An adaptive time spectral viscosity (TSV) approach is proposed to stabilize the time-spectral method (TSM) by dealiasing its solution. Instead of being assigned uniformly in space, the cut-off wave number for TSV is determined locally by spectrum analysis of the flow variables. On each grid cell, the significant low-frequency modes are adaptively separated from the TSV targeted high-frequency ones according to local flow physics. The space-time Lower-Upper Symmetric Gauss-Seidel(ST-LU-SGS) implicit scheme is used to solve the modified time-spectral equations. TSV operator is treated implicitly in the same way as the time spectral operator to facilitate fast convergence. Computational results of inviscid and turbulent flows over a pitching NACA0012 airfoil are presented for validation of the adaptive TSV approach. For the turbulent flow case, the proposed approach is also applied to the Spalart–Allmaras (S-A) turbulence model equation. The accuracy and the convergence rate of the adaptive TSV approach is demonstrated in both test cases.

提出了一种自适应时间谱粘度 (TSV) 方法，通过对其解进行去混叠来稳定时间谱方法 (TSM)。TSV 的截止波数不是在空间中均匀分配，而是通过流动变量的频谱分析在本地确定。在每个网格单元上，重要的低频模式根据局部流动物理与 TSV 目标高频模式自适应分离。时空下-上对称高斯-赛德尔(ST-LU-SGS)隐式方案用于求解修正的时谱方程。TSV 算子以与时间谱算子相同的方式隐式处理，以促进快速收敛。提供了俯仰 NACA0012 翼型上无粘性和湍流的计算结果，用于验证自适应 TSV 方法。对于湍流情况，所提出的方法也适用于 Spalart-Allmaras (SA) 湍流模型方程。自适应 TSV 方法的准确性和收敛速度在两个测试案例中都得到了证明。