Rational Large Eddy Simulation Model Research Articles

The equivalence of the Lagrangian-averaged Navier-Stokes-α model and the rational large eddy simulation model in two dimensions

In the large eddy simulation (LES) framework for modeling a turbulent flow, when the large scale velocity field is defined by low-pass filtering the full velocity field, a Taylor series expansion of the full velocity field in terms of the large scale velocity field leads (at the leading order) to the nonlinear gradient model for the subfilter stresses. Motivated by the fact that while the nonlinear gradient model shows excellent a priori agreement in resolved simulations, the use of this model by itself is problematic, we consider two models that are related, but better behaved. The rational LES model that uses a sub-diagonal Pade approximation instead of a Taylor series expansion, and the Lagrangian averaged Navier-Stokes-α model that uses a regularization approach to modeling turbulence. In this article, we show that these two latter models are identical in two dimensions.

Regularity criteria for the rational large eddy simulation model

We consider the Rational Large Eddy Simulation (RLES) model introduced by Galdi and Layton (Math. Models Methods Appl. Sci. 10 (2000) 343-350). Various regularity criteria for the strong solution of this model are established here, which improve previous ones.

Finite element LES and VMS methods on tetrahedral meshes

Finite element methods for problems given in complex domains are often based on tetrahedral meshes. This paper demonstrates that the so-called rational Large Eddy Simulation model and a projection-based Variational Multiscale method can be extended in a straightforward way to tetrahedral meshes. Numerical studies are performed with an inf–sup stable second order pair of finite elements with discontinuous pressure approximation.

Analytical and Numerical Results for the Rational Large Eddy Simulation Model

In this paper we analyze the Rational Large Eddy Simulation model. We start by introducing the system of partial differential equations we shall consider, together with its derivation. Then, we prove a result of full regularity for strong solutions in the space periodic setting. We also construct some exact solutions useful for the numerical benchmarking and finally we provide the results of some numerical experiments we performed.

On the consistency of the Rational Large Eddy Simulation model

In this paper we consider the Rational Large Eddy Simulation model for turbulent flows (RLES in the sequel), introduced by Galdi and Layton [11]. We recall some analytical results regarding the RLES model and the main result we will prove is the convergence of the strong solutions to the RLES model to those of the Navier–Stokes (in some Sobolev spaces), as the averaging radius goes to zero. Estimates on the rates of convergence are also obtained. These results give more weight to the validity of the method in either computational or physical experiments.We also consider the error arising from the derivation of the model in presence of boundaries. In particular, the equations present an extra-term involving the boundary value of the stress tensor. By using some recent estimates on this “commutation error” we show that, with a Smagorinsky sub-grid scale term, the kinetic energy remains bounded.

On the consistency of the Rational Large Eddy Simulation model

On the consistency of the Rational Large Eddy Simulation model

Backscatter in the rational LES model

This paper presents a comparison for the backscatter (the inverse transfer of energy from small to large scales) in the rational and the gradient large eddy simulation (LES) models. We applied both LES models in the numerical simulation of turbulent channel flows at Re τ =180 and 395. The rational LES model yielded improved results and was more stable numerically.

Erratum: “The angular momentum equation for a finite element of a fluid: A new representation and application to turbulent modeling” [Phys. Fluids 14, 2673 (2002)

Abstract

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

The rational large eddy simulation (RLES) model is applied to turbulent channel flows. This approximate deconvolution model is based on a rational (subdiagonal Padé) approximation of the Fourier transform of the Gaussian filter and is proposed as an alternative to the gradient (also known as the nonlinear or tensor-diffusivity) model. We used a spectral element code to perform large eddy simulations of incompressible channel flows at Reynolds numbers based on the friction velocity and the channel half-width Reτ=180 and Reτ=395. We compared the RLES model with the gradient model and the Smagorinsky model with Van Driest damping. The RLES model was much more stable than the gradient model and yielded improved results. Both the RLES model and the gradient model predicted the off-diagonal Reynolds stresses better than the Smagorinsky model with Van Driest damping. The latter, however, yielded better results for the diagonal Reynolds stresses.

MATHEMATICAL ANALYSIS FOR THE RATIONAL LARGE EDDY SIMULATION MODEL

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.