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https://hdl.handle.net/2142/77690
Description
Title
Toward Ideal Large-Eddy Simulation
Author(s)
Langford, Jacob Anthony
Issue Date
2000
Doctoral Committee Chair(s)
Moser, Robert D.
Department of Study
Mechanical Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Physics, Fluid and Plasma
Language
eng
Abstract
It is established that there is a subgrid model for large-eddy simulation (LES) of turbulence that is provably ideal in at least two important senses: a simulation using the ideal model matches all spatial statistics and minimizes error in the large-scale dynamics. However, the ideal model embodies a tremendous amount of information, making it impractical to determine. Instead, it must be approximated. The ideal subgrid model is approximated with a simple class of stochastic estimates, and the resulting optimal models retain some of the statistical properties of the ideal model. Statistics required to find the optimal subgrid models are computed from realizations of a direct numerical simulation (DNS) of forced isotropic turbulence with microscale Reynolds number Rlambda = 164. Optimal models are studied for two LES representations.
In the first case, a sharp cutoff filter defines the LES scales. When the model of subgrid force is expressed as a linear functional of the LES velocity data, an a priori test correctly predicts a detailed subgrid energy transfer. In an actual simulation, the optimal linear model correctly predicts second and third-order statistics. The mean-square difference between the subgrid force and the linear model is large, and the difference is not significantly reduced when a comprehensive set of nonlinear terms is included in the formulation. It is hypothesized that the optimal linear model possesses the dominant characteristics of the ideal subgrid model, that the subgrid force is mostly stochastic, and that the best model represents detailed subgrid energy transfers only. The optimal linear model is equivalent to a wavenumber-dependent eddy viscosity and has the well-known plateau-cusp behavior.
In the second case, a coarse finite-volume representation defines the LES scales. Optimal flux models are expressed as modifications of standard fourth-order schemes, so that numerical and subgrid effects are treated simultaneously. The LES obeys only a bulk conservation of mass, but it is shown that errors introduced by enforcing a second-order divergence-free condition are small.
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