Abstract
Turbulence can generally not be computed directly from the Navier-Stokes equations, because the flow possess far too many scales of motion. Therefore numerical simulations of turbulence have to resort to models of the small scales of motion for which numerical resolution is not available. Large-eddy simulation (LES) seeks to predict the dynamics of spatially filtered flows. If a spatial filter \(u \mapsto \overline{u}\) is applied to the (incompressible) Navier-Stokes equations an expression depending on both full velocity field u and the filtered field \(\overline{u}\) results, due to the nonlinearity. The dependence on u can be removed by adopting an eddy-viscosity model, for instance (Sagaut, 2001). The governing equation is then given by
where ν and ν e denote the fluid viscosity and the eddy viscosity, respectively; S(v) is the symmetric part of the velocity gradient (the rate-of-strain tensor). The solution v is supposed to approximate the filtered Navier-Stokes solution \(\overline{u}\).
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© 2011 Springer Science+Business Media B.V.
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Verstappen, R. (2011). An eddy-viscosity model based on the invariants of the rate-of-strain tensor. In: Kuerten, H., Geurts, B., Armenio, V., Fröhlich, J. (eds) Direct and Large-Eddy Simulation VIII. ERCOFTAC Series, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2482-2_14
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DOI: https://doi.org/10.1007/978-94-007-2482-2_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-2481-5
Online ISBN: 978-94-007-2482-2
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