Comparison of Parallel Time-Periodic Navier-Stokes Solvers

In this paper we compare two different methods to compute time-periodic steady states of the Navier-Stokes equations. The first one is a traditional time-stepping scheme which has to be evolved until the state is reached. The second one uses periodic boundary conditions in time and uses a spectral discretization in time. The methods are compared with regard to accuracy and scalability by solving for a time-periodic Taylor-Green vortex. We show that the time-periodic steady state can be computed much faster with the spectral in time method than with the standard time-stepping method if the Womersley number is sufficiently large.