Turbulence Models#
Gradient Dynamics groups turbulence modelling into four simulation types: RANS, LES, DES, and URANS. Select the simulation type first, then choose the specific model within it.
RANS#
Reynolds-Averaged Navier-Stokes (RANS) models solve for a time-averaged flow field. All turbulent fluctuations are modelled rather than resolved, making RANS the fastest and most practical approach for the majority of engineering CFD.
When to use: Steady-state external aerodynamics, internal flows, rotating machinery, heat transfer — any application where time-averaged quantities (drag, lift, pressure drop, temperature) are the primary output.
Tier: Starter and above
k-ω SST#
The Shear Stress Transport model combines k-ω near walls with k-ε in the freestream. The most versatile RANS model and the recommended starting point for most applications.
Strengths:
Accurate prediction of flow separation under adverse pressure gradients
Robust wall treatment — works with both y+ ≈ 1 and y+ ≈ 30
Good all-around performance for external and internal flows
Limitations:
Can overpredict turbulence in regions of strong streamline curvature
Best for: Vehicle aerodynamics, wing analysis, duct flows, general-purpose CFD
Near-wall AMR: Medium (y+ ≈ 30) or Fine (y+ ≈ 1)
k-ε#
A two-equation model solving for turbulent kinetic energy (k) and dissipation rate (ε). The most numerically stable RANS model.
Strengths:
Very robust and stable convergence
Good for fully turbulent flows away from walls
Well-validated for pipe flows and free shear layers
Limitations:
Overpredicts turbulence in stagnation regions
Requires wall functions (y+ ≈ 30–300)
Less accurate for separated flows
Best for: Internal pipe flows, industrial duct systems, fully turbulent flows
Near-wall AMR: Medium (y+ ≈ 30–300)
Spalart-Allmaras#
A one-equation model solving a single transport equation for turbulent viscosity. The lightest RANS model computationally.
Strengths:
Lowest computational cost of all RANS models
Good for attached boundary layers
Stable and fast-converging
Limitations:
Less accurate for separated flows
Overpredicts turbulence in free shear layers
Not well-suited for complex 3D flow patterns
Best for: Streamlined bodies, aerospace applications with attached flow, preliminary analysis
Near-wall AMR: Medium (y+ ≈ 30) or Fine (y+ ≈ 1)
Reynolds Stress Model (RSM)#
A second-order closure solving transport equations for all six Reynolds stress components. The most physically complete RANS model.
Strengths:
Captures anisotropic turbulence effects
Accurate for swirling flows and strong streamline curvature
Best RANS accuracy for complex 3D flows
Limitations:
Computationally expensive — 7 additional transport equations
Can be less stable; typically initialized from a converged k-ω SST solution
Requires more careful relaxation/CFL tuning
Best for: Swirling flows, cyclones, rotating machinery, complex 3D separation
Near-wall AMR: Medium (y+ ≈ 30) or Fine (y+ ≈ 1)
LES#
Large Eddy Simulation directly resolves large-scale turbulent structures and only models the smallest (sub-grid) scales using a Sub-Grid Scale (SGS) model. It provides time-accurate, physically rich results but at significantly higher cost than RANS.
When to use: Aeroacoustics, vortex shedding, wake dynamics, bluff body flows, or any case where the time-resolved turbulence structure matters — not just the mean flow.
Requirements: Very fine mesh (Fine or Very Fine near-wall AMR), transient simulation with small time steps.
Tier: Pro and above
Smagorinsky#
The classical SGS model. Applies a constant eddy-viscosity based on the local strain rate and a mixing-length coefficient (Smagorinsky constant Cs).
Strengths:
Simple, robust, and computationally cheap
Well-understood behaviour
Limitations:
Overly dissipative in transitional or near-wall regions
Cs must be tuned for different flow types
Best for: High-Reynolds fully turbulent flows, channel flows, jets
Dynamic Smagorinsky#
Extends the Smagorinsky model by computing the Cs coefficient dynamically from the resolved flow field using Germano’s identity — no manual constant tuning required.
Strengths:
Automatically adapts to local flow conditions
More accurate in transitional and near-wall regions
Better performance for complex geometries
Limitations:
Slightly higher cost than static Smagorinsky
Can occasionally produce negative eddy viscosity (clipped automatically)
Best for: General-purpose LES, complex geometries, transitional flows
WALE#
The Wall-Adapting Local Eddy-viscosity model uses a formulation based on the velocity gradient tensor that naturally goes to zero at solid walls — no damping function needed.
