Large Eddy Simulation for turbulent flows with critical regularization

Abstract

In this paper, we establish the existence of a unique "regular" weak solution to the Large Eddy Simulation (LES) models of turbulence with critical regularization. We first consider the critical LES for the Navier-Stokes equations and we show that its solution converges to a solution of the Navier-Stokes equations as the averaging radii converge to zero. Then we extend the study to the critical LES for Magnetohydrodynamics equations. MSC: 35Q30, 35Q35, 76F60

Approximate deconvolution model in a bounded domain with vertical regularization

“…For this reason one can replace the classical Laplace operator by the Laplace operator with fractional regularization θ and seek for the limiting case where we can prove global existence and uniqueness of regular solutions. In a series of papers [10,4,1,2], it was shown that the LES models which are derived by using instead of the operator (1.1), the operator A θ = I + α 2θ (−∆) θ for suitable (large enough) θ < 1, are still well-posed. In this paper, we consider LES models with fractional filter acting only in one variable…”

Theory for the rotational deconvolution model of turbulence with fractional regularization

“…Proof of Theorem 4.1. The proof of Theorem 4.1 follows the lines of the proof of the Theorem 4.1 in [5], that we have to modify in order to treat the cases when θ ≤ 3 4 . Thus we will use [5] as a reference and only point out the differences between their proof of convergence to the mean Navier-Stokes equations and the proof of convergence in the present study.…”

“…For θ > 3 4 , Berselli and Lewandowski [5] showed the convergence of the ADM solution, with fractional regularization, to a solution of the average Navier-Stokes Equations when N goes to infinity. The existence and the uniqueness of a solution to this model in the case N = 0 and θ ≥ 1 6 are studied in [3].…”