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 via a blending function. 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
Multiple variants available for specific applications

Limitations:

Can overpredict turbulence in regions of strong streamline curvature

Variants: The standard SST-2003 formulation is the default. A vorticity-based production variant and rotation correction variant are available for flows with strong swirl or curved streamlines — these can be selected through the AI Assistant for advanced use cases.

Best for: Vehicle aerodynamics, wing analysis, duct flows, general-purpose CFD

Near-wall resolution: 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 resolution: Medium (y+ ≈ 30-300)

Spalart-Allmaras¶

A one-equation model solving a single transport equation for turbulent viscosity. The lightest RANS model computationally. Several variants are available to handle specific flow conditions.

Strengths:

Lowest computational cost of all RANS models
Good for attached boundary layers
Stable and fast-converging
Well-suited for compressible flows

Limitations:

Less accurate for separated flows
Overpredicts turbulence in free shear layers
Not well-suited for complex 3D flow patterns

Variants:

Variant	Description
Standard	Classic SA formulation — recommended starting point
SA-neg	Handles negative turbulence variable values gracefully — more robust for difficult initializations
SA-noft2	Removes the ft2 laminar suppression term — simpler and often equivalent for fully turbulent flows
Compressibility correction	Accounts for compressibility effects on turbulence at high Mach numbers
Rotation correction	Improved accuracy in rotating or strongly curved flows

The default is the standard variant. Studio selects the appropriate variant automatically based on your solver and flow configuration, or you can select one explicitly through the AI Assistant.

Best for: Streamlined bodies, aerospace applications, compressible flows, preliminary analysis

Near-wall resolution: Medium (y+ ≈ 30) or Fine (y+ ≈ 1)

Reynolds Stress Model (RSM)¶

A second-order closure solving transport equations for all six Reynolds stress components plus a dissipation equation. The most physically complete RANS model available.

Strengths:

Captures anisotropic turbulence effects that eddy-viscosity models cannot
Accurate for swirling flows, strong streamline curvature, and 3D separation
Best RANS accuracy for complex flows with turbulence anisotropy

Limitations:

Computationally expensive — 7 additional transport equations
Can be less stable; typically initialized from a converged k-ω SST solution
Requires more conservative solver tuning

Pressure-strain correlation models:

Model	Description
LRR-IP	Launder-Reece-Rodi with isotropization of production — robust general-purpose default
SSG	Speziale-Sarkar-Gatski — quadratic pressure-strain; better for complex 3D flows

The default is LRR-IP. Studio applies conservative relaxation factors automatically for RSM to ensure stable convergence.

Best for: Swirling flows, cyclones, rotating machinery, complex 3D separation, turbomachinery

Near-wall resolution: 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 near-wall mesh, 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 resolution for the RANS region; the LES region is handled automatically by the DES switching function.

Tier: Pro and above

SA-DES¶

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

SST-DES¶

DES formulation using k-ω SST as the RANS backbone. Offers the same RANS-to-LES switching but with SST’s superior wall-bounded flow prediction in the RANS region.

Best for: Cases where SST is preferred for the near-wall RANS treatment — vehicle aerodynamics, wing flows with trailing-edge separation

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). Available with both SA and SST backbones. Recommended over standard DES for most applications.

Best for: All cases where DES would be used — DDES is the safer default

IDDES¶

Improved Delayed DES extends DDES with wall-modelled LES capability. When the mesh is fine enough near walls, IDDES can operate as a wall-modelled LES in the inner layer, providing higher accuracy than standard DDES in the near-wall region.

Best for: High-fidelity analysis of massively separated flows where near-wall LES accuracy is needed

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 (LRR-IP / SSG)	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+
SA-DES	DES	Hybrid	High	Very Good	Transient	Pro+
SST-DES	DES	Hybrid	High	Very Good	Transient	Pro+
DDES	DES	Hybrid	High	Very Good	Transient	Pro+
IDDES	DES	Hybrid	Very High	Excellent	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¶

Use this selection path:

If you do not need time-accurate results, start with RANS.
If you need time-accurate results but not detailed turbulence structures, use URANS.
If detailed turbulence structures matter and the budget allows it, use LES.
If detailed separated-flow behaviour matters but full LES is too expensive, use DES or DDES.
For strong swirl or rotation in RANS, consider RSM.
For quick preliminary studies, consider Spalart-Allmaras.
For most general studies, start with k-ω SST.

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.