A study on the statistical convergence of turbulence simulations around a cylinder

The turbulent flow around a circular cylinder at a Reynolds number equal to 3900 is studied by an implicit Large Eddy Simulation performed by means of a discontinuous Galerkin finite element solver. The average velocity field in the wake is evaluated and compared with experimental data from the literature. The focus of the present work is on the estimation of the statistical uncertainty which is related to the use of a finite time window for the averaging operation. This topic represents an open problem for both Direct Numerical Simulations and Large Eddy Simulations in which it is difficult to define a priori the size of the time window which gives statistically converged averaged quantities. Different techniques to estimate this uncertainty are compared in order to get a quantitative criterion for checking the convergence of statistics. In particular, the Non-Overlapping Batch Means and the Batch Means Batch Correlations techniques are applied to the present test case.