Turbulence
With increased computing power over the last three decades, researchers can numerically solve the governing equations to obtain a complete description of a turbulent flow, where the flow variable (e.g., velocity, temperature, and pressure) is expressed as a function of space and time. The direct numerical simulation (DNS) of turbulence is the most straightforward approach to the solution of turbulent flows; however, DNS of high-Reynolds-number flow like atmospheric boundary layer (ABL) is not possible with today's computer resources. Large-eddy simulation (LES) has been introduced to simulate turbulence since the 1960s. In LES, the large-scale motions of the flow are calculated, while the effects of the smaller scales are modeled through the use of a sub-grid scale (SGS) model. The main advantage of LES over computationally cheaper Reynolds-averaged Navier-Stokes (RANS) is the increased level of detail that LES can deliver. While RANS provides "averaged" results, LES can potentially provide the kind of high-resolution spatial and temporal information needed for applications.
DNS
solves fluid governing equations without any turbulence model.
RANS
solves the Reynolds averaging equations (the long-time average of a quantity or ensemble average) for fluid flow
LES
a practice to solve only for large eddies explicitly and to model the effect of the smaller and more universal eddies on the larger ones