Finite volume implementation of the harmonic balance method for periodic non–linear flows

Harmonic Balance Method for non-linear periodic flows is presented in this paper. As- sumption of temporal periodicity can be used to convert harmonic transient equations into a set of coupled steady state equations. Solution of coupled equations yields flow fields at discrete instants of time throughout a representative harmonic period. The method uses second-order accurate, polyhedral Finite Volume Method. It is developed for a general transport equation and generalised to coupled non-linear equation sets, including incom- pressible Navier-Stokes equations and is implemented in OpenFOAM. Verification of the model is carried out by comparing the results with transient simulations. Preliminary re- sults for weakly and strongly harmonic incompressible flow around oscillating airfoil are presented.