Grid refinement test of time-periodic flows over bluff bodies

A grid refinement study of the time-periodic flow over a circular cylinder at Re = 200 is presented. An efficient numerical solution method of the time-dependent incompressible Navier-Stokes equations allowed the solution of the problem on several meshes up to 513 × 513 points. The time-periodic solution was presented in the frequency domain by expanding it into a Fourier series in time. The dependence of the solution on the mesh size has been studied both in the physical and Fourier domains. In the physical domain, very fine meshes are needed to obtain a spatially converged solution, i.e. a solution that varies with the mesh size as the spatial accuracy of the scheme. The amplitudes of the Fourier components converge on coarser grids than the phase angle or the solution in the physical domain. These findings indicate that the mesh resolution has a more pronounced effect on the phase velocity of the vortices than on phenomena related to magnitude. Consequently, if one is interested only in magnitude effects, such as the force coefficients, coarser meshes can be used. The characteristics of the far-wake region are governed by both the amplitude and phase angle (propagation velocity) and, therefore, very fine meshes are required to resolve it. The study of the Fourier components of the solution proved to yield new insights on the effects of mesh resolution on the simulation of time-periodic flows over bluff bodies.