N-S方程数值模拟方法研究及边界层中相干结构的非线性演化

The study of numerical method of Navier-Stokes equations and non-linear evolution of the coherent structure in a boundary layer

建立了一套三维不可压流动的直接数值模拟方法。该算法在x及y向构造了基于非等间距网格的紧致有限差分格式和非线性项的迎风紧致型格式,在z向采用Fourier谱方法。并研究、提出了三维、非定常流体运动下游边界的无反射出流条件。另外,本文还构建了多涡结构的初始扰动理论模型,利用直接数值模拟的方法研究了边界层中多涡结构的非线性演化特点。结果表明多涡结构非线性演化中的许多特点,如雷诺应力分布、高剪切层的形成、喷射和扫掠等与壁湍流中相干结构的发展规律和现象十分相似。同时,通过对边界层中多涡结构的非线性演化问题的直接数值模拟,验证了该算法具有计算精度高,稳定性好,收敛速度快,出流边界影响小等优点。

A method for direct numerical simulation of three-dimensional incompressible Navier-Stokes equations has been built up. With the Fourier spectral expansion in the spanwise direction, the compact finite difference and the non-linear terms upwind compact finite difference schemes on non-uniform meshes in the x , y direction are constructed. The nonreflecting outflow boundary conditions of three-dimensional unsteady fluid flow have been studied and put forward. Besides, an initial theory model for the eddy structures in a laminar boundary layer is proposed in this paper. The non-linear evolution of the eddy structures in a laminar boundary layer has been studied by the method of the direct numerical simulations. It is found that the numerical results of the distribution of Reynolds stress, the formation of high shear layer, the event of ejection and sweeping etc resemble what was observed in the characteristics of the eddy structures of wall region in a turbulence boundary layer. As the problem of non-linear evolution of the eddy structures in a boundary layer is directly simulated, it has shown that the numerical method has a lot of advantages on high accuracy, all right stabilization, fast convergence, and less influence upon the outflow boundary conditions etc..