Abstract
AbstractWe put forth a dynamic closure modeling framework for the large eddy simulations of the Burgers equation based upon the use of the approximate deconvolution (AD) procedure to compute the Smagorinsky constant self-adaptively from the resolved flow quantities. In our proposed framework, the test filtering process of the standard dynamic model is replaced by the AD procedure. The robustness of the model has been tested considering the Burgers equation in its conservative and skew-symmetric forms. Our numerical assessments for solving the single-mode sine wave and the decaying Burgers turbulence problems show that the present framework effectively damps grid-to-grid oscillations and yields an improved shock capturing property for central numerical schemes as underlying discretizations.
Highlights
Turbulent flows are encountered in a variety of engineering and geophysical systems involving a wide range of spatial and temporal scales
We put forth a dynamic closure modeling framework for the large eddy simulations of the Burgers equation based upon the use of the approximate deconvolution (AD) procedure to compute the Smagorinsky constant self-adaptively from the resolved flow quantities
Results we present our results for two test cases: (i) the shock formation problem initiated by a single-mode sine wave, u(x, 0) = sin(x), and (ii) the decaying Burgers turbulence problem initiated by a specified energy spectrum considering the 64 sample initial conditions associated with randomly generated phases
Summary
Turbulent flows are encountered in a variety of engineering and geophysical systems involving a wide range of spatial and temporal scales. The approach presented here is fundamentally different from the mixed methods where the AD model is coupled with the eddy viscosity models by adding a dynamically computed source term to increase the stability of the AD model (Gullbrand & Chow 2003; Habisreutinger, Bouffanais, Leriche, & Deville 2003), and it is different from the dynamic mixed scale-similarity models (Bouffanais, Deville, & Leriche, 2007; Sarghini, Piomelli, & Balaras, 1999; Zang, Street, & Koseff, 1993) In this framework, the test filtering process of the standard dynamic model is replaced by the AD procedure, and it is shown that the order of accuracy increases by increasing the number of the Van Cittert iterations (i.e. damping grid-to-grid oscillations more effectively). We note that ũdenotes the filtered velocity field on the coarse numerical grid (i.e. LES numerical resolution) which is readily available from the LES computations
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