Investigating an advective approach to subgrid modeling in large-eddy simulations (original) (raw)
Related papers
Large-eddy simulations with explicit equations for subgrid-scale quantities
Proceedings of Summer Program, 2002
Various alternative formulations of the LES equations have been explored in which additional evolution equations for variables such as the acceleration, the subgrid-scale stress tensor, or the subgrid-scale force are explicitly carried. Statistics of the velocity field obtained from the equation for the acceleration are shown to depend strongly on the initial conditions. This feature, which is independent of LES modeling issues, seems to prove that the velocity-acceleration formulation of the Navier-Stokes is not useful for numerical simulation. Equations for the subgrid-scale quantities appear to be much more stable. However, models required by this formulation of the LES problem still require additional study.
Physics of Fluids
We study the construction of subgrid-scale models for large-eddy simulation of incompressible turbulent flows. In particular, we aim to consolidate a systematic approach of constructing subgrid-scale models, based on the idea that it is desirable that subgrid-scale models are consistent with the mathematical and physical properties of the Navier-Stokes equations and the turbulent stresses. To that end, we first discuss in detail the symmetries of the Navier-Stokes equations, and the near-wall scaling behavior, realizability and dissipation properties of the turbulent stresses. We furthermore summarize the requirements that subgrid-scale models have to satisfy in order to preserve these important mathematical and physical properties. In this fashion, a framework of model constraints arises that we apply to analyze the behavior of a number of existing subgrid-scale models that are based on the local velocity gradient. We show that these subgrid-scale models do not satisfy all the desired properties, after which we explain that this is partly due to incompatibilities between model constraints and limitations of velocity-gradient-based subgrid-scale models. However, we also reason that the current framework shows that there is room for improvement in the properties and, hence, the behavior of existing subgrid-scale models. We furthermore show how compatible model constraints can be combined to construct new subgrid-scale models that have desirable properties built into them. We provide a few examples of such new models, of which a new model of eddy viscosity type, that is based on the vortex stretching magnitude, is successfully tested in large-eddy simulations of decaying homogeneous isotropic turbulence and turbulent plane-channel flow.
Subgrid-scale modeling for large-eddy simulations of compressible turbulence
Physics of Fluids, 2002
We present two phenomenological subgrid-scale ͑SGS͒ models for large-eddy simulations ͑LES͒ of compressible turbulent flows. A nonlinear model and a stretched-vortex model are tested in LES of compressible decaying isotropic turbulence. Results of LES at 32 3 , 48 3 , and 64 3 resolution are compared to corresponding 256 3 direct numerical simulations ͑DNS͒ at a turbulent Mach number, M t ϳ0.4. We use numerical schemes based on compact finite differences and study the effects of their order of accuracy on LES results. Both models give satisfactory agreement with DNS for the decay of the total turbulent kinetic energy. The probability densities ͑pdf͒ of energy transfer to subgrid scales obtained from filtered DNS and the SGS models are compared. Both models produce a narrower distribution of energy transfer than corresponding filtered DNS data, with less backscatter. The pdf of the alignment of components of the subgrid stress tensor and the eigenvectors of the rate-of-strain tensor obtained from the models reproduces some features of the DNS results. The pdfs of both energy transfer and relative eigenvector alignment are obtained from DNS and LES after about one large-eddy turnover time from the same initial condition. All tests of the present LES models are therefore a posteriori and none is a priori.
2006
We present subgrid closures for large-eddy Simulation (LES) likely to be implemented in stabilized finite element methods. Selection criterion, dynamic procedure and multiscale approach are compared within simulations of freely decaying isotropic turbulence. In all cases, the numerical dissipation coming from the least-squares stabilization dominates the subgrid model. Despite this large numerical dissipation, the LES model, whichever it is, provides a sufficient physical dissipation to have a clear and major effect on the results. In particular the dynamic procedures and the multiscale models turn out to be very efficient, highlighting a self-adaptive behaviour of the turbulent viscosity and consequently predict the correct energy transfer mechanisms, by accounting for the numerical part of the total dissipation.
Implicit Subgrid-Scale Modeling for the Large-Eddy Simulation of Compressible Turbulence
2009
The objective of this paper is the analysis and the control of local truncation errors in Large Eddy Simulations. We show that physical reasoning can be incorporated into the design of discretization schemes. Using systematic procedures, a nonlinear discretization method is developed where numerical and turbulence-theoretical modeling are fully merged. The truncation error itself functions as an implicit turbulence model which accurately represents the effects of unresolved turbulence.
A Tensor-Diffusivity Subgrid Model for Large-Eddy Simulation
ERCOFTAC Series, 1999
Subgrid-scale models for large-eddy simulation that are based on exact series expansions for ltered products are considered. In particular, if the rst two terms are retained, the result is a di usive subgrid term with a tensor di usivity. T h i s tensor is proportional to the rate-of-strain tensor of the large-scale velocity eld. This leads to negative di usion in the stretching directions. Implications of this result are considered for the ltered scalar advection-di usion equation and for the momentum equation for incompressible uid ow. When coupled with a dynamic Smagorinsky term to form a mixed model, very encouraging results are shown for turbulent, isotropic decay and for turbulent c hannel ow. In addition, it is shown that the model, mixed or not, transforms appropriately when di ering frames of reference are considered. Modi cations to the model are suggested for the case in which the un ltered eld(s) has discontinuities.
Testing of subgrid scale (SGS) models for large-eddy simulation (LES) of turbulent channel flow
2015
Sub-grid scale (SGS) models are required in order to model the influence of the unresolved small scales on the resolved scales in large-eddy simulations (LES), the flow at the smallest scales of turbulence. In the following work two SGS models are presented and deeply analyzed in terms of accuracy through several LESs with different spatial resolutions, i.e. grid spacings. The first part of this thesis focuses on the basic theory of turbulence, the governing equations of fluid dynamics and their adaptation to LES. Furthermore, two important SGS models are presented: one is the Dynamic eddy-viscosity model (DEVM), developed by \cite{germano1991dynamic}, while the other is the Explicit Algebraic SGS model (EASSM), by \cite{marstorp2009explicit}. In addition, some details about the implementation of the EASSM in a Pseudo-Spectral Navier-Stokes code \cite{chevalier2007simson} are presented. The performance of the two aforementioned models will be investigated in the following chapters, ...
On discretization errors and subgrid scale model implementations in large eddy simulations
Journal of Computational Physics, 2009
We analyze the impact of discretization errors on the performance of the Smagorinsky model in large eddy simulations (LES). To avoid difficulties related to solid boundaries, we focus on decaying homogeneous turbulence. It is shown that two numerical implementations of the model in the same finite volume code lead to significantly different results in terms of kinetic energy decay, time evolutions of the viscous dissipation and kinetic energy spectra. In comparison with spectral LES results, excellent predictions are however obtained with a novel formulation of the model derived from the discrete Navier-Stokes equations. We also highlight the effect of discretization errors on the measurement of physical quantities that involve scales close to the grid resolution.