LES, DES & Higher-Fidelity Turbulence Modelling

What Is It?

LES (Large Eddy Simulation), DES (Detached Eddy Simulation) and hybrid RANS-LES methods are higher-fidelity turbulence modelling approaches that resolve more of the turbulent motion than RANS models. LES directly resolves the large turbulent eddies and models only the smallest (sub-grid) scales. DES blends RANS near walls (where resolving all eddies is too expensive) with LES in the separated flow regions. These methods provide more physical detail than RANS — they capture unsteady turbulent structures, transient separation and coherent vortices — but at significantly higher computational cost.

Why It Matters

For some flows, RANS models are not adequate. Flows with massive separation, unsteady vortex shedding, aeroacoustic noise or complex three-dimensional turbulent structures may require higher-fidelity methods to capture the physics. LES and DES can provide this fidelity, but the computational cost is orders of magnitude higher than RANS. Understanding when higher fidelity is justified, what it costs, and what additional verification it requires is essential for making informed modelling decisions. LES is not simply "more accurate RANS" — it is a fundamentally different approach with different requirements.

Higher fidelity does not remove the need for good boundary conditions or adequate resolution. An LES with poor inlet turbulence, an inadequate mesh or an insufficient time step is not better than a well-set-up RANS — it is just more expensive and equally wrong.

LES Concept

LES resolves the large turbulent eddies directly — the eddies that contain most of the turbulent kinetic energy and that are specific to the flow geometry. The small eddies, which are more universal and isotropic, are modelled by a sub-grid scale (SGS) model. The separation between resolved and modelled scales is determined by the mesh resolution — the mesh cell size acts as a filter, and eddies larger than the cell size are resolved while smaller eddies are modelled. LES is always transient — the large eddies are unsteady and must be resolved in time.

LES concept:

Large eddies (geometry-dependent, high energy) → RESOLVED directly
Small eddies (universal, low energy) → MODELLED by sub-grid scale (SGS) model

Mesh acts as filter: eddies > cell size → resolved
                 eddies < cell size → modelled

LES is always transient — large eddies are unsteady

Spatial and Temporal Resolution Requirements

LES requires fine spatial resolution — the mesh must be fine enough to resolve the energy-containing eddies, which are typically of the order of the flow geometry. It also requires fine temporal resolution — the time step must be small enough to resolve the unsteady eddy motion, constrained by the CFL (Courant–Friedrichs–Lewy) condition. Both requirements make LES much more expensive than RANS. The cost scales with Reynolds number — at high Reynolds number, the range of eddy sizes is larger and the mesh must be finer, increasing the cost dramatically.

Inlet Turbulence for LES

LES requires time-resolved turbulent fluctuations at the inlet — not just the mean velocity and turbulence intensity. The inlet must contain realistic eddy structures that will be convected into the domain. Generating synthetic turbulence at the inlet is a significant challenge — methods include random fluctuations (too simplistic), vortex methods and recycling/rescaling techniques. If the inlet turbulence is not realistic, the turbulent structures in the domain will take time to develop, and the results near the inlet will not be credible. The inlet turbulence generation method should be appropriate for the flow and the geometry.

COMMON MISTAKE: Running LES with steady or uniform inlet conditions. LES requires time-resolved turbulent fluctuations at the inlet. Without realistic inlet turbulence, the turbulent structures in the domain develop incorrectly and the results near the inlet are not credible.

Statistical Averaging

LES produces unsteady, fluctuating flow fields. To obtain mean flow quantities — the average velocity, pressure or force — the instantaneous fields must be averaged over time. This averaging requires the simulation to run for sufficient time after the initial transient has passed — the flow must reach a statistically stationary state. The averaging period must be long enough to converge the statistics. If the averaging period is too short, the mean quantities will be unreliable. The need for statistical averaging adds to the computational cost — the simulation must run for many flow-through times after the initial transient.

DES / Hybrid RANS-LES

DES (Detached Eddy Simulation) is a hybrid approach that uses RANS near the wall and LES in the separated flow regions away from the wall. The rationale is that resolving all turbulent eddies near the wall (wall-resolved LES) is extremely expensive — the eddies near the wall are very small and require very fine mesh. By using RANS near the wall, DES avoids this cost while still resolving the large separated eddies with LES. DES is triggered automatically by the mesh and the model — when the mesh is fine enough away from the wall, the model switches from RANS to LES. DES is less expensive than wall-resolved LES but more expensive than RANS.

Wall-Resolved LES Cost

Wall-resolved LES — resolving all turbulent eddies including those near the wall — is the most expensive LES approach. The mesh near the wall must be fine enough to resolve the small wall-bounded eddies, and the time step must be small enough to resolve their motion. The cost scales approximately as Re^(1.8) or higher, making wall-resolved LES impractical for high Reynolds number engineering flows. DES and other hybrid methods exist specifically to avoid this cost by modelling the near-wall region with RANS.

When Higher Fidelity May Be Justified

• Massive separation with unsteady vortex shedding that RANS cannot capture
• Aeroacoustic noise prediction where the turbulent fluctuations generate the noise
• Flows where RANS models have been shown to be inadequate (validated against benchmark data)
• Research and validation of RANS models for a specific flow type
• Flows where the unsteady turbulent structures are the engineering quantity of interest

Key Takeaways

• LES resolves large turbulent eddies directly and models only the smallest scales
• LES requires fine spatial and temporal resolution — orders of magnitude more expensive than RANS
• LES requires time-resolved inlet turbulence — not just mean quantities
• DES blends RANS near walls with LES in separated regions — cheaper than wall-resolved LES
• Higher fidelity is justified when RANS is demonstrably inadequate — not as a default