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@article{vremanEddyviscositySubgridscaleModel2004,
title = {An eddy-viscosity subgrid-scale model for turbulent shear flow: {Algebraic} theory and applications},
volume = {16},
issn = {1070-6631, 1089-7666},
shorttitle = {An eddy-viscosity subgrid-scale model for turbulent shear flow},
url = {https://pubs.aip.org/pof/article/16/10/3670/255289/An-eddy-viscosity-subgrid-scale-model-for},
doi = {10.1063/1.1785131},
abstract = {An eddy-viscosity model is proposed and applied in large-eddy simulation of turbulent shear flows with quite satisfactory results. The model is essentially not more complicated than the Smagorinsky model, but is constructed in such a way that its dissipation is relatively small in transitional and near-wall regions. The model is expressed in first-order derivatives, does not involve explicit filtering, averaging, or clipping procedures, and is rotationally invariant for isotropic filter widths. Because of these highly desirable properties the model seems to be well suited for engineering applications. In order to provide a foundation of the model, an algebraic framework for general three-dimensional flows is introduced. Within this framework several types of flows are proven to have zero energy transfer to subgrid scales. The eddy viscosity is zero in the same cases; the theoretical subgrid dissipation and the eddy viscosity have the same algebraic structure. In addition, the model is based on a fundamental realizability inequality for the theoretical subgrid dissipation. Results are shown for a transitional and turbulent mixing layer at high Reynolds number and a turbulent channel flow. In both cases the present model is found to be more accurate than the Smagorinsky model and as good as the standard dynamic model. Unlike the Smagorinsky model, the present model is able to adequately handle not only turbulent but also transitional flow.},
language = {en},
number = {10},
urldate = {2025-01-04},
journal = {Physics of Fluids},
author = {Vreman, A. W.},
month = oct,
year = {2004},
pages = {3670--3681},
file = {PDF:/home/syver/Zotero/storage/U3KSURFI/Vreman - 2004 - An eddy-viscosity subgrid-scale model for turbulent shear flow Algebraic theory and applications.pdf:application/pdf},
}
@article{verstappenWhenDoesEddy2011,
title = {When {Does} {Eddy} {Viscosity} {Damp} {Subfilter} {Scales} {Sufficiently}?},
volume = {49},
issn = {0885-7474, 1573-7691},
url = {http://link.springer.com/10.1007/s10915-011-9504-4},
doi = {10.1007/s10915-011-9504-4},
language = {en},
number = {1},
urldate = {2025-01-04},
journal = {Journal of Scientific Computing},
author = {Verstappen, Roel},
month = oct,
year = {2011},
pages = {94--110},
file = {PDF:/home/syver/Zotero/storage/PE2PSIRI/Verstappen - 2011 - When Does Eddy Viscosity Damp Subfilter Scales Sufficiently.pdf:application/pdf},
}
@article{smagorinskyGeneralCirculationExperiments1963,
title = {General circulation experiments with the primitive equations: {I}. {The} basic experiment},
volume = {91},
issn = {0027-0644, 1520-0493},
shorttitle = {{GENERAL} {CIRCULATION} {EXPERIMENTS} {WITH} {THE} {PRIMITIVE} {EQUATIONS}},
url = {http://journals.ametsoc.org/doi/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2},
doi = {10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2},
abstract = {An extended period numerical integration of a baroclinic priniitive equation model has been made for the simulation and the study of the dynamics of the atmosphere’s general circulation. The solution corresponding t o external gravitational propagation is filtered b y requiring the vertically integrated divergence to vanish identically. Thc vertical structure permits as dependent variables the horizontal wind at two internal levels and a single temperature, wit8hthe static stability entering as a parameter.},
language = {en},
number = {3},
urldate = {2025-01-04},
journal = {Monthly Weather Review},
author = {Smagorinsky, J.},
month = mar,
year = {1963},
pages = {99--164},
