An overset adaptive time spectral method for periodic flows

The time spectral approach, a spectral method based on the Fourier series with an appropriate convergence speed, can be utilized for a time-varying problem like the flow around a pitching airfoil. This approach has the drawback of having a constant number of time intervals over the entire computational domain, which unnecessarily uses up more computer memory and central processing unit (CPU) time. By distributing time intervals in the computational domain optimally (proportional to the flow gradient), the adaptive time spectral approach can overcome the shortcoming of the time spectral method. In the current study, the adaptive time spectral method is added to an inviscid fluid flow solver. Also, in the airfoil with pitching motion, a grid known as an overset grid has been used, including two grids with an overlapping region. The results for the three cases (Cases 1, 2, and 5) of the NACA0012 pitching airfoil with different angles of attack studied by AGARD Institute, with Mach numbers 0.6, 0.6, and 0.755, respectively, showed that while having an acceptable solution accuracy, the amount of computer memory and CPU time is significantly reduced compared to the standard time spectral method.