Computational Fluid Dynamics (CFD) usually requires advanced and accurate diagnostics to help improve our understanding especially in the context of fully unsteady 3D simulations. To do so, two kinds of tools exist today: operator-based and data-based analyses. The most well known data-based analysis used in fluid mechanics is probably the dynamic mode decomposition. This method has indeed shown to be powerful to study CFD results without assumption. It is, however, memory consuming and very sensitive to noise while being used a posteriori. The objective of the following contribution is to relax such issues thanks to an operator-based analysis called Dynamic Mode Tracking (DMT). Based on the well-known selective frequency damping method, DMT relies on a specific implementation allowing the identification of flow activity of specific interest as the data are generated. The method shows to be well adapted for flows exhibiting a clear limit cycle with multiple specific frequencies. Focusing on one of these frequencies, DMT parameters can be adapted to study its temporal evolution giving insight into the mode spatial and temporal features. Thanks to DMT, a variant called Dynamic Mode Tracking and Control (DMTC) allows then to control the identified feature in the CFD simulation. To do so, DMT is coupled with the flow equations thanks to a feedback relaxation method resulting in an artificial control of the flow physics for a specific feature. The development and application of DMT as well as DMTC are illustrated on three problems. First, a simple flow problem based on the propagation of three acoustics waves to evidence the tracking capability of DMT is presented. The second example deals with the vortex shedding of a cylinder wake. For these two cases, DMTC is then applied to demonstrate the capacity of the approach. Finally, the method is applied to a complex configuration: a 3D swirled burner exhibiting a thermo-acoustic instability.
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