Turbulence models and numerical methods can be classified into three categories according to the resolved scales: (1) Direct Numerical Simulation (DNS), (2) Large-Eddy Simulation (LES) and (3) the Reynolds-Averaged Navier-Stokes (RANS) method.

DNS solves the Navier-Stokes equations without any turbulence model, and all the spatial and temporal scales of the turbulence are resolved. Consequently, the DNS mesh must be fine enough to capture eddies of sizes ranging from the smallest dissipation scale (Kolmogorov scale) up to the characteristic length scale of the domain size. Turbulence theory shows that the number of mesh points in 3D DNS is of the order of \(O(\text{Re}^{9/4})\), where \(\text{Re}\) is the turbulent Reynolds number. The computational costs of DNS are therefore very high for high Reynolds numbers.

Unlike DNS, LES resolves only the large structures of the flows by filtering the Navier-Stokes equations with a spatial filter, and the small, unresolved scale is modelled using subgrid models. The range of resolved scales in LES is much smaller than in DNS and consequently the computational costs are significantly reduced. The two main LES models are presented in the Large-Eddy Simulation page.

Finally, RANS models consist of a set of averaged Navier-Stokes equations, with turbulence models to close the additional Reynolds tensor induced by the fluctuations. RANS models solve only the mean flow at the macroscopic scales and constitute the most economical method for the simulation of turbulence. The RANS models are presented in the RANS Models page.

Note: Planned content. The previous documentation outlined the following additional turbulence topics, not yet written: a "do and do not" guide, the dataset structure, the C++ organisation of the turbulence module (where to find what, what is available in which discretisation), initial-condition computation, scalar models, the validation forms (who does what), and the post-processings.