LES / DNS Turbulence Simulation — Overview

Great question. Think of turbulence like ocean waves. Big waves carry most of the energy and are strongly geometry-dependent — they look totally different near a car versus near a building. Small waves (ripples) behave more universally regardless of geometry. RANS averages everything out and models all of it. LES directly solves the big energy-carrying eddies on the grid and only models the tiny universal ones. That's the key idea.

Exactly. The spectrum of turbulence runs from large integral-scale eddies (size ~ L) down to tiny Kolmogorov eddies (size ~ η). DNS resolves all the way to η. RANS resolves nothing — it solves only the time-mean field. LES draws a "filter width" Δ somewhere in the inertial subrange and resolves everything larger than Δ, while modeling everything smaller with a sub-grid scale (SGS) model. Since the small eddies are nearly isotropic and universal, you can get away with a simple model — that's the beautiful assumption behind LES.

The spatial filter is a convolution of the flow field with a filter kernel $G(\mathbf{x}, \mathbf{x}'; \Delta)$. The filtered velocity $\bar{u}_i$ is defined as:

Most SGS models use the eddy-viscosity assumption — they relate $\tau_{ij}^{sgs}$ to the resolved strain rate $\bar{S}_{ij}$ via a sub-grid viscosity $\nu_{sgs}$. The formula is $\tau_{ij}^{sgs} = -2\nu_{sgs}\bar{S}_{ij}$. The differences are in how $\nu_{sgs}$ is computed. Let me walk you through the main ones.

DNS is the opposite direction — it models nothing. The Navier-Stokes equations are solved on a grid fine enough to resolve the smallest turbulent structures, the Kolmogorov eddies with length scale $\eta = (\nu^3/\varepsilon)^{1/4}$. This means the grid spacing must be $\Delta x \lesssim \eta$ everywhere in the domain. There are no SGS models, no wall functions — just pure physics.

Cost. The ratio of large-scale to Kolmogorov scale goes as $L/\eta \sim Re^{3/4}$. To resolve a 3D volume you need $(L/\eta)^3 \sim Re^{9/4}$ grid points. And the time steps need to be small too, so total cost scales roughly as $Re^3$. For a car at highway speed, Re ≈ 10^7. DNS would need on the order of $10^{21}$ grid points — that's not happening in our lifetimes. DNS is mainly used for canonical flows like channel flow (Re < 5000) and pipe flow to generate benchmark datasets and develop turbulence models.

Your boss is right for most industrial cases — SST handles 80% of engineering problems well. But there are specific scenarios where RANS fundamentally fails and LES becomes necessary. The key ones are: combustion (turbulent flame interaction depends on unresolved mixing — RANS gets it wrong), aeroacoustics (noise prediction requires resolved turbulent pressure fluctuations — RANS can only give broadband estimates), massively separated flows (bluff bodies, stalled airfoils where RANS misses recirculation size), and any application where you need time-resolved unsteady spectra — fan noise, HVAC rumble, cavity tones.

Exactly. BMW, Toyota, Airbus — they all run LES or DES for acoustic predictions because RANS simply cannot give you frequency-dependent noise levels. For a combustor, the reaction rate depends on local mixing between fuel and oxidizer at the sub-grid level, and that's precisely what LES SGS models are designed to capture. Without it you'll get the wrong flame shape and possibly predict extinction or flashback incorrectly.

That's the dirty secret of wall-resolved LES. Near the wall, the turbulent structures get extremely thin — the smallest streaks scale with the viscous length $\ell^* = \nu/u_\tau$, requiring $\Delta x^+ \approx 100$, $\Delta z^+ \approx 30$, and $\Delta y^+ \approx 1$ in the wall-normal direction. For a full aircraft at cruise, this means $\sim 10^{15}$ cells — completely infeasible. The solution is Wall-Modeled LES (WMLES): use RANS equations in the inner boundary layer (say $y^+ < 200$) to provide a wall stress, and LES everywhere else. You lose some accuracy near the wall but gain enormous savings.

Pretty much. In constant/turbulenceProperties, change the simulation type from RAS to LES and choose your SGS model. The big change is your time-step: LES must run transiently with small time steps (Courant number Co < 0.5 ideally), and you need to collect statistics over many flow-through times after the initial transient dies out — typically 5–10 flow-through times for statistics, after a 2–5 flow-through time startup.