On hydrodynamic stability and the computability of filtered quantities for the Burgers' equation

Details On hydrodynamic stability and the computability of filtered quantities for the Burgers' equation On hydrodynamic stability and the computability of filtered quantities for the Burgers' equation

2011-11-04

arxiv.org/abs/1111.1182v1

Mathematics

Numerical Analysis

17 pages

Scientific paper

We discuss the rationale of large eddy simulation using filtering from the viewpoint of hydrodynamic stability and computability. In the simple model case of the Burgers' equation discretized using a stabilized finite element method we show that the $L^2$-error of filtered quantities converges with an order, independent of both the regularity of the exact solution and the Reynolds number. The convergence order is associated to the width of the filter. Similar estimates for the unfiltered quantities on the other hand leads to the huge exponential factors that are known to haunt all analysis of high Reynolds flows.

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