Modified Spectral Operators for Time-Collocation and Time-Spectral Solvers

摘要

A new set of pseudo-spectral operators is developed for time-spectral harmonic balance solutions of periodic unsteady flows. The method utilizes smoothing filters that alter the inverse of the discrete Fourier transformation matrix, leading to a modified pseudo-spectral operator. The pseudo-spectral operator is used instead of the original operator that mimics the time-derivative term of the unsteady governing equations. The modified operator is capable of damping high frequency nonlinearities in the harmonic balance solution, thus alleviating the effects of high frequency oscillations that result in Gibbs-type phenomena. The effectiveness of the technique is demonstrated for two different test cases.