Computational Fluid Dynamics as good as it gets.

Analysis of truncation errors and design of physically optimized discretizations

S. Hickel, N.A. Adams (2008)
Quality and Reliability of Large-Eddy Simulations, Springer. doi: 10.1007/978-1-4020-8578-9_4

Further development of Large Eddy Simulation (LES) faces as major obstacle the strong coupling between subgrid-scale (SGS) model and the truncation error of the numerical discretization. Recent analyzes indicate that for certain discretizations and certain flow configurations the truncation error itself can act as implicit SGS model. In this paper, we explore how implicit SGS models can be derived systematically and propose a procedure for design, analysis, and optimization of nonlinear discretizations.

Implicit LES can be made rigorous by requiring that the numerical dissipation approximates the SGS dissipation obtained from the analysis of nonlinear interactions in turbulence.

 

Spectral numerical viscosity of −−− de-aliased spectral scheme,  − · − 2nd order central FD,  − · · −  4th order central FD,  ◦ EDQNM theory.
Numerical viscosity of ALDM with optimized parameters compared to the prediction of turbulence theory. −−− LES with N = 32, - - - LES with N = 64, ◦ EDQNM theory.

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