Building proper invariants for eddy-viscosity subgrid-scale models
Tipus de documentArticle
Condicions d'accésAccés obert
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, . 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 P GG T , Q GG T , and R GG T of the tensorGG T , and imposing the proper cubic near-wall behavior, i.e., , we deduce that the eddy-viscosity is given by . Moreover, only R GG T -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 ; this guarantees both numerical stability and that the models have less or equal dissipation than Vreman’s model, i.e., . 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, C s3pqr , should be higher than 0.458 to obtain the right amount of subgrid-scale dissipation, i.e., C s3pq = 0.572 (p = - 5/2), C s3pr = 0.709 (p = - 1), and C s3qr = 0.762 (p = 0).
Copyright 2015 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.
CitacióTrias, F. X., Folch, D., Gorobets, A., Oliva, A. Building proper invariants for eddy-viscosity subgrid-scale models. "Physics of fluids", 23 Juny 2015, vol. 27, núm. 6, p. 065103-1-065103-17.
Versió de l'editorhttp://scitation.aip.org/content/aip/journal/pof2/27/6/10.1063/1.4921817