Mathematical Analysis for the Rational Large Eddy Simulation Model

Abstract

In this paper we consider the Rational Large Eddy Simulation model recently introduced by Galdi and Layton. We briefly present this model, which (in principle) is similar to others commonly used, and we prove the existence and uniqueness of a class of strong solutions. Contrary to the gradient model, the main feature of this model is that it allows a better control of the kinetic energy. Consequently, to prove existence of strong solutions, we do not need subgrid-scale regularization operators, as proposed by Smagorinsky. We also introduce some breakdown criteria that are related to the Euler and Navier-Stokes equations.

Horizontal Approximate Deconvolution for Stratified Flows: Analysis and Computations

“…Results in [4,1] show that the term ∇ · (I − α 2 2 ∆) −1 α 2 ∇w∇w T plays the same role (in terms of Sobolev spaces inequalities) of the convective term. This prevents from proving global-in-time estimates.…”

“…It is well-known that instabilities occur in the numerical implementation and that some kind of smoothing must be added in order to have effective simulations, see [17]. In particular, a filtered version of the Gradient method is called Rational or 4 Clark-α method, and the stress-tensor reads as…”

“…The Rational method has been derived [16] by a rational approximation of wave-numbers, while the Clark-α method is based on analogies with the Helmholtz filtering. The mathematical analysis of these models can be found in [8,4]. Following the approach described in the introduction we consider a smoothing acting only in the horizontal variables, which can be performed by means of convolution with the following kernel:…”

“…The proof is obtained by direct integration by parts (cf. [8,4]). In fact, as usual D (w · ∇)w · w dx = 0 and next, observe that…”

Large eddy simulation of turbulent channel flows by the rational large eddy simulation model

“…35 The mathematical analysis associated with the RLES model ͑12͒ was presented in Ref. 36. The first steps in the numerical analysis and validation of the RLES model ͑12͒ were made in Refs.…”