, Zhang Aman. A NOVEL LATTICE BOLTZMANN MODEL SIMULATING GAS-LIQUID TWO-PHASE FLOW[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(2): 224-233. DOI: 10.6052/0459-1879-13-243
[4]	Shuangbing Liu Haihu Liu. Subgrid scale stabilized finite element for solution of incompressible viscous flows[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(6): 1083-1090. DOI: 10.6052/0459-1879-2011-6-lxxb2010-268
[5]	Hu Haiyang Bai Peng. Numerical simulation of nozzle's flow field based on mixed implicit iteration-analysis algorithm for two equation turbulence model[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(4): 646-652. DOI: 10.6052/0459-1879-2011-4-lxxb2010-288
[6]	Tieqiao Tang, Haijun Huang, S.C. Wong, Rui Jiang. Lane changing analysis for two-lane traffic flow[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(1): 49-54. DOI: 10.6052/0459-1879-2007-1-2006-282
[7]	Kejun Yang, Shuyou Cao, Xingnian Liu. Flow resistance in compound channels and its prediction methods[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(1): 23-31. DOI: 10.6052/0459-1879-2007-1-2006-017
[8]	An iterative stabilized fractional step algorithm for finite element analysis in high-viscosity fluid flows[J]. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(1): 16-24. DOI: 10.6052/0459-1879-2006-1-2004-405
[9]	AN EFFICIENT ALGORITHM FOR HYPERSONIC VISCOUS FLOWS[J]. Chinese Journal of Theoretical and Applied Mechanics, 1991, 23(6): 641-649. DOI: 10.6052/0459-1879-1991-6-1995-887
[10]	DIAGONAL IMPLICIT ALGORITHM FOR THE EULER EQUATIONS IN THE TRANSONIC CASOADE FLOW FIELD[J]. Chinese Journal of Theoretical and Applied Mechanics, 1990, 22(6): 732-736. DOI: 10.6052/0459-1879-1990-6-1995-1004

Cited By

Cited by

Periodical cited type(12)

1.	张建书，陈菲菲. 方向余弦矩阵的特征值与特征向量及其性质研究. 南京理工大学学报. 2025(01): 25-31 .
2.	纪永. 考虑外部扰动的四轮移动机器人运动轨迹控制优化方法. 机械与电子. 2023(02): 23-26 .
3.	张硕，杨洋，李媛媛，葛玉梅，杨翊仁. 多体柔性机械臂的非线性能量阱被动控制研究. 四川轻化工大学学报(自然科学版). 2023(01): 33-40 .
4.	张华. 基于非线性优化算法的工业机器人轨迹跟踪自动控制. 机械与电子. 2023(04): 55-59 .
5.	熊宇，曾贵娥，崔晓. 柔性关节机器人抓取末端振动自动化控制方法. 自动化与仪表. 2023(09): 51-55+91 .
6.	张福礼，袁朝辉. 基于递归Gibbs-Appell的柔性空间机器人建模与特性分析. 航空动力学报. 2023(10): 2545-2560 .
7.	党卫军，冯诺旼，曾文凡，孙奇珍，李剑峰. 配电网电缆通道巡检机器人越障机构与控制系统设计. 机械设计与制造工程. 2023(12): 49-54 .
8.	刘许亮. 智能制造机器人多手臂自适应协同控制方法研究. 制造业自动化. 2022(01): 110-113 .
9.	傅景礼，陆晓丹，项春. 爬壁机器人系统的Noether对称性和守恒量. 力学学报. 2022(06): 1680-1693 . 本站查看
10.	高钰清，靳葳，徐鉴，方虹斌 . 踝关节外骨骼人机耦合动力学与助力性能分析. 力学学报. 2022(12): 3496-3512 . 本站查看
11.	钱佳伟，孙秀婷，徐鉴，方虹斌. 一类新型仿生起竖结构设计及其动力学分析. 力学学报. 2021(07): 2023-2036 . 本站查看
12.	张文静，牛江川，申永军，温少芳. 基于分数阶磁流变液阻尼器模型的车辆悬架组合控制. 力学学报. 2021(07): 2037-2046 . 本站查看

Other cited types(13)

Get Citation

PDF

XML

Article Metrics

Article views (1986) PDF downloads (871) Cited by(25)

VISCOUS FLOWFIELD BASED ON DISCONTINUOUS BOUNDARY ELEMENT METHOD AND VORTEX METHOD