【摘要】 构造了基于非等距网格的迎风紧致格式，并将其与三阶精度的Ａｄａｍｓ半隐方法相结合，构造了求解不可压Ｎ－Ｓ方程高效算法．该算法利用基于交错网格的离散形式的压力Ｐｏｉｓｓｏｎ方程求解压力项，解决了边界处的残余散度问题；同时还利用快速Ｆｏｕｒｉｅｒ变换将方程的隐式部分解耦，离散后的代数方程组利用追赶法求解，大大减少了计算量．通过对二维槽道流动的数值模拟，证实了所构造的数值方法具有精度高，稳定性好，能抑制混淆误差等优点，同时具有很高的计算效率，是进行壁湍流直接数值模拟的有效方法． 在数值模拟的基础上对一维槽道流动进行了分析，得到了Ｒｅｙｎｏｌｄｓ数从６０００到１５０００的二维流动饱和态解（所谓“二维槽道湍流”）；定性及定量结果均与他人的数值计算结果吻合十分理想．对流场进行了统计分析，指出了“二维湍流”与三维湍流统计特性的区别．更多还原

【Abstract】 A new method is developed to solve incompressible Navier-Stokes equations. The method includes sib order upwind compact difference schemes on non-uniform meshes, high-order time-splitting methods based on staggered grid with discrete pressure equation, and spectral meth- ods. The upwind compact difference schemes on non-uniform grids have very high-order accuracy on interior grids as well as near-boundary grids. The dissipative nature of upwind scheme results in a damping of the higher frequency content, as a result very little energy is alising back. Discrete pressure equation based on staggered grids can avoid difficulties of boundary conditions of res- sure. By using FFT the equations of pressure and viscous term can be decoupled, large computing amount can be saved. In the second part of this paper, fully developed two dimensional turbulent channel flow (Reynolds number from 6000 to 15000) is simulated and analysed. According to this papers time evolutions of averaged vorticity at lower wall goes from the laminar to the chaotic as Reynolds number goes higher. The results are very close to the results of Ref.[8]. In addition, the flows of Re=12000 and 15000 are also simulated correctlys indicating that the numerical schemes in this paper are better than those of Ref.[8]. The difference and similarity between two-dimensional and three-dimensional turbulence are also showed in this paper, which shows the importance of the span-wise disturbance to form the core area of turbulence.更多还原