Generalized Deconvolution Procedure for Structural Modeling of Turbulence

Approximate deconvolution forms a mathematical framework for the structural modeling of turbulence. The sub-filter scale flow quantities are typically recovered by using the Van Cittert iterative procedure. In this paper, however, we put forth a generalized approach for the iterative deconvolution process of sub-filter scale recovery of turbulent flows by introducing Krylov space iterative methods. Their accuracy and efficiency are demonstrated through a systematic a-priori analysis of solving the Kraichnan and Kolmogorov homogeneous isotropic turbulence problems in two- and three-dimensional domains, respectively. Our numerical assessments show that the conjugate gradient based iterative techniques lead to significantly improved performance over the Van Cittert procedure and offer great promise for approximate deconvolution turbulence models. In fact, our energy spectra analysis illustrates that a substantially longer inertial range can be recovered by using the proposed procedure equipped with the BiCGSTAB iterative scheme. This trend is also confirmed by capturing tails of the probability density function of turbulent flow quantities.