Modeling and discretization errors in large eddy simulations of hydrodynamic and magnetohydrodynamic channel flows (original) (raw)
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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.
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.
Investigating an advective approach to subgrid modeling in large-eddy simulations
Computers & Fluids, 2010
The purpose of this paper is to investigate and validate an alternative subgrid model to be used in largeeddy simulations, based on an advective formulation. Rather than modeling the subgrid tensor that appears in the LES formulation as is commonly done, the subgrid force vector, which is the divergence of the subgrid tensor, is modeled directly. It is designed to comply with two basic principles. First, it is required to act only on the smallest scales that the mesh can represent. Second, it must be of an advective nature, which means it must have a preferred direction aligned with the fluid velocity. The results for two benchmark test cases, including Homogeneous Isotropic Turbulence and Turbulent Channel Flow, show that this approach can successfully represent the effect of the small scales on the resolved ones, while guaranteeing numerical stability and greater robustness in adverse mesh environments, when compared to some traditional eddy-viscosity based models, such as the Smagorinsky and the dynamic model from Germano.
Is plane-channel flow a friendly case for the testing of large-eddy simulation subgrid-scale models?
2007
We present the grid-convergence behavior of channel-flow direct numerical simulations ͑DNS͒ at coarse resolutions typically encountered in large-eddy simulation subgrid-model testing. An energy-conservative discretization method is used to systematically vary the streamwise ͑N x ͒ and spanwise ͑N z ͒ resolution. We observe that the skin friction does not converge monotonously, and at coarse resolutions, a line of N x-N z combinations is found where the error on the skinfriction is zero. Along this line, mean profiles are evaluated and found to fit surprisingly well fully resolved DNS results. The location of this line is shown to depend on the Reynolds number and the wall-normal resolution.
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, ...
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 dynamic subgrid-scale eddy viscosity model
Physics of Fluids A: Fluid Dynamics, 1991
One major drawback of the eddy viscosity subgrid-scale stress models used in large-eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input apriori. The model is based on an algebraic identity between the subgrid-scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid-scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near-wall region of a turbulent boundary layer. The results of large-eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.
On the Effect of Numerical Errors in Large Eddy Simulations of Turbulent Flows
Journal of Computational Physics, 1997
Aliased and dealiased numerical simulations of a turbulent channel flow are performed using spectral and finite difference methods. The problem of aliasing errors in spectral simulations Analytical and numerical studies show that aliasing errors are more of turbulent flows has been discussed in the literature [4-7]. destructive for spectral and high-order finite-difference calculations It has been demonstrated that, depending on the form of than for low-order finite-difference simulations. Numerical errors the nonlinear terms [5] in the Navier-Stokes equations, have different effects for different forms of the nonlinear terms in aliased spectral simulations can become unstable, exhibit the Navier-Stokes equations. For divergence and convective forms, spectral methods are energy-conserving only if dealiasing is per-decay, or give reasonable results. Zang [5] performed sevformed. For skew-symmetric and rotational forms, both spectral eral spectral simulations of transition and turbulence in and finite-difference methods are energy-conserving even in the incompressible flow and reported that, without dealiasing, presence of aliasing errors. It is shown that discrepancies between the simulations with convective and divergence forms of the results of dealiased spectral and standard nondialiased finitethe nonlinear terms were numerically unstable, whereas difference methods are due to both aliasing and truncation errors with the latter being the leading source of differences. The relative the computations with the rotational form produced inacimportance of aliasing and truncation errors as compared to subgrid curate results. The aliasing errors associated with the rotascale model terms in large eddy simulations is analyzed and distional form were reported to be even more damaging in cussed. For low-order finite-difference simulations, truncation ersimulations of transition. The poor behavior of the rotarors can exceed the magnitude of the subgrid scale term. ᮊ 1997 tional form was also reported earlier by Horiuti [8] who Academic Press carried out large eddy simulations of turbulent channel flow. No dealiasing was performed in that study. Horiuti found that turbulence decayed when the rotational form 310