Application of harmonic balance method in simulations of low speed unsteady flows

The harmonic balance method is an effective computational method in simulating time periodic unsteady flows. When using the harmonic balance method based on compressible flow equations to solve low Mach number flows, both the accuracy and convergence of the solution would be deteriorated due to the large dissipation of the convective scheme which is specially designed for compressible flows. To solve this problem, the low speed preconditioning was adopted; therefore, the harmonic balance method based on compressible flow equations could be used to compute low speed periodic unsteady flow directly. Both the time marching calculation and the harmonic balance calculation were performed in simulating the incompressible lid-driven flow and the low Reynolds number vortex shedding cylinder flow. The results show the capability of using the preconditioned harmonic balance equation in simulating low speed periodic unsteady flows, and the unsteady flowfield could be well reconstructed by using only a few harmonics retained in the harmonic balance method.