Fourier伪谱方法在不可压缩平板边界层研究中的应用

李宁; 罗纪生

Fourier伪谱方法在不可压缩平板边界层研究中的应用

李宁¹,
罗纪生^1,2

1.
天津大学力学系, 天津 300072
2.
南开大学天津大学刘徽应用数学中心, 天津 300072

基金项目: 国家自然科学基金项目(10632050)

计量
- 文章访问数: 1506
- HTML浏览量: 103
- PDF量: 453
- 被引次数: 0
出版历程
- 收稿日期: 2006-11-30
- 修回日期: 2007-05-27
- 刊出日期: 2007-12-28

Application of fourier pseudo-spectral method in the incompressible boundary layer on a flat plate

LI Ning¹,
LUO Ji-sheng^1,2

1.
Department of Mechanics, Tianjin University, Tianjin 300072, China
2.
LIU Hui Center of Applied Mathematics, Nankai University and Tianjin University, Tianjin 300072, China

摘要

摘要: 以三维不可压缩平板边界层为研究对象,扰动形式N-S方程为控制方程,从空间模式的角度,直接数值模拟了三维不稳定T-S波传播的过程.时间离散采用三阶精度混合显隐分裂格式,空间离散则结合Fourier伪谱方法及高精度紧致有限差分逼近,法向采用非等间距网格坐标变换,出口边界条件采用嵌边函数法,程序采用MPI(Message passing interface)并行方法编写.实例验证,该方法计算结果与流动稳定性分析的结果一致.
- 不可压缩边界层 /
- Fourier伪谱方法 /
- 紧致有限差分 /
- 直接数值模拟(DNS)
Abstract: Three-dimensional incompressible boundary layer on a flat plate was studied where disturbance N-Sequation was taken as governing equation.The evolution of three-dimensional instability T-Swave was simulated by spatial DNS(direct numerical simulation) in which third-order precision mixed explicit-implicit scheme was employed for temporal discretization while a method combining Fourier pseudo-spectral method with high precision compact finite difference was implemented for spatial discretization.Acoordinate transform of nonuniform meshes was applied in normal direction,fringe method was adopted as exit boundary condition and MPImethod was used in programming.Through a simple case,the results obtained by this method were tested to be in consistence with the ones obtained with stability theory.
- incompressible boundary layer /
- Fourier pseudo-spectral method /
- compact finite difference /
- DNS(direct numerical simulation)

HTML

参考文献(12)

[1]	王新军,罗纪生,周恒.平面槽道中层流-湍流转捩的"breakdown"过程的内在机理[J].中国科学:G辑,2005,35(1):71-78.WANG Xinjun,LUO Jisheng,ZHOU Heng.Inherent mechanism of breakdown in laminar-turbulent transition of channel flow[J].Science in China:Series G,2005,35(1):71-78.
[2]	Rist U,Fasel H.Direct numerical simulation of controlled transition in a flat-plate boundary layer[J].J Fluid Mech,1995,(298):211-248.
[3]	Liu C,Liu Z.Multigrid mapping box relaxation for simulation of the whole process of flow transition in 3D boundary layer[J].J Compute Phys.,1995,(119):325-341.
[4]	Wang Z,Yeo K S,Khoo B C.Spatial direct numerical simulation of transitional boundary layer over compliant surfaces[J].Computers & Fluids.,2005,(34):1062-1095.
[5]	杨琳,邹正平,宁方飞,等.边界层转捩的数值模拟[J].航空动力学报,2005,20(3):355-360.YANG Lin,ZOU Zhengping,NING Fangfei,et al.Simulation of boundary layer transition[J].Journal of Aerospace Power,2005,20(3):355-360.
[6]	周恒.新世纪对流体力学提出的要求[J].自然科学进展,2000,10(6):491-494.ZHOU Heng.The expectation for fluid mechanics in 21st century[J].Progress in Natural Science,2000,10(6):491-494.
[7]	Karniadakis G E,Israeli M,Orszag S A.High-order splitting methods for the incompressible navier-stokes equations[J].Journal of Computational Physics,1991,(97):414-443.
[8]	傅德薰,马延文.平面混合流拟序结构的直接数值模拟[J].中国科学:A辑,1996,26(7):657-664.FU Dexun,MA Yanwen.Numerical Simulation of Coherent Structure in Two-dimensional Compressible Mixing Layers[J].Science in China:Series A,1996,26(7):657-664.
[9]	Lele S K.Compact finite difference schemes with spectral-like resolution[J].J Comp Phys,1992,103:16-43.
[10]	Kloker M,Konzelmann U,Fasel H.Outflow boundary conditions for spatial navier-stokes simulations of transition boundary layers[J].AIAA Journal,1993,31(4):620-628.
[11]	苏彩虹.嵌边法出流条件在可压缩流直接数值模拟中的应用[D].天津:天津大学,2005.SU Caihong.The application of fringe method as the outflow boundary condition for the direct numerical simulation of compressible flows[D].Tianjing:Tianjing University,2005.
[12]	Lundbladh A,Schmid P J,Berlin S,et al.Simulation of bypass transition for spatially evolving disturbances[J].In AGARDCP-551,1994,18:1-13.