Stabilization of High-Dimensional Harmonic Balance Solvers Using Time Spectral Viscosity

作者：Huang Huang^*; Ekici Kivanc

来源：AIAA Journal, 2014, 52(8): 1784-1794.

DOI：10.2514/1.J052698

We investigate the application of a temporal spectral viscosity operator to eliminate aliasing errors associated with the high-dimensional harmonic balance technique, which is an efficient method for modeling nonlinear time-periodic problems. Previous studies have shown that aliasing errors resulting from the discrete Fourier transformation may slow down convergence, trigger a nonlinear instability, or lead to nonphysical solutions. A temporal spectral viscosity operator, similar to that used for pseudospectral methods, is introduced. The temporal spectral viscosity is added to the high-frequency modes of the solution to eliminate aliasing errors so as to ensure the convergence to the physical solution. The implementation of the technique is straightforward and can be incorporated into the high-dimensional harmonic balance solver as a matrix product operator. The accuracy and effectiveness of the modified method is demonstrated for different test cases including a Duffing oscillator and unsteady flow about an oscillating circular cylinder. Finally, the temporal spectral viscosity is applied to a turbomachinery aeroelasticity problem to investigate the effect of added dissipation on the accuracy of unsteady solutions.

• 出版日期2014-8