Comparative analysis of computational methods for periodic transonic flows at low and high frequencies

This paper presents a comparative analysis via simulation of time-periodic unsteady inviscid flow at low and high frequencies using Time Spectral Method (TSM) and comparing it with the traditional methods such as BDF and Explicit Structured Adaptive Grid Method. The TSM uses a Fourier representation in time. Mathematical tools used here are discrete Fourier transformations. The TSM has been proposed for the fast and efficient computation of periodic unsteady flows. This method has been evaluated and has been validated with NACA pitching airfoils that are widely used and prevalent 2D external aerodynamics test cases. To validate the results presented by the TSM are compared with experimental data and two the other methods. It shows a significant reduction in the computational expense compared to the conventional time-accurate methods, due to taking advantage of the periodic nature of flow by Fourier representation for temporal discretization that has a high accuracy. Also it has shown that TSM can be applied accurately for ample rang of variations of frequency (NACA 64A010 (CT6)) and variations in angle of attacks (NACA 0012 (CT1)).