Constructing Physically Consistent Subgrid-Scale Models for Large-Eddy Simulation of Incompressible Turbulent Flows

Silvis, Maurits H.; Verstappen, Roel

doi:10.1007/978-3-319-60387-2_26

Cited by 2 publications

(8 citation statements)

References 25 publications

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“…Secondly, we will assume that the transport terms in Eq. (38) can be neglected. Any body forces involving second derivatives of the velocity field are furthermore rewritten in terms of first derivatives using a Rayleigh quotient.…”

Section: Discussion Of the Production Of Subgrid-scale Kinetic Energymentioning

confidence: 99%

“…In view of the requirements of Nicoud et al (P2a, P2b), a possibly attractive quantity to base an eddy viscosity model on is the nonnegative quantity 4pI 5´1 2 I 1 I 2 q " 4ptrpS 2 Ω 2 q´1 2 trpS 2 q trpΩ 2 qq [38,39]. This quantity equals the (squared) magnitude of the vortex stretching, S ij ω j [45], where the components of the vorticity vector are related to the rate-of-rotation tensor via ω i "´ ijk Ω jk and ijk again represents the Levi-Civita symbol.…”

Section: Derivation and Propertiesmentioning

confidence: 99%

“…Summary of the size of the flow algebra of the true subgrid dissipation D τ , Eq. (33), and of several quantities based on the tensor invariants of Eq (39)…”

mentioning

confidence: 99%

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

2017

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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.

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Section: Discussion Of the Production Of Subgrid-scale Kinetic Energymentioning

confidence: 99%

Section: Derivation and Propertiesmentioning

confidence: 99%

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

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%

“…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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Constructing Physically Consistent Subgrid-Scale Models for Large-Eddy Simulation of Incompressible Turbulent Flows

Cited by 2 publications

References 25 publications

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

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

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

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