Global in Time Analysis and Sensitivity Analysis for the Reduced NS-α Model of Incompressible Flow

TLDR: In this article, a detailed global in time analysis, and sensitivity analysis and testing, for the recently proposed reduced NS-α model is provided, and an efficient numerical scheme for the sensitivity system is proposed and analyzed, and proven to be stable and optimally accurate.

Abstract: We provide a detailed global in time analysis, and sensitivity analysis and testing, for the recently proposed (by the authors) reduced NS-α model. We extend the known analysis of the model to the global in time case by proving it is globally well-posed, and also prove some new results for its long time treatment of energy. We also derive PDE system that describes the sensitivity of the model with respect to the filtering radius parameter, and prove it is well-posed. An efficient numerical scheme for the sensitivity system is then proposed and analyzed, and proven to be stable and optimally accurate. Finally, two physically meaningful test problems are simulated: channel flow past a cylinder (including lift and drag calculations) and turbulent channel flow with $${Re_{\tau}=590}$$ . The numerical results reveal that sensitivity is created near boundaries, and thus this is where the choice of the filtering radius is most critical.