Turbulence Models

This page explains the model and its SU2 implementation. For numerical setup choices, see the setup guide; use its tutorial and V&V links for worked examples and comparisons.

A RANS simulation does not resolve turbulent eddies. A turbulence model adds transport equations that give the eddy viscosity, which models the extra mixing caused by turbulence. SU2 has two model families: the one-equation Spalart-Allmaras (SA) model and the two-equation k-omega Shear Stress Transport (SST) model, each with several variants.

Select a model

  • Set SOLVER= RANS (compressible) or SOLVER= INC_RANS (incompressible). The discrete adjoint of both solvers uses the same model options.
  • Set KIND_TURB_MODEL to SA or SST. The default is NONE.
  • SU2 stops with an error if SOLVER is RANS or INC_RANS and KIND_TURB_MODEL= NONE. It also stops if SOLVER is NAVIER_STOKES or INC_NAVIER_STOKES and a turbulence model is set.
  • Choose the variant with SA_OPTIONS (for SA) or SST_OPTIONS (for SST). Both take a list of keywords. An empty list gives the default variant.
  • SU2 prints the full name of the variant it runs at the start of the run, for example Spalart-Allmaras-noft2 or Menter's k-omega SST-2003m.

Other options that act on all turbulence models:

Option Default What it does
PRANDTL_TURB 0.9 Turbulent Prandtl number. It turns the eddy viscosity into a turbulent heat conductivity. Takes one value per species for mixtures.
TURBULENT_CONDUCTIVITY_MODEL CONSTANT_PRANDTL_TURB In incompressible flow, NONE switches off the fluid model’s turbulent heat conductivity. Compressible viscous fluxes still add Cp × mu_t / PRANDTL_TURB, independently of this setting.
TURB_FIXED_VALUES NO Keeps the turbulence variables at their free-stream values in the region upstream of a plane.
TURB_FIXED_VALUES_DOMAIN none Position of that plane, as a distance along the free-stream direction. Required with TURB_FIXED_VALUES= YES.

Old values of KIND_TURB_MODEL (SST_SUST, SA_NEG, SA_E, SA_COMP, SA_E_COMP) and KIND_TRANS_MODEL= BC are no longer accepted. SU2 stops and prints the new option to use.

Hybrid RANS-LES models (DES, DDES and stochastic backscatter) build on these models. The SA_* variants and stochastic backscatter build on SA. The SST_* variants (DDES and IDDES for SST, from PR #2150) build on SST. See Hybrid RANS-LES. Wall functions and wall roughness, including the SST roughness boundary conditions, are on Wall Treatment.

Spalart-Allmaras (SA)

Select it with KIND_TURB_MODEL= SA. The model solves one equation for the SA working variable, nu-tilde (NU_TILDE in the output). The NASA Turbulence Modeling Resource (TMR) SA page gives the equations of every variant.

SA_OPTIONS keywords

Keyword Effect TMR name
(empty list) or NONE SA without the ft2 term. This is the SU2 default. SA-noft2
WITHFT2 Adds the ft2 term (the laminar suppression term). SA
NEGATIVE Negative SA: allows negative nu-tilde with modified source and diffusion terms. SA-neg
EDWARDS Edwards modification: uses the strain rate instead of the vorticity. SA-noft2-Edwards
ROTATION Rotation correction of Dacles-Mariani et al. SA-R
COMPRESSIBILITY Mixing-layer compressibility correction. SA-comp
QCR2000 Quadratic constitutive relation: adds a nonlinear term to the turbulent stresses. SA-QCR2000
BCM Bas-Cakmakcioglu algebraic transition model. See Transition Models. SA-BCM
EXPERIMENTAL Turns off the checks on combinations (see below). none

Combinations that SU2 accepts

SU2 follows the variant names of the TMR. It stops with an error for combinations that the TMR does not list:

  • NEGATIVE and EDWARDS cannot be used together, even with EXPERIMENTAL.
  • NEGATIVE needs WITHFT2, because SA-neg is defined with the ft2 term. It cannot be combined with BCM.
  • EDWARDS must be alone. It cannot be combined with WITHFT2, ROTATION, COMPRESSIBILITY, QCR2000 or BCM.
  • BCM cannot be combined with WITHFT2, ROTATION, COMPRESSIBILITY or QCR2000.
  • Without NEGATIVE, EDWARDS or BCM, any mix of WITHFT2, ROTATION, COMPRESSIBILITY and QCR2000 is accepted.

Add EXPERIMENTAL to the list to run a combination that SU2 rejects, for example SA_OPTIONS= NEGATIVE, EXPERIMENTAL (SA-neg without ft2).

Examples:

TMR name Setting
SA-noft2 SA_OPTIONS= NONE (or leave the option out)
SA SA_OPTIONS= WITHFT2
SA-neg SA_OPTIONS= NEGATIVE, WITHFT2
SA-noft2-R-comp SA_OPTIONS= ROTATION, COMPRESSIBILITY
SA-neg-R-comp-QCR2000 SA_OPTIONS= NEGATIVE, WITHFT2, ROTATION, COMPRESSIBILITY, QCR2000
SA-noft2-Edwards SA_OPTIONS= EDWARDS
SA-BCM SA_OPTIONS= BCM

Original papers:

  • SA: P. R. Spalart and S. R. Allmaras, “A One-Equation Turbulence Model for Aerodynamic Flows”, La Recherche Aérospatiale, No. 1, 1994, pp. 5-21.
  • SA-neg: S. R. Allmaras, F. T. Johnson and P. R. Spalart, “Modifications and Clarifications for the Implementation of the Spalart-Allmaras Turbulence Model”, ICCFD7-1902, 2012.
  • SA-R: J. Dacles-Mariani, G. G. Zilliac, J. S. Chow and P. Bradshaw, AIAