Building proper invariants for eddy-viscosity subgrid-scale models

Trias, F. X.; Folch, David C.; Gorobets, A.; Oliva, A.

doi:10.1063/1.4921817

Cited by 73 publications

(84 citation statements)

References 44 publications

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“…Figure 5 shows the results obtained from numerical simulations of a turbulent channel flow at Re τ " 395 for a set of (artificially) refined grids. The results are compared with the DNS data of Figure 5: Results for a turbulent channel flow at Re τ " 395 obtained with a set of anisotropic meshes using the S3PQ model [38]. Solid lines correspond to the direct numerical simulation of Moser et al [20].…”

Section: Turbulent Channel Flowmentioning

confidence: 99%

“…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%

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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: Turbulent Channel Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A new subgrid characteristic length for turbulence simulations on anisotropic grids

et al. 2017

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“…where the model constants, C s3xx , can be related with the Vreman's constant, C V r , with the following inequality (see details in [6]) [7] 0…”

Section: Building New Proper Invariants For Les Modelsmentioning

confidence: 99%

Building Proper Invariants for Eddy-Viscosity Models

Trias

Gorobets

Oliva

2016

Springer Proceedings in Physics

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Direct numerical simulations of the incompressible Navier-Stokes equations are limited to relatively low-Reynolds numbers. Therefore, dynamically less complex mathematical formulations are necessary for coarse-grain simulations. Regularization and eddy-viscosity models for LES are examples thereof. They rely on differential operators that should capture well different flow configurations (laminar and 2D flows, near-wall behavior, transitional regime …). Most of them are based on the combination of invariants of a symmetric second-order tensor that is derived from the gradient of the resolved velocity field. In the present work, they are presented in a framework where the models are represented as a combination of elements of a 5D phase space of invariants. In this way, new models can be constructed by imposing appropriate restrictions in this space. Theory: A 5D Phase Space for Eddy-Viscosity ModelsThe essence of turbulence are the smallest scales of motion. They result from a subtle balance between convective transport and diffusive dissipation. Numerically, if the grid is not fine enough, this balance needs to be restored by a turbulence model. The success of a turbulence model depends on the ability to capture well this (im)balance. In this regard, many eddy-viscosity models for LES have been proposed in the last decades. In order to be frame invariant, most of them rely on differential operators that are based on the combination of invariants of a symmetric second-order tensor (with the proper scaling factors). To make them locally dependent such tensors are derived from the gradient of the resolved velocity field, G ≡ ∇u. This is a second-order

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“…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%

“…The Smagorinsky model (Smagorinsky 1963) and its dynamic variant (Germano et al 1991;Lilly 1992) are, without a doubt, the most well-known eddy viscosity models. Examples of other, more recently developed eddy viscosity models are the WALE model (Nicoud and Ducros 1999), Vreman's model (Vreman 2004), the σ model (Nicoud et al 2011), the QR model (Verstappen et al 2010;Verstappen 2011;Verstappen et al 2014), the S3PQR models (Trias et al 2015), the anisotropic minimum-dissipation model (Rozema et al 2015), the scaled anisotropic minimum-dissipation model (Verstappen 2018) and the vortex-stretching-based eddy viscosity model (Silvis et al 2017b;Silvis and Verstappen 2018).…”

Section: Introductionmentioning

confidence: 99%

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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Building proper invariants for eddy-viscosity subgrid-scale models

Cited by 73 publications

References 44 publications

A new subgrid characteristic length for turbulence simulations on anisotropic grids

A new subgrid characteristic length for turbulence simulations on anisotropic grids

Building Proper Invariants for Eddy-Viscosity Models

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

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