Strengths:
Correct near-wall scaling without explicit damping
Well-suited for wall-bounded flows
Good performance on coarser near-wall meshes than Dynamic Smagorinsky
Limitations:
Slightly more expensive than static Smagorinsky
Best for: Wall-bounded LES, turbulent channel flows, complex internal geometries
Vreman#
An algebraic SGS model with similar near-wall behaviour to WALE but at lower computational cost.
Strengths:
Zero SGS viscosity in laminar and transitional regions (no manual switching)
Lower cost than WALE and Dynamic Smagorinsky
Robust on moderately coarse LES meshes
Best for: Transitional flows, cost-sensitive LES, engineering LES on moderate meshes
DES#
Detached Eddy Simulation is a hybrid approach: RANS is used in attached boundary layers (where it is efficient and accurate), and LES is used in detached separated regions (where it is needed). This combines the wall-efficiency of RANS with the accuracy of LES in wakes and separated zones.
When to use: Flows with large separated regions where RANS is inaccurate but full LES is unaffordable — ground vehicle wakes, bluff bodies, buffet, stall.
Requirements: Fine near-wall AMR for the RANS region; the LES region is handled automatically by the DES switching function.
Tier: Pro and above
DES (Spalart-Allmaras based)#
The original DES formulation, using Spalart-Allmaras as the RANS backbone. The DES limiter switches the model from RANS to LES mode based on the ratio of wall distance to local grid spacing.
Best for: External aerodynamics with significant separation, ground vehicles, bluff bodies
DDES#
Delayed DES adds a shielding function to prevent the LES mode from activating prematurely inside attached boundary layers (a known issue with the original DES). Recommended over standard DES for most applications.
Best for: All cases where DES would be used — DDES is the safer default
URANS#
Unsteady RANS solves the RANS equations as a time-accurate transient simulation. The same turbulence models as steady RANS are used, but the flow is allowed to evolve in time. This captures large-scale periodic unsteadiness without the cost of LES.
When to use: Periodic vortex shedding, pulsating flows, rotating machinery with transient effects, any flow where large-scale unsteadiness exists but full LES resolution is not required.
Note: URANS does not resolve turbulent fluctuations — it only captures deterministic, large-scale unsteadiness. Use LES or DES when turbulence structure itself matters.
Tier: Pro and above
URANS k-ω SST#
Time-accurate integration of the k-ω SST equations. The most common URANS setup and the recommended starting point.
Best for: Vortex shedding behind bluff bodies, oscillating airfoil flows, transient wake interactions
URANS k-ε#
Time-accurate k-ε for flows where the high stability of k-ε is beneficial in a transient context.
Best for: Transient internal flows, pulsating pipe flows, HVAC transients
URANS RSM#
Time-accurate Reynolds Stress Model for transient flows with strong anisotropy or swirl.
Best for: Transient swirling flows, transient rotating machinery, precessing vortex cores
Comparison Table#
Model |
Type |
Equations |
Relative Cost |
Separation Accuracy |
Steady/Transient |
Tier |
|---|---|---|---|---|---|---|
k-ω SST |
RANS |
2 |
Low |
Good |
Steady |
Starter+ |
k-ε |
RANS |
2 |
Low |
Fair |
Steady |
Starter+ |
Spalart-Allmaras |
RANS |
1 |
Very Low |
Fair |
Steady |
Starter+ |
RSM |
RANS |
7 |
High |
Very Good |
Steady |
Starter+ |
Smagorinsky |
LES |
SGS |
Very High |
Excellent |
Transient |
Pro+ |
Dynamic Smagorinsky |
LES |
SGS |
Very High |
Excellent |
Transient |
Pro+ |
WALE |
LES |
SGS |
Very High |
Excellent |
Transient |
Pro+ |
Vreman |
LES |
SGS |
High |
Excellent |
Transient |
Pro+ |
DES (SA) |
DES |
Hybrid |
High |
Very Good |
Transient |
Pro+ |
DDES |
DES |
Hybrid |
High |
Very Good |
Transient |
Pro+ |
URANS k-ω SST |
URANS |
2 |
Medium |
Good |
Transient |
Pro+ |
URANS k-ε |
URANS |
2 |
Medium |
Fair |
Transient |
Pro+ |
URANS RSM |
URANS |
7 |
Very High |
Very Good |
Transient |
Pro+ |
Choosing a Simulation Type#
When in doubt, start with RANS k-ω SST. It covers the widest range of applications at the lowest cost and provides a good initial field for switching to higher-fidelity methods if needed.