Editing Large eddy simulation (section)

=== Filter implementation ===

The filtering operation in large eddy simulation can be implicit or explicit.  Implicit filtering recognizes that the subfilter scale model will dissipate in the same manner as many numerical schemes.  In this way, the grid, or the numerical discretization scheme, can be assumed to be the LES low-pass filter.  While this takes full advantage of the grid resolution, and eliminates the computational cost of calculating a subfilter scale model term, it is difficult to determine the shape of the LES filter that is associated with some numerical issues.  Additionally, truncation error can also become an issue.<ref name="Grinstein_2007">{{cite book
|title=Implicit large eddy simulation
|author1=Grinstein, Fernando
|author2=Margolin, Len
|author3=Rider, William
|year=2007
|publisher=Cambridge University Press
|isbn=978-0-521-86982-9}}</ref>

In explicit filtering, an [[Filter (large eddy simulation)|LES filter]] is applied to the discretized Navier–Stokes equations, providing a well-defined filter shape and reducing the truncation error.  However, explicit filtering requires a finer grid than implicit filtering, and the computational cost increases with <math>(\Delta x)^4</math>. Chapter 8 of Sagaut (2006) covers LES numerics in greater detail.<ref name="Sagaut_2006" />