The Application of Adaptive Time Spectral Method for Analyzing Inviscid Compressible Flow around a Pitching Airfoil

A pitching airfoil, the time-spectral method can be used, which is a Fourier series-based spectral method with a suitable convergence speed. The disadvantage of the time spectral method is that in the entire computational domain, the number of time intervals is constant, which unnecessarily increasing the amount of computer memory and CPU time (The dependent variables). By using the adaptive time spectral method, this weakness of the time spectral method can be eliminated by the optimal distribution of time intervals (independent variable) in the computational domain (proportional to the flow gradient). In the present research, the adaptive time spectral method was added to an inviscid flow solver. The results of this method were compared with the results of the standard (non-adaptive) time spectral method and experimental data. Also, two components of computer memory and CPU time were studied. The results obtained for the three cases (Case1, Case2, and Case5) with Mach numbers 0.6, 0.6, and 0.755 respectively of the NACA0012 pitching airfoil 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. The CPU time for Case2 and Case5 for 4-time intervals has been reduced by 21 and 24 percent, respectively. And for Case1 for 4, 8, 1,0 and 12-time intervals, it has been reduced by 16, 38, ,31 and 29 percent respectively.