file = {PDF:/home/syver/Zotero/storage/UYPGZHUJ/Smagorinsky - 1963 - GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS I. THE BASIC EXPERIMENT.pdf:application/pdf},
}
@book{popeTurbulentFlows2000,
address = {Cambridge ; New York},
title = {Turbulent flows},
isbn = {978-0-521-59125-6 978-0-521-59886-6},
language = {en},
publisher = {Cambridge University Press},
author = {Pope, S. B.},
year = {2000},
keywords = {Turbulence},
file = {PDF:/home/syver/Zotero/storage/7ERG3DLJ/Pope - 2000 - Turbulent flows.pdf:application/pdf},
}
@article{triasBuildingProperInvariants2015,
title = {Building proper invariants for eddy-viscosity subgrid-scale models},
volume = {27},
issn = {1070-6631},
url = {https://doi.org/10.1063/1.4921817},
doi = {10.1063/1.4921817},
abstract = {Direct simulations of the incompressible Navier-Stokes equations are limited to relatively low-Reynolds numbers. Hence, dynamically less complex mathematical formulations are necessary for coarse-grain simulations. Eddy-viscosity models for large-eddy simulation is probably the most popular example thereof: they rely on differential operators that should properly detect different flow configurations (laminar and 2D flows, near-wall behavior, transitional regime, etc.). Most of them are based on the combination of invariants of a symmetric tensor that depends on the gradient of the resolved velocity field, G = ∇ u ¯ . In this work, models are presented within a framework consisting of a 5D phase space of invariants. In this way, new models can be constructed by imposing appropriate restrictions in this space. For instance, considering the three invariants PGGT, QGGT, and RGGT of the tensor G GT, and imposing the proper cubic near-wall behavior, i.e., ν e = O ( y 3 ) , we deduce that the eddy-viscosity is given by ν e = ( C s 3 p q r Δ ) 2 P G G T p Q G G T − ( p + 1 ) R G G T ( p + 5 / 2 ) / 3 . Moreover, only RGGT-dependent models, i.e., p \> − 5/2, switch off for 2D flows. Finally, the model constant may be related with the Vreman’s model constant via C s 3 p q r = 3 C V r ≈ 0 . 458 ; this guarantees both numerical stability and that the models have less or equal dissipation than Vreman’s model, i.e., 0 ≤ ν e ≤ ν e V r . The performance of the proposed models is successfully tested for decaying isotropic turbulence and a turbulent channel flow. The former test-case has revealed that the model constant, Cs3pqr, should be higher than 0.458 to obtain the right amount of subgrid-scale dissipation, i.e., Cs3pq = 0.572 (p = − 5/2), Cs3pr = 0.709 (p = − 1), and Cs3qr = 0.762 (p = 0).},
number = {6},
urldate = {2025-01-09},
journal = {Physics of Fluids},
author = {Trias, F. X. and Folch, D. and Gorobets, A. and Oliva, A.},
month = jun,
year = {2015},
pages = {065103},
file = {Full Text PDF:/home/syver/Zotero/storage/XYXLCANN/Trias et al. - 2015 - Building proper invariants for eddy-viscosity subgrid-scale models.pdf:application/pdf},
}
@article{clarkEvaluationSubgridscaleModels1979,
title = {Evaluation of subgrid-scale models using an accurately simulated turbulent flow},
volume = {91},
issn = {1469-7645, 0022-1120},
url = {https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/evaluation-of-subgridscale-models-using-an-accurately-simulated-turbulent-flow/3DAEEC51F4433891450FE815F6E379F9},
doi = {10.1017/S002211207900001X},
abstract = {We use a calculation of periodic homogeneous isotropic turbulence to simulate the experimental decay of grid turbulence. The calculation is found to match the experiment in a number of important aspects and the computed flow field is then treated as a realization of a physical turbulent flow. From this flow, we compute the large eddy field and the various averages of the subgrid-scale turbulence that occur in the large eddy simulation equations. These quantities are compared with the predictions of the models that are usually applied in large eddy simulation. The results show that the terms which involve the large-scale field are accurately modelled but the subgridscale Reynolds stresses are only moderately well modelled. It is also possible to use the method to predict the constants of the models without reference to experiment. Attempts to find improved models have not met with success.},
