= Large eddy simulation
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A <large eddy simulation> computes the time-dependent large-scale motion of a <turbulent flow> while representing the influence of unresolved motion through a <subgrid-scale model>. A <spatial averaging filter> specifies which information is retained. The distinction concerns spatial resolution, rather than simply replacing a fluctuating flow by its time average.<A dynamic subgrid-scale eddy viscosity model by Massimo Germano and others (1990)>[§2, filtered velocity and momentum equations]{ref}
For an elementary illustration, take one component of a periodic <velocity field>,
$$
u_x(y)=U\sin(2\pi y/L)+a\sin(20\pi y/L).
$$
An ideal filter retaining <Fourier modes> with integer index at most four keeps the first term and removes the second, whose index is ten. The removed term still contributes to products such as $u_x^2$. Filtering the nonlinear <Navier-Stokes equations> consequently introduces a <subgrid-scale stress> that cannot generally be reconstructed from the retained <velocity field> alone.
This gives a computational compromise. <Direct numerical simulation> must resolve the dynamically relevant dissipative motion, whereas a <large eddy simulation> resolves a chosen coarser field and models its missing influence. Doubling grid counts in all three directions multiplies the cell count by eight, before any additional time-step cost. The filter, numerical discretization and closure must work together; a coarse grid by itself does not certify a useful approximation.
An early concrete demonstration was <James W. Deardorff>'s 1970 calculation of turbulent channel flow using 6720 uniform grid intervals and strain-dependent coefficients for subgrid effects. The paper compared computed statistics with experimental measurements and reported agreement ranging from good to marginal. That comparison tests a particular simulation, rather than establishing that every resolved structure or model is exact.<A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers by James W. Deardorff>[Printed p. 453, abstract: channel geometry, grid intervals, modeled subgrid effects and statistical comparison]{ref}
Implementations can supply subgrid dissipation in different ways. The Cardinal documentation, for example, describes a spectral filter used to drain energy from the smallest retained wavelengths; that is a particular numerical treatment, not the definition of all <large eddy simulation>.<Large Eddy Simulation in the Cardinal documentation>[Opening paragraph and modal-filter description]{ref}
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