by Dunca, A., John V., Layton W.J..

**Series:** 2002-01, Preprints

- MSC:
- 35Q30 ~Navier-Stokes equations

**Abstract:**

In Large Eddy Simulation

of turbulent flows, the Navier--Stokes equations are convolved with

a filter and differentiation and convolution are interchanged,

introducing

an extra commutation error term, which is nearly

universally dropped from the resulting equations. We show that the

commutation error

is asymptotically negligible in $L^p(\mathbb R^d)$

(i.e., it vanishes as the averaging

radius $\delta \to 0$) if and only if the fluid and the boundary

exert exactly zero force on each other. Next, we show that

the commutation error tends to zero in $H^{-1}(\Omega)$

as $\delta\to 0$. Convergence is proven also for a weak form of the

commutation error. The order of convergence is studied in both cases.

Last, we study the

influence of the commutation error on the energy balance of the

filtered equations.

**Keywords:**

large eddy simulation, commutation error