An Extension of the Time-Spectral Method to Overset Solvers

Relative motion in a Cartesian or overset framework results in dynamic blanking of spatial nodes which move interior to impermeable bodies. The solution at these nodes is therefore undefined over specific time intervals. This proves problematic for the conventional Time-Spectral approach, which expands the temporal variation at every node into a Fourier series spanning the period of motion. The current work extends the Time-Spectral method by representing the solution at dynamically-blanked nodes with barycentric rational interpolants that span the sub-periodic intervals through which the solution is defined. Fourier- and rational-based differentiation operators are used in tandem to provide a consistent hybrid Time-Spectral scheme to resolve the relative motion. The hybrid scheme is demonstrated on a linear model problem and also implemented within NASA’s OVERFLOW Reynolds-averaged Navier-Stokes solver. The hybrid Time-Spectral OVERFLOW solver is applied to airfoils oscillating in plunging and pitching motions, and the results compared against time-accurate simulations and experimental data (where available). Further, a Time-Spectral gradient limiter is developed which eliminates non-physical states of the undamped turbulent eddy viscosity when using the Spalart-Allmaras turbulence model. The results demonstrate that the hybrid scheme mirrors the performance of the conventional Time-Spectral method, and monotonically converges to the comparable timeaccurate simulations with increasing Time-Spectral modes.