Time Spectral Method for Periodic Unsteady Computations over Two- and Three- Dimensional Bodies

Abstract

The Time Spectral Algorithm is proposed for the fast and ecient computation of timeperiodic turbulent Navier-Stokes calculations past two- and three-dimensional bodies. The eciency of the approach derives from these attributes: 1)time discretization based on a Fourier representation in time to take advantage of its periodic nature, 2)multigrid to drive a fully implicit time stepping scheme. The accuracy and eciency of this technique is verified by Euler and Navier-Stokes calculations for a pitching airfoil and a pitching wing. Results verify the small number of time intervals per pitching cycle required to capture the flow physics. Spectral convergence is demonstrated for pitching motion characterised by many frequencies.