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传统的双时间方法在非定常计算中长时间的过渡迭代推进求解导致其计算效率相对较低,针对周期性非定常流动问题的流动特征,发展了一种基于离散傅里叶变换的高效时间谱方法,用于求解振荡翼型和机翼的非定常黏性绕流。在时空耦合的雷诺平均Navier-Stokes(RANS)方程的求解中,对流项的离散应用了Roe的通量差分格式,物理时间项的离散方法为时间谱方法,伪时间推进采用了隐式LU-SGS(Lower-Upper Symmetric Gauss-Seidel)格式。考虑到湍流的时空耦合效应,时空耦合的Spalart-Allmaras一方程湍流模型的物理时间项同样采用时间谱方法进行离散。为了进一步提高计算效率,当地时间步长和多重网格技术等加速收敛的措施均被采用。算例对俯仰振荡NACA0012翼型和Lann机翼的周期性非定常流场进行了数值计算。结果表明:对于周期性非定常流场的数值模拟,相比于传统的双时间方法,用时间谱方法近似物理时间项,不仅能够提高流场的计算精度,而且更能够大幅度提高计算效率。
The traditional two-time method solves the problem of long-term transition iteration in unsteady computation, resulting in a relatively low computational efficiency. For the flow characteristics of periodic unsteady flow problems, an efficient time-spectrum based on discrete Fourier transform Method for solving unsteady viscous flow around oscillation airfoils and wings. In the solution of the coupled Navier-Stokes (RANS) equation of time-space coupling, the Roe flux difference scheme is applied to the discretization of the convection term, the discrete time-domain method is the time spectrum method, the implicit LU- SGS (Lower-Upper Symmetric Gauss-Seidel) format. Considering the temporal-spatial coupling effect of turbulence, the spatio-temporal coupled Spalart-Allmaras turbulence model’s physical time terms are also discrete by time-spectrum method. In order to further improve computational efficiency, measures such as local time steps and multi-grid techniques to accelerate convergence have been adopted. A numerical example is given to calculate the periodic unsteady flow field of the pitch oscillation NACA0012 airfoils and the Lann airfoils. The results show that for the numerical simulation of periodic unsteady flow field, compared with the traditional two-time method, using the time spectrum method to approximate the physical time item can not only improve the calculation accuracy of the flow field, but also greatly improve the computational efficiency.