language = {en},
number = {1},
urldate = {2025-01-09},
journal = {Journal of Fluid Mechanics},
author = {Clark, Robert A. and Ferziger, Joel H. and Reynolds, W. C.},
month = mar,
year = {1979},
pages = {1--16},
file = {Full Text PDF:/home/syver/Zotero/storage/IVRLJSC7/Clark et al. - 1979 - Evaluation of subgrid-scale models using an accurately simulated turbulent flow.pdf:application/pdf},
}
@article{nicoudUsingSingularValues2011,
title = {Using singular values to build a subgrid-scale model for large eddy simulations},
volume = {23},
issn = {1070-6631},
url = {https://doi.org/10.1063/1.3623274},
doi = {10.1063/1.3623274},
abstract = {An eddy-viscosity based, subgrid-scale model for large eddy simulations is derived from the analysis of the singular values of the resolved velocity gradient tensor. The proposed σ-model has, by construction, the property to automatically vanish as soon as the resolved field is either two-dimensional or two-component, including the pure shear and solid rotation cases. In addition, the model generates no subgrid-scale viscosity when the resolved scales are in pure axisymmetric or isotropic contraction/expansion. At last, it is shown analytically that it has the appropriate cubic behavior in the vicinity of solid boundaries without requiring any ad-hoc treatment. Results for two classical test cases (decaying isotropic turbulence and periodic channel flow) obtained from three different solvers with a variety of numerics (finite elements, finite differences, or spectral methods) are presented to illustrate the potential of this model. The results obtained with the proposed model are systematically equivalent or slightly better than the results from the Dynamic Smagorinsky model. Still, the σ-model has a low computational cost, is easy to implement, and does not require any homogeneous direction in space or time. It is thus anticipated that it has a high potential for the computation of non-homogeneous, wall-bounded flows.},
number = {8},
urldate = {2025-01-10},
journal = {Physics of Fluids},
author = {Nicoud, Franck and Toda, Hubert Baya and Cabrit, Olivier and Bose, Sanjeeb and Lee, Jungil},
month = aug,
year = {2011},
pages = {085106},
file = {Full Text PDF:/home/syver/Zotero/storage/W8K7KMNS/Nicoud et al. - 2011 - Using singular values to build a subgrid-scale model for large eddy simulations.pdf:application/pdf;Snapshot:/home/syver/Zotero/storage/H2QDSRPA/Using-singular-values-to-build-a-subgrid-scale.html:text/html},
}
@article{morinishiFullyConservativeHigher1998,
title = {Fully {Conservative} {Higher} {Order} {Finite} {Difference} {Schemes} for {Incompressible} {Flow}},
volume = {143},
issn = {0021-9991},
url = {https://www.sciencedirect.com/science/article/pii/S0021999198959629},
doi = {10.1006/jcph.1998.5962},
abstract = {Conservation properties of the mass, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations. Existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out. In particular, it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass, momentum, and kinetic energy. This deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems. Finite difference schemes in a collocated grid system are also analyzed, and a violation of kinetic energy conservation is revealed. The predicted conservation properties are demonstrated numerically in simulations of inviscid white noise, performed in a two-dimensional periodic domain. The proposed fourth order schemes in a staggered grid system are generalized for the case of a non-uniform mesh, and the resulting scheme is used to perform large eddy simulations of turbulent channel flow.},
number = {1},
urldate = {2025-01-21},
journal = {Journal of Computational Physics},
author = {Morinishi, Y. and Lund, T. S. and Vasilyev, O. V. and Moin, P.},
month = jun,
year = {1998},
pages = {90--124},
file = {PDF:/home/syver/Zotero/storage/BMFQEYJM/Morinishi et al. - 1998 - Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow.pdf:application/pdf},
}