多体静止绕流和振荡流系统的研究：分块耦合法和虚拟体法程序的设计和应用
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摘要
多体系统绕流场是典型的复连通区域,此类流场的典型代表是多柱体和多球
体绕流问题,它们广泛存在于自然界和各种工程生产设备中。多体系统绕流研究
涉及到流动模式的转捩、流场涡结构的识别及其相互作用分析以及工程应用中特
别关注的宏观流体力响应行为等等多方面的物理特性研究。由于复连通区域的复
杂性使得对于多体系统绕流场很难甚至不可能获得满意的分析解,因此实验研究
和数值模拟代替理论分析成为多体系统研究的主要手段,特别是在计算手段和计
算技术飞跃发展的今天数值模拟发挥着越来越大的作用。然而复连通区域的网格
生成困难阻碍了单区域贴体系统求解方法的应用,而研究多体系统在振荡状态下
的流场物理特性更是对数值模拟技术提出了巨大的挑战。根据作者的文献查新工
作发现,建立在非结构网格基础上的有限元方法及谱元方法在复杂几何形体绕流
的数值模拟上做出了巨大贡献;而传统的有限差分方法由于采用的网格系统具有
很强的结构性限制,缺乏对复杂计算域的适应能力,因此有限差分算法极少涉足
复杂多体系统的研究。本文作者根据合则分之、分则合之的辩证思想,分别采用
区域分解算法和虚拟体方法解决了复连通区域的网格生成问题,在此基础上选用
合适的差分离散算法,很好的模拟研究了多体振荡系统的绕流场,分析了若干典
型复杂多体系统的流态转捩情况和动力响应特征。本文设计的基于分块思想及虚
拟体思想上的差分算法在解决复杂区域网格生成困难的同时,很好的保留了传统
差分算法的高精度和高分辨率特性,这对于研究流体流动这一具有多尺度特征的
物理问题起着不可或缺的重要性。
本文第一部分设计和实现了高精度的分块耦合算法程序。算法专门针对不可
压缩粘性流体,采用任意曲线坐标系下的原始变量形式的N-S方程进行描述。差
分离散过程中对粘性空间导数项选用四阶精度的Pade紧致格式;为了保证算法的
稳定性,对流空间项用傅德薰、马延文等人提出的三阶迎风紧致格式离散:时间
坐标上采用低存储要求的四阶显式Runge-Kutta格式离散。程序中实现了两类内边
界处理算法处理子域之间的流场信息传递:即处理重叠对接子域的Dirichlet条件,
相当于Schwarz算法:对于异构子域网格之间的信息传递采用Dirichlet-Neumann
边界耦合算法。借助公开的MPI并行库编写了算法的并行机版本,并在浙江大学
工程与科学计算中心的SGI Onyx3900并行机上平稳的运行了绝大多数的计算任
务,避免了传统PC机上运行大容量问题对硬件配置的苛刻要求。对流场进行分区
时需要同时兼顾每个子域上的计算载荷平衡问题,这对提高并行效率至关重要。
文中用高精度分块程序模拟了雷诺数在20～1000之间的单圆球绕流场,揭示
The flow past multi-bodies, i.e. multi-cylinders or multi-shperes, is multi-connected and a number of natural and engineering applications exist. The study on the flow past multi-bodies focuses on the capturing of mode transitions, the identification of vortex structures, the dynamic response, etc. Due to the complexity introduced by 'multi-bodies', it is hard to achieve some analytical solution for such flow problems. The experimental and numerical methods have shown wonderful perspective to investigate the flow past multi-bodies. While the difficulty in the grid generation for multi-connected region make it impossible to solve the 'mulit-bodies' problem by using the traditional body-fitted grid system. Further more, the oscillating motion of multi-bodies challenge the CFD researchers to design a more powerful numerical technique. In this paper, two novel numerical techniques, i.e. Domain Decomposition and Overlapping method and Virtual Body method, have been applied to successfully compute the oscillating flow of multi-bodies. These two numerical techniques hold the high-accuracy and high-resolution behaviors as well as they solve the difficulty in grid generation for multi-bodies, which are important to simulate the fluid flow with multi-scales.The first part of this paper implemented high accurate domain decopmosition and overlapping method (DDM) code, which specially aims at imcopressible viscous fluid flow described with primitive N-S equations under arbitrary curvilinear coordinate system. We used fourth-order Pade scheme for viscous terms and the fourth-order Runge-Kutta scheme for time discretization. To guarantee the numerical stability, the third-order upwind scheme provided by Fu Dexun and Ma, Yanwen is applied to convective terms. In our code, two kind of means are designed to handle the message passing between two adjacent sub-regions: Dirichlet condition for one-layer-overlapping sub-regions and Dirichlet-Neumann condition for sub-regions with different grid direction. In virtue of the open MPI library, the parallel version of this code was writed and the most running cases were finished on the SGI Onyx3900 machine located in the Center for Engineering and Scientific Computation of Zhejiang University.The high accurate DDM was used to simulate the flow past a single sphere
for Reynolds numbers between 20 and 1000. The exact vortex structures transitions were numerically discovered and the code proved to be feasible to simulate 3D fluid flow. The flow separation was captured at Re=25 which has good agreement with the available experimental result. The stable and plane-symmetric mode was computed at 210r~nted and the flow characteristics of two spheres in tandem arrangement were given as the function of the spacing ratio and Reynolds number. The flow transitions and the competition mechanism of vortex structures were obtained. As a typical case of more complicated fluid flows, the four spheres located in a cross-plane were studied and the interference between the vortex structures were analyzed, which will show important introduction to the study on the multiphase flow and the oscillating flow in engineering applications.
