中文摘要：

采用时间谱方法求解周期性非定常Navier-Stokes方程，对绕振荡翼型非定常粘性流动进行了数值模拟研究。方程中对流项离散采用Roe’s FDS格式，时间项采用基于时间谱方法的傅里叶表达式离散，并引入伪时间项。为提高计算效率，时间推进采用隐式BLU—SGS方法。对绕振荡NACA0012翼型的亚声速和跨声速非定常粘性绕流进行数值模拟，计算结果与实验值吻合很好。

英文摘要：

The time spectral method casts a time-periodic flow computation into the solution of N coupled steady computations, where N indicates the number of time intervals. This method solves the periodic state directly without resolving transients, by enforcing periodicity and using a Fourier representation in time. This technique is presented to solve time-periodic unsteady Navier-Stokes equations for unsteady viscous flow over an oscillating airfoil. The Rocks FDS scheme is used to discrete convective terms, and physical time de- rivative terms are discretized by a Fourier representation, in which the time derivative is formulated with the combination of flow variables at all time levels, leading to spectral accuracy. A pseudo-time derivative term is added into the original equations and the fully implicit BLU-SGS method in the pseudo-time direction is employed. The solution is obtained by marching towards a steady-state in the pseudo-time variable. A sub- sonic case and a transonic case about the NACA0012 airfoil are calculated. Baldwin-Lomax turbulence model has been used in viscous flow analysis. The numerical results agree well with the experimental data. The computational results show that the small number of time intervals is sufficient to capture the flow physics phenomena.