Physical consistency of subgrid-scale models for large-eddy simulation of incompressible turbulent flows

Silvis, Maurits H.; Remmerswaal, Ronald A.; Verstappen, Roel

doi:10.1063/1.4974093

Cited by 59 publications

(72 citation statements)

References 58 publications

(194 reference statements)

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“…Examples thereof are the WALE model [21], Vreman's model [42], the QR model [40] and the σ-model [22]. This list can be completed with a novel eddy-viscosity model proposed by Ryu and Iaccarino [25] and two eddy-viscosity models recently proposed by the authors of this paper: namely, the S3PQR models [38] and the vortex-stretching-based eddy-viscosity model [30].…”

Section: Introductionmentioning

confidence: 99%

A new subgrid characteristic length for turbulence simulations on anisotropic grids

et al. 2017

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Direct numerical simulations of the incompressible Navier-Stokes equations are not feasible yet for most practical turbulent flows. Therefore, dynamically less complex mathematical formulations are necessary for coarse-grained simulations. In this regard, eddy-viscosity models for Large-Eddy Simulation (LES) are probably the most popular example thereof. This type of models requires the calculation of a subgrid characteristic length which is usually associated with the local grid size. For isotropic grids this is equal to the mesh step. However, for anisotropic or unstructured grids, such as the pancake-like meshes that are often used to resolve near-wall turbulence or shear layers, a consensus on defining the subgrid characteristic length has not been reached yet despite the fact that it can strongly affect the performance of LES models. In this context, a new definition of the subgrid characteristic length is presented in this work. This flow-dependent length scale is based on the turbulent, or subgrid stress, tensor and its representations on different grids. The simplicity and mathematical properties suggest that it can be a robust definition that minimizes the effects of mesh anisotropies on simulation results. The performance of the proposed subgrid characteristic length is successfully tested for decaying isotropic turbulence and a turbulent channel flow using artificially refined grids. Finally, a simple extension of the method for unstructured meshes is proposed and tested for a turbulent flow around a square cylinder. Comparisons with existing subgrid characteristic length scales show that the proposed definition is much more robust with respect to mesh anisotropies and has a great potential to be used in complex geometries where highly skewed (unstructured) meshes are present. *

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Section: Introductionmentioning

confidence: 99%

A new subgrid characteristic length for turbulence simulations on anisotropic grids

et al. 2017

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“…Secondly, we impose the desired near-wall scaling of ν e " Opx 3 i q for a wall-normal coordinate x i (Silvis and Verstappen n.d.). We so obtain the definition of the eddy viscosity given by (Silvis et al 2017b;Silvis and Verstappen 2018)…”

Section: Defining the Model Coefficientsmentioning

confidence: 99%

“…We require that the average subgrid dissipation due to the eddy viscosity term matches the average dissipation of the Smagorinsky model in (nonrotating) homogeneous isotropic turbulence (Nicoud and Ducros 1999;Nicoud et al 2011;Trias et al 2015). We estimate the average subgrid dissipation of the eddy viscosity term and the Smagorinsky model using a large number of synthetic velocity gradients, given by traceless random matrices (Nicoud et al 2011;Trias et al 2015) sampled from a uniform distribution (Silvis et al 2017b). We then equate the two averages to obtain an estimate of the model constant C ν .…”

Section: Implementing the New Sgs Modelmentioning

confidence: 99%

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Nonlinear Subgrid-Scale Models for Large-Eddy Simulation of Rotating Turbulent Flows

Silvis

Verstappen

2019

Direct and Large-Eddy Simulation XI

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Rotating turbulent flows form a challenging test case for large-eddy simulation (LES). We, therefore, propose and validate a new subgrid-scale (SGS) model for such flows. The proposed SGS model consists of a dissipative eddy viscosity term as well as a nondissipative term that is nonlinear in the rate-of-strain and rate-of-rotation tensors. The two corresponding model coefficients are a function of the vortex stretching magnitude. Therefore, the model is consistent with many physical and mathematical properties of the Navier-Stokes equations and turbulent stresses, and is easy to implement. We determine the two model constants using a nondynamic procedure that takes into account the interaction between the model terms. Using detailed direct numerical simulations (DNSs) and LESs of rotating decaying turbulence and spanwise-rotating plane-channel flow, we reveal that the two model terms respectively account for dissipation and backscatter of energy, and that the nonlinear term improves predictions of the Reynolds stress anisotropy near solid walls. We also show that the new SGS model provides good predictions of rotating decaying turbulence and leads to outstanding predictions of spanwise-rotating plane-channel flow over a large range of rotation rates for both fine and coarse grid resolutions. Moreover, the new nonlinear model performs as well as the dynamic Smagorinsky and scaled anisotropic minimum-dissipation models in LESs of rotating decaying turbulence and outperforms these models in LESs of spanwise-rotating plane-channel flow, without requiring (dynamic) adaptation or near-wall damping of the model constants.

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“…A further extension could be to include non-dissipative terms in the AMD model, e.g. related to the skew-symmetric part of the velocity gradient, while staying consistent with the exact sub-filter tensor [78,79].…”

Section: Low-dissipation Large-eddy Simulation Modelsmentioning

confidence: 99%

Low-Dissipation Simulation Methods and Models for Turbulent Subsonic Flow

Rozema

Verstappen

Veldman

et al. 2018

Arch Computat Methods Eng

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The simulation of turbulent flows by means of computational fluid dynamics is highly challenging. The costs of an accurate direct numerical simulation (DNS) are usually too high, and engineers typically resort to cheaper coarse-grained models of the flow, such as large-eddy simulation (LES). To be suitable for the computation of turbulence, methods should not numerically dissipate the turbulent flow structures. Therefore, energy-conserving discretizations are investigated, which do not dissipate energy and are inherently stable because the discrete convective terms cannot spuriously generate kinetic energy. They have been known for incompressible flow, but the development of such methods for compressible flow is more recent. This paper will focus on the latter: LES and DNS for turbulent subsonic flow. A new theoretical framework for the analysis of energy conservation in compressible flow is proposed, in a mathematical notation of square-root variables, inner products, and differential operator symmetries. As a result, the discrete equations exactly conserve not only the primary variables (mass, momentum and energy), but also the convective terms preserve (secondary) discrete kinetic and internal energy. Numerical experiments confirm that simulations are stable without the addition of artificial dissipation. Next, minimum-dissipation eddyviscosity models are reviewed, which try to minimize the dissipation needed for preventing sub-grid scales from polluting the numerical solution. A new model suitable for anisotropic grids is proposed: the anisotropic minimum-dissipation model. This model appropriately switches off for laminar and transitional flow, and is consistent with the exact sub-filter tensor on anisotropic grids. The methods and models are first assessed on several academic test cases: channel flow, homogeneous decaying turbulence and the temporal mixing layer. As a practical application, accurate simulations of the transitional flow over a delta wing have been performed. The Compressible Navier-Stokes Equations Primary ConservationOur objective is the development of simulation methods for aerodynamic flow, governed by the Navier-Stokes equations for compressible flow [21]:

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Physical consistency of subgrid-scale models for large-eddy simulation of incompressible turbulent flows

Cited by 59 publications

References 58 publications

A new subgrid characteristic length for turbulence simulations on anisotropic grids

A new subgrid characteristic length for turbulence simulations on anisotropic grids

Nonlinear Subgrid-Scale Models for Large-Eddy Simulation of Rotating Turbulent Flows

Low-Dissipation Simulation Methods and Models for Turbulent Subsonic Flow

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