Introduction to large-eddy simulation

General issues

This chapter is devoted to large-eddy simulation (LES) of turbulent flows. The framework is restricted to Newtonian, single-phase, nonreactive fluids without external forcing or coupling as in magnetohydrodynamics. The primary approximations for unsteady simulations of turbulent flows are the following:

• Direct numerical simulation (DNS), which is based on the direct resolution of the full, unsteady Navier–Stokes equations without any additional physical assumptions or models. To get reliable results, one must represent all the dynamically active scales of motion in the simulation. This means that the grid spacing Δx and the time step Δt must be fine enough to capture the dynamics of the smallest scales of the flow down to the Kolmogorov scale, referred to as η, and that the computational domain must be large enough to represent the largest scales. These criteria lead to a high computational cost, which is responsible for the fact that DNS is nowadays almost only used for theoretical analysis and accurate understanding of flow dynamics and is not a “brute force” engineering tool.

• Averaged or filtered simulations: To reduce the complexity of the simulation (and then lower the computational effort), a classical technique is to apply an averaging or filtering procedure to the Navier–Stokes equations, yielding new equations for a variable that is smoother than the original solution of the Navier–Stokes equations because the averaging or filtering procedure removes the small scales or high frequencies of the solution.

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