Resolution of Gibbs phenomenon using a modified pseudo-spectral operator in harmonic balance CFD solvers* |
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Authors: | Reza Djeddi Kivanc Ekici |
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Institution: | Mechanical, Aerospace and Biomedical Engineering Department, The University of Tennessee, Knoxville, TN, USA |
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Abstract: | A new pseudo-spectral operator is developed for time-spectral harmonic balance solutions of periodic unsteady flows. The method utilises a mechanism similar to sigma-approximation technique with Lanczos filtering function that alters the inverse of the discrete Fourier transformation matrix, leading to a modified pseudo-spectral operator. The modified operator is then 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 and robustness of the technique are demonstrated through various test cases. |
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Keywords: | Gibbs phenomenon modified pseudo-spectral operator harmonic balance time-spectral methods Fourier series computational fluid dynamics (CFD) |
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