Combined spectral-finite difference time discretization for periodic and quasi-periodic flows

An accurate and efficient treatment of periodic and quasi-periodic flows based on the temporal Fourier decomposition of the Navier-Stokes equations is suggested. A numerical implementation for a laminar afterbody wake in a two-dimensional channel is presented. This implementation is formulated in primitive variables and uses an ordinary 2nd-order accurate finite volume space discretization combined with a standard pressure correction procedure. A multi-step time marching scheme for numerical and physical transients is developed. For flows with a variable dominant period, a period correction algorithm is used. The transients characterizing the instability development are simulated. The numerical results obtained for the afterbody wake confirm the expectations concerning the efficiency and high time accuracy of the method. Moreover, the method provides direct access to quantities difficult to obtain by other methods such as the envelope and the angular velocity variation of the unstable mode.