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• Aliasing decreases accuracy and causes instability in solution of flow problems. • An Adaptive Time Spectral Viscosity method removes the aliasing error. • The method enables efficient prediction of turbulent flows with shock waves. 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. [ABSTRACT FROM AUTHOR]