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The Large Eddy Simulation technique is enjoying widespread success in the engineering analysis as a result of the recent advances in computer performance. Initially limited to the simulation of turbulent flows in simple geometries, current LES tools are being applied to multidisciplinary problems involving a variety of physical processes. Several examples of recent advances in LES methodology and complex multi-physics applications are presented.

Subgrid-scale models in LES operate on a range of scales which is marginally resolved by the discrete approximation. Accordingly, the discrete approximation method and the subgrid-scale model are linked. One can exploit this link by developing discretization methods from subgrid-scale models, or vice versa. Approaches where SGS models and numerical discretizations are fully linked are called implicit SGS models. Different approaches to SGS modeling can be taken. Mostly, given nonlinearly stable discretizations schemes for the convective fluxes are used as main element of implicit SGS models. Recently we have proposed to design nonlinear discretization schemes in such a way that their truncation error functions as SGS model in regions where the flow is turbulent and as a second-order accurate discretization in regions where the flow is laminar. In this paper we review the current status on this so-called adaptive local deconvolution method (ALDM) and provide some application results.

The mathematical framework for a-posteriori error estimation of functionals elucidated by Eriksson et al. [1] and Becker and Rannacher [2] is revisited in a space-time context. Using these theories, a hierarchy of exact and approximate error representation formulas are presented for use in error estimation and mesh adaptivity. Numerical space-time results for simple model problems as well as compressible Navier-Stokes flow at = 300 over a 2D circular cylinder are then presented to demonstrate elements of the error representation theory for time-dependent problems.

We present novel multiresolution particle methods with extended dynamic adaptivity in areas where increased resolution is required. The inherent Lagrangian adaptivity of smooth particle methods is complemented by adaptation of the particle size based on criteria such as flow strain and wavelet-based decomposition. In this context we present two particle multiresolution techniques: one based on globally adaptive mappings and one employing a wavelet-based multiresolution analysis of the transported quantities to guide the allocation of computational elements. Results are presented from the application of these methods to level sets and two-dimensional vortical flows.

In this paper, the turbulent cascade with intermittency is presented in the framework of universalities of eddy fragmentation under scaling symmetry. Based on these universalities, the stochastic estimation of the velocity increment at sub-grid scales is introduced in order to simulate the response of light solid particle to inhomogeneity of the flow at small spatial scales. The LES of stationary box turbulence was performed, and the computed Lagrangian statistics of tracking particle was compared with measurements. The main effects from recent experimental study of high Reynolds number stationary turbulence are reproduced by computation. For the velocity statistics, the numerical results were in agreement with classical Kolmogorov 1941 phenomenology. However the distribution of velocity increment, computed at different time lag, revealed the strong intermittency: at time lag of order of integral time scale, the velocity increment was distributed as Gaussian, at small time lags this distribution exhibited the long stretched tails.

Rotating homogeneous turbulence is known to exhibit strongly anisotropic features at low Rossby number, as well as a modified dynamics. These are the result of the presence of inertial waves due to the Coriolis force. The spectral distribution of kinetic energy in spectral space also reflects this strong anisotropy through a dependence of the energy on the wavevector orientation at almost all wavenumbers. Up to now, subgrid scale models for large eddy simulation are not adapted to describing strongly anisotropic dissipative scales, therefore we introduce a means of deriving an eddy viscosity from the orientation-dependent structure function equation. Only at the end of the derivation of a first version, the model is simplified by neglecting directional anisotropy in the final eddy viscosity, in a first stage for assessing the method. In order to illustrate qualitatively the relevance of the approach, and to prepare improved anisotropic subgrid-scale modelling, we compare the results of high Reynolds number large eddy simulations based on this model to energy density spectra obtained at lower Reynolds number by direct numerical simulations, and to spectra obtained by a recent two-point statistical model. The subgrid-scale model is shown to perform well, all the more when looking at the reduction of interscale energy transfer due to rotation, quantified here by the dependence of the velocity derivatives skewness on the micro-Rossby number.

An anisotropic subgrid-scale model with five terms depending on strain and rotation rate is investigated. Single terms and the combinations of two of the five terms are tested in a turbulent channel flow at a turbulent Reynolds number of τ = 395. The model constants, one for each term, are determined dynamically. Some double term models showed significant improvement compared to the dynamic Smagorinsky model. Determination of two coupled dynamic constants reduces the stochastic behaviour of the constants, which may preserve local stability and no averaging is needed.

This paper: (i) discusses an algorithm that addresses the problems posed by low Mach numbers and high Reynolds numbers in large-eddy simulation of compressible turbulent flows, (ii) uses numerical solutions of the RDT equations to suggest the possibility that the linear effects of pressure might be more important to model in the near-wall problem, than nonlinear transfer, and (iii) a simple kinematic model that possibly explains why large-eddy simulation predicts turbulent mixing accurately, even though the viscous processes are not being represented.

In this paper, a possible solution to the long-standing problem of nearwall modeling in Large-Eddy Simulation (LES) is presented. It is observed that in an LES, in which resolution is finite, it is inconsistent to locate the wall with precision. Instead we propose filtering through the wall using homogeneous or nearly homogeneous filters, effectively smearing it. The resulting filtered equations then have an explicit wall term, which is modeled using a novel optimization technique. To test the validity of this approach, simulations were done with optimal LES models for the subgrid stress term which were derived from DNS statistical data, with very good results. The properties of subgrid models that appear to be important for this application are discussed.

A near-wall eddy-viscosity formulation for LES is presented. This formulation consists of imposing a RANS eddy-viscosity dynamically corrected with the resolved turbulent stress in the near-wall region. The RANS eddy-viscosity is obtained from an averaged velocity profile of a resolved LES of channel flow at τ = 395 and stored in a look-up table. Results are presented for channel flow at τ = 395 with no-slip boundary conditions, and up to τ = 1, 000, 000 using a wall model.