Implicit Time Spectral Method for time-periodic Incompressible flows
This Ph.D work deals with the implementation and analysis of a Time Spectral Method (TSM) dedicated to the efficient calculation of time-periodic flows. The main interest of the formulation lies in the fact that the calculation of the flow transient is not needed anymore and, instead, the final periodic solution can be directly looked for. Besides, the use of large physical time step is made possible by the spectral accuracy of the TSM time deriva- tive operator. The Time Spectral Method converts a time-periodic flow computation into the solution of 2N + 1 coupled steady computations where N denotes the number of harmonics retained in the Fourier analysis of the flow. The TSM is implemented into a Navier-Stokes solver in the context of general moving unstructured grids using an ALE (Arbitary Lagrangian Eulerian) formulation. An implicit scheme is proposed to make the approach even more at- tractive in terms of computational cost. An original contribution of this thesis is the extension of the TSM to the computation of laminar incompressible flows using the artificial compress- ibility method. Numerical simulations of oscillating and heaving airfoils allow a fine analysis of the TSM and show that it can lead to substantial computational cost reduction.