Demonstration of Nonlinear Frequency Domain Methods

This paper demonstrates the accuracy of the nonlinear frequency domain method in applications to unsteady flow calculations. The basis of the method is a pseudospectral approach to recast a nonlinear unsteady system of equations in the temporal domain into a stationary system in the frequency domain. The nonlinear frequency domain method, in principle, provides the rapid convergence of a spectral method with increasing numbers of modes, and, in this sense, it is an optimal scheme for time-periodic problems. In practice it can also be effectively used as a reduced order method in which users deliberately choose not to resolve temporal modes in the solution. A variable-time-period method has been proposed such that the nonlinear frequency domain method can be applied to problems where the time period of the unsteadiness is either known or unknown a priori. To validate the latter case, results from this method have been compared with experimental results of vortex shedding in low Reynolds number flows past cylinders. Validation of the first case utilizes experimental data of a pitching airfoil in transonic flow. These comparisons demonstrate the efficiency of the nonlinear frequency domain method in representing complex nonlinear flow field physics with a limited number of temporal modes. Nomenclature A, B, C, D = coefficients used in the Strouhal data curve fit b = component of the control volume face velocity