圆柱突然启动后绕流的最小二乘等几何模拟
Least Squares Isogeometric Method for Transient Flow around an Impulsively Started Circular Cylinder
DOI: 10.12677/IJFD.2017.53010, PDF,   
作者: 徐大勇：海军驻南京地区航天机电系统军事代表室，江苏 南京；陈德祥, 郭建, 汤继保：合肥通用机械研究院，压缩机技术国家重点实验室，安徽 合肥
关键词: 瞬态流动；圆柱绕流；最小二乘等几何方法；隐式差分；Transient Flow； Flow around Circular Cylinder； Least Squares Isogeometric Method； Implicit Difference Scheme
摘要: 为研究最小二乘几何方法处理较复杂流动的特性，用该方法求解了圆柱突然启动后的瞬态流场。控制方程的时间离散采用三阶精度的隐式差分格式，空间离散采用二阶以上精度的最小二乘等几何方法。对雷诺数为550~9500的流动进行了模拟，并与其它实验及数值方法的结果进行了对比，数值解中捕捉到了不同雷诺数下的产生的鼓包、孤立涡、α-现象和β-现象等流动模式。计算结果表明高精度的最小二乘等几何法可用于复杂瞬态流动的模拟。
Abstract: To investigate the capability of least squares isogeometric method for complex flow, the method was used to simulate the transient flow around an impulsively started circular cylinder. The governing equations were first discretized in time by implicit difference scheme with third order of accuracy, and then discretized in space by least squares isogeometric method with order of accuracy more than two. The flow over a range of Reynolds numbers from 550 to 9500 was numerically simulated. Results were compared to those from other experimental and computational works. The flow modes like bulge, isolated secondary eddy, α-phenomena and β-phenomena at different Reynolds number were resolved correctly. The results show that the high order accuracy least squares isogeometric method can be used for simulation of complex transient flow.
文章引用：徐大勇, 陈德祥, 郭建, 汤继保. 圆柱突然启动后绕流的最小二乘等几何模拟[J]. 流体动力学, 2017, 5(3): 83-90. https://doi.org/10.12677/IJFD.2017.53010

参考文献

[1] 陈德祥, 徐自力, 刘石, 冯永新. 求解Stokes方程的最小二乘等几何分析方法[J]. 西安交通大学学报, 2013, 47(5): 51-55.
[2] Chen, D.X., Xu, Z.L., Liu, S. and Feng, Y.X. (2014) Least Squares Finite Element Method with High Continuity NURBS Basis for Incompressible Navier-Stokes Equations. Journal of Computational Physics, 260, 204-221. [Google Scholar] [CrossRef] 
[3] 陈德祥, 刘帅, 徐自力. 非稳态流动的隐式最小二乘等几何方法[J]. 计算力学学报, 2015(5): 639-643.
[4] Bochev, P.B. and Gunzburger, M.D. (2009) Least-Squares Finite Element Methods. Springer, New York.
[5] Cottrell, J.A., Hughes, T.J.R. and Bazilevs, Y. (2009) Isogeometric Analysis: Toward Integration of CAD and FEA. Wiley, Chichester. [Google Scholar] [CrossRef] 
[6] 陈德祥, 徐自力. 多重网格在粘性流动最小二乘等几何模拟中的应用[J]. 西安交通大学学报, 2014, 48(11): 122- 127.
[7] Anderson, C.R. and Reider, M.B. (1996) A High Order Explicit Method for the Computation of Flow about a Circular Cylinder. Journal of Computational Physics, 125, 207-224. [Google Scholar] [CrossRef] 
[8] George, A., Huang, L.C., Tang, W.P. and Wu, Y.D. (2000) Numerical Simulation of Unsteady Incompressible Flow (Re <= 9500) on the Curvilinear Half-Staggered Mesh. Siam Journal on Scientific Computing, 21, 2331-2351. [Google Scholar] [CrossRef] 
[9] Koumoutsakos, P. and Leonard, A. (1995) High-Resolution Simulations of the Flow around an Impulsively Started Cylinder Using Vortex Methods. Journal of Fluid Mechanics, 296, 1-38. [Google Scholar] [CrossRef] 
[10] Ploumhans, P. and Winckelmans, G.S. (2000) Vortex Methods for High-Resolution Simulations of Viscous Flow Past Bluff Bodies of General Geometry. Journal of Computational Physics, 165, 354-406. [Google Scholar] [CrossRef] 
[11] Li, Y.B., Shock, R., Zhang, R.Y. and Chen, H.D. (2004) Numerical Study of Flow Past an Impulsively Started Cylinder by the Lattice-Boltzmann Method. Journal of Fluid Mechanics, 519, 273-300. [Google Scholar] [CrossRef] 
[12] Niu, X.D., Chew, Y.T. and Shu, C. (2003) Simulation of Flows, around an Impulsively Started Circular Cylinder by Taylor Series Expansion- and Least Squares-Based Lattice Boltzmann Method. Journal of Computational Physics, 188, 176-193. [Google Scholar] [CrossRef] 
[13] Dupuis, A., Chatelain, P. and Koumoutsakos, P. (2008) An Immersed Boundary-Lattice-Boltzmann Method for the Simulation of the Flow Past an Impulsively Started Cylinder. Journal of Computational Physics, 227, 4486-4498. [Google Scholar] [CrossRef] 
[14] Kevlahan, N.K.R. and Vasilyev, O.V. (2005) An Adaptive Wavelet Collocation Method for Fluid-Structure Interaction at High Reynolds Numbers. Siam Journal on Scientific Computing, 26, 1894-1915. [Google Scholar] [CrossRef] 
[15] Bouard, R. and Coutanceau, M. (1980) The Early Stage of Development of the Wake behind an Impulsively Started Cylinder for 40 < Re < 104. Journal of Fluid Mechanics, 101, 583-607. [Google Scholar] [CrossRef] 

为你推荐