Determining when a numerical simulation is fully converged is important in getting accurate and reliable results. In unsteady problems, especially those involving periodic flows, it is not easy to judge convergence based on the existing convergence criteria. In this study, a convergence criterion based on an analysis of the frequency content of several flow variables using the fast Fourier transform (FFT) is suggested. This FFT convergence criterion has an advantage in that it is based on evaluation of the physical flow variables. Two conditions are set to judge convergence using the FFT convergence criterion. The first condition deals with the errors associated with the selection of the number of samples, whereas the other deals with the physical frequencies and their amplitudes.The FFT convergence criterion is tested and applied to two different unsteady flow problems, which have been solved numerically using two different flow solver codes. The results show that the suggested FFT convergence criterion can be applied successfully and easily to judge the degree of convergence of numerical simulations of periodic fluid flows.
NomenclatureA = normalized amplitude Dt = sampling rate d = hydraulic diameter of jet, m f = frequency, Hz H = computational domain height, m J = momentum flux ratio L = computational domain length, m N = number of data p = point Sr = Strouhal number t = time, s u = axial-velocity component, m/s v = vertical-velocity component, m/s W = computational domain depth, m w = spanwise-velocity component, m/s x = axial distance, m y = vertical distance, m z = spanwise distance, m Subscripts c = cutoff ds = data samples eb = error band FFT = fast Fourier transform max = maximum p = predicted sp = spacing 1 = error frequency 2 = dominant physical frequency 3 = secondary physical frequency