Implicit Time Spectral Method for Periodic Incompressible Flows

International audienceThe time spectral method converts a time-periodic flow computation into the solution of 2N+1 coupled steady computations, whereN denotes the number of harmonics retained in the Fourier analysis of the flow. The efficiency of the method has been previously demonstrated by several authors for compressible flow applications on structured grids using implicit solution of the large-scale steady system introduced by the coupling. In this paper, the time spectral method is extended to periodic incompressible viscous flows using a finite volume formulation of the artificial compressibility system on general moving unstructured grids. Numerical simulations of low-Reynolds flows over an airfoil show the time spectral method can afford, though not systematically, a reduction by a factor up to 5 of the computational cost with respect to a conventional unsteady technique, which computes the whole transient flow behavior