About the convergence of POD and EPOD modes computed from CFD simulation

In most fluid mechanic applications, the dominant high energy content POD modes are generally well converged justifying the great use of POD to extract the associated large scale flow structures of a turbulent flow. However for particular studies related to the characterization of smaller flow structures, it is necessary to take into account high order POD modes. In this paper based on a particular numerical database available on a finite-discrete spatio-temporal domain, the sensibility of POD modes to both spatial discretization and independent temporal samples is highlighted as a function of integral time and space scale content. A systematic procedure is then proposed in order to verify the spatial convergence of POD modes for a given number of points per integral space scale and per integral time scale and also for a given number of uncorrelated samples that is the number of integral time scale contained in the original signal. The convergence of Extended POD modes is also verified by an error threshold definition that permits to avoid any misinterpretation of the results. A new extension of the EPOD procedure based on the snapshot POD technique is then proposed aiming at using only the converged EPOD modes to characterize the correlated part of the signal.