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Analysis of Numerical Errors in Large Eddy Simulation

by V. John, W.J. Layton.

Series: 2000-19, Preprints

65M60 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods

We consider the question of ``numerical errors'' in large eddy
simulation. It is often claimed that straightforward discretization and
solution using centered methods of models for large eddy motion can simulate
the motion of turbulent flows with complexity independent of the Reynolds
number and depending only on the resolution
``$\delta$'' of the eddies sought. This report considers precisely this
question analytically: is it possible to prove error estimates for
discretizations of {\it actually used} large eddy models whose error constants
depend only on $\delta$ but not $Re$? We consider the most common, simplest
and most mathematically tractable model and the most mathematically clear
discretization. In two cases, we prove such an error estimate and carefully
detail why our argument fails in the most general case. Our analysis aims to
assume as little time regularity on the true solution as possible.

large eddy simulation, Navier-Stokes equations, turbulence, finite element methods