三维方腔拖曳流的数值模拟

Numerical simulation of viscous incompressible Navier-Stokes equations using a fractional-step approach

本文推导出一种适用于定常和不定常粘性不可压缩Navier Stokes方程的分裂步方法。采用Taylor Galerkin有限元格式进行求解,对有限元等式中关于速度的时间项进行三点向后差分,深入考虑粘性不可压缩流Navier Stokes方程中对流项的作用,利用二阶Taylor展开完成时间项向空间项的转化,采用张量分析的方法推导了N S方程分裂步方法的有限元离散格式,并采用低Reynolds数三维方腔拖曳粘性流[23,24]作为基本算例,检验了这种分裂步方法的稳定性和有效性,同时与大涡模拟相结合对Reynolds数为10000的三维方腔拖曳湍流流场进行了相关的分析,进一步揭示了方腔回流运动的非定常非对称性、流动结构表现为竖轴环流与立面环流相叠加、流速沿垂线分布相对均匀等流动规律,显示了该方法与大涡模拟相结合能够有效地捕捉涡系及其时变过程。

A fractional step method for the solution of steady and unsteady viscous incompressible Navier-Stokes equations was outlined. The method is based on Taylor-Galerkin finite element method. Three-point-backward difference scheme is used in the process of time discritizing. In considering the role of each term of Navier-Stokes equations, incooperated with second order Taylor expansion, a new fractional step method of second order precision is deduced. 3D lid driven flow in cavities are used to verify the stability and efficiency of the method. The 3D analysis are helpful to show the unsteadiness, asymmetry of the flow structure.