Periodic Unsteady Flow Analysis Using a Diagonally Implicit Harmonic Balance Method

Abstract

An implicit harmonic balance method is applied to periodic unsteady flow problems. Diagonal terms of the harmonic source vector are treated implicitly and easily implemented on a diagonalized implicit solver that is very similar to a flow solver. The multi-grid performance and solution convergence of the present implicit harmonic balance method are investigated with a 2-D oscillating airfoil and a 3-D wing with pitching motion. Computational results are compared with results from explicit trials and a dual timestepping method in the time-domain. The present harmonic balance method provides fast and stable convergence characteristics regardless of the number of harmonics. Results show that the present method can largely reduce the computing time for unsteady flow problems, compared to that necessary in the dual time-stepping and explicit harmonic balance methods.