Vol. 3, No. 1, 2008

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
Analysis of implicit LES methods

Andrew Aspden, Nikos Nikiforakis, Stuart Dalziel and John B. Bell

Vol. 3 (2008), No. 1, 103–126
Abstract

Implicit LES methods are numerical methods that capture the energy-containing and inertial ranges of turbulent flows, while relying on their own intrinsic dissipation to act as a subgrid model. We present a scheme-dependent Kolmogorov scaling analysis of the solutions produced by such methods. From this analysis we can define an effective Reynolds number for implicit LES simulations of inviscid flow. The approach can also be used to define an effective Reynolds number for under-resolved viscous simulations. Simulations of maintained homogeneous isotropic turbulence and the Taylor–Green vortex are presented to support this proposal and highlight similarities and differences with real-world viscous fluids. Direct comparison with data from high resolution DNS calculations provides validation of the effective viscosity and effective Kolmogorov length scale.

Keywords
Implicit LES, ILES, MILES
Mathematical Subject Classification 2000
Primary: 76F05, 76F65, 76M12, 76M55
Milestones
Received: 28 July 2008
Accepted: 22 January 2009
Published: 16 March 2009
Authors
Andrew Aspden
Lawrence Berkeley National Laboratory
1 Cyclotron Road, MS 50A-1148
Berkeley, CA 94720
United States
Department of Applied Mathematics and Theoretical Physics
University of Cambridge
Cambridge CB3 0WA
United Kingdom
Nikos Nikiforakis
Department of Applied Mathematics and Theoretical Physics
University of Cambridge
Cambridge CB3 0WA
United Kingdom
Stuart Dalziel
Department of Applied Mathematics and Theoretical Physics
University of Cambridge
Cambridge CB3 0WA
United Kingdom
John B. Bell
Lawrence Berkeley National Laboratory
1 Cyclotron Road, MS 50A-1148
Berkeley, CA 94720
United States