体绕流问题,它们广泛存在于自然界和各种工程生产设备中。多体系统绕流研究
涉及到流动模式的转捩、流场涡结构的识别及其相互作用分析以及工程应用中特
别关注的宏观流体力响应行为等等多方面的物理特性研究。由于复连通区域的复
杂性使得对于多体系统绕流场很难甚至不可能获得满意的分析解,因此实验研究
和数值模拟代替理论分析成为多体系统研究的主要手段,特别是在计算手段和计
算技术飞跃发展的今天数值模拟发挥着越来越大的作用。然而复连通区域的网格
生成困难阻碍了单区域贴体系统求解方法的应用,而研究多体系统在振荡状态下
的流场物理特性更是对数值模拟技术提出了巨大的挑战。根据作者的文献查新工
作发现,建立在非结构网格基础上的有限元方法及谱元方法在复杂几何形体绕流
的数值模拟上做出了巨大贡献;而传统的有限差分方法由于采用的网格系统具有
很强的结构性限制,缺乏对复杂计算域的适应能力,因此有限差分算法极少涉足
复杂多体系统的研究。本文作者根据合则分之、分则合之的辩证思想,分别采用
区域分解算法和虚拟体方法解决了复连通区域的网格生成问题,在此基础上选用
合适的差分离散算法,很好的模拟研究了多体振荡系统的绕流场,分析了若干典
型复杂多体系统的流态转捩情况和动力响应特征。本文设计的基于分块思想及虚
拟体思想上的差分算法在解决复杂区域网格生成困难的同时,很好的保留了传统
差分算法的高精度和高分辨率特性,这对于研究流体流动这一具有多尺度特征的
物理问题起着不可或缺的重要性。
本文第一部分设计和实现了高精度的分块耦合算法程序。算法专门针对不可
压缩粘性流体,采用任意曲线坐标系下的原始变量形式的N-S方程进行描述。差
分离散过程中对粘性空间导数项选用四阶精度的Pade紧致格式;为了保证算法的
稳定性,对流空间项用傅德薰、马延文等人提出的三阶迎风紧致格式离散:时间
坐标上采用低存储要求的四阶显式Runge-Kutta格式离散。程序中实现了两类内边
界处理算法处理子域之间的流场信息传递:即处理重叠对接子域的Dirichlet条件,
相当于Schwarz算法:对于异构子域网格之间的信息传递采用Dirichlet-Neumann
边界耦合算法。借助公开的MPI并行库编写了算法的并行机版本,并在浙江大学
工程与科学计算中心的SGI Onyx3900并行机上平稳的运行了绝大多数的计算任
务,避免了传统PC机上运行大容量问题对硬件配置的苛刻要求。对流场进行分区
时需要同时兼顾每个子域上的计算载荷平衡问题,这对提高并行效率至关重要。
文中用高精度分块程序模拟了雷诺数在20～1000之间的单圆球绕流场,揭示
The flow past multi-bodies, i.e. multi-cylinders or multi-shperes, is multi-connected and a number of natural and engineering applications exist. The study on the flow past multi-bodies focuses on the capturing of mode transitions, the identification of vortex structures, the dynamic response, etc. Due to the complexity introduced by 'multi-bodies', it is hard to achieve some analytical solution for such flow problems. The experimental and numerical methods have shown wonderful perspective to investigate the flow past multi-bodies. While the difficulty in the grid generation for multi-connected region make it impossible to solve the 'mulit-bodies' problem by using the traditional body-fitted grid system. Further more, the oscillating motion of multi-bodies challenge the CFD researchers to design a more powerful numerical technique. In this paper, two novel numerical techniques, i.e. Domain Decomposition and Overlapping method and Virtual Body method, have been applied to successfully compute the oscillating flow of multi-bodies. These two numerical techniques hold the high-accuracy and high-resolution behaviors as well as they solve the difficulty in grid generation for multi-bodies, which are important to simulate the fluid flow with multi-scales.The first part of this paper implemented high accurate domain decopmosition and overlapping method (DDM) code, which specially aims at imcopressible viscous fluid flow described with primitive N-S equations under arbitrary curvilinear coordinate system. We used fourth-order Pade scheme for viscous terms and the fourth-order Runge-Kutta scheme for time discretization. To guarantee the numerical stability, the third-order upwind scheme provided by Fu Dexun and Ma, Yanwen is applied to convective terms. In our code, two kind of means are designed to handle the message passing between two adjacent sub-regions: Dirichlet condition for one-layer-overlapping sub-regions and Dirichlet-Neumann condition for sub-regions with different grid direction. In virtue of the open MPI library, the parallel version of this code was writed and the most running cases were finished on the SGI Onyx3900 machine located in the Center for Engineering and Scientific Computation of Zhejiang University.The high accurate DDM was used to simulate the flow past a single sphere
for Reynolds numbers between 20 and 1000. The exact vortex structures transitions were numerically discovered and the code proved to be feasible to simulate 3D fluid flow. The flow separation was captured at Re=25 which has good agreement with the available experimental result. The stable and plane-symmetric mode was computed at 210
引文
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Gu, W., Chyu, C, Rockwell, D., 1994. Timing of vortex formation from an oscillating cylinder. Physics of Fluids. 6(11), 3677-3682.
