中文摘要：

采用谱方法，在曲线坐标系下对不可压缩Newton流体的N—S方程进行求解，采用定义在物理空间中的流动物理量以避免使用协变、逆变形式的控制方程．在计算空间采用Fourier—Chebyshev谱方法进行空间离散，时间推进采用高精度时间分裂法．为了减小时间分裂带来的误差，采用了高精度的压力边界条件．与其他求解协变、逆变形式控制方程的谱方法相比，该方法在保持谱精度的同时减小了计算量．首先通过静止波形壁面和行波壁面槽道湍流的直接数值模拟，对该数值方法进行了验证；其次，作为初步应用，利用该方法研究了槽道湍流中周期振动凹坑所产生的流动结构．

英文摘要：

A numerical scheme was developed to extend the scope of the spectral method without solving the covariant and contra-variant form of Navier-Stokes equations in curvilinear coordinates. The primitive variables were represented by Fourier series and Chebyshev polynomials in computational space. The time advancement was accomplished by a high-order time-splitting method, and a corresponding high-order pressure condition at the wall was introduced to reduce the splitting error. Compared with the previous pseudo-spectral scheme, in which the Navier-Stokes equations were solved in covariant and contxa-variant form, the present scheme reduced the computational cost, at the same time kept the spectral accuracy. The scheme was tested by the simulation of turbulent flow in a channel with a static streamwise wavy wall and turbulent flow over a flexible wallundergoing streamwise traveling wave motion. Turbulent flow over an oscillating dimple was studied using present numerical scheme, and the periodic generation of vortical structures was analyzed.