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Abdallah, S., Dreyer, J., 1988. Dirichlet and Nuemann Boundary Conditions for the Pressure Poisson Equation of Incompressible Flow. International Journal for Numerical Methods in Fluids. 8, 1029-1036.
Achenbach, E, 1974. Vortex shedding from spheres. Journal of Fluid Mechanics. 62, 209-221.
Baban, F., So, R. M. C., Otugen, M. V., 1989. Unsteady forces on circular cylinders in a cross-flow. Experiments in Fluids. 7, 293-302.
Batchelor, G.. K., 1967. An introduction to Fluid Dynamics. Cambridge University Press.
Bearman, P. W., Wadcock, A. J., 1973. The interaction between a pair of circular cylinders normal to a stream. Journal of Fluid Mechanics. 61, 499-511.
Braza, M. B., Chassaing, P., Mirth, H. Ha., 1986. Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder. Journal of Fluid Mechanics. 165, 79-130.
Carpenter, M.H., Gottlieb, D., Abarbanel, S., 1993. The stability of numerical boundary treatments for compact high-order finite difference schemes. Journal of Computational Physics. 108, 272-295.
Chang, K., Song, C, 1990. Interactive vortex shedding from a pair of circular cylinders in a transverse arrangement. International Journal for Numerical Methods in Fluids. 11, 317-329.
Chong, M.S., Perry, A.E., Cantwell, B.J., 1990. A general classification of three-dimensitional flow field. Physics of Fluids A. 2(5),765-777.
Clift, R., Grace, J.R., Weber, W.E., 1978. Bubbles, drops, and particles. New York: Academic Press.
Fadlun, E.A., Verzicco, R., Orlandi, P., Mohd, Y., 2000. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. Journal of Computational Physics. 161, 35-60.
Fornberg, B., 1988. Steady viscous flow past a sphere at high Reynolds numbers. Journal of Fluid Mechanics. 190, 471-489.
Goldstein, D., Handler, R., Sirovich, L., 1993. Modeling a no-slip flow boundary with an external force field. Journal of Computational Physics. 105, 354-366.
Gu, W., Chyu, C, Rockwell, D., 1994. Timing of vortex formation from an oscillating cylinder. Physics of Fluids. 6(11), 3677-3682.
Hanazaki, H., 1988. A numerical study of three-dimensional stratified flow past a sphere. Journal of Fluid Mechanics. 192, 393-419.
Harlow, F.H., Welch, J.E., 1965. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Physics of Fluids. 8(12), 2182-2189.
Hunt, J.C.R., Wray, A.A., Moin, P. Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Report CTR-S88. 193-.
Jameson, A., Schmidt, W., 1985. Some recent development in numerical methods for transonic flow. Computer Methods in Applied Mechanics and Engineering. 51,467-493.
Jeong, J., Hussain, F., 1995. On the identification of a vortex. Journal of Fluid Mechanics. 285, 69-94.
Johnson, T.A., Patel, V.C., 1999. Flow past a sphere up to a Reynolds number of 300. Journal of Fluid Mechanics. 378,19-70.
Kalro, V., Tezduyar, T., 1998. 3D computation of unsteady flow past a sphere with a parallel finite element method. Computer Methods in Applied Mechanics and Engineering. 151,267-276.
Kim, I., Elghobashi, S., 1993. Three-dimensional flow over two spheres placed side by side. Journal of Fluid Mechanics. 246,465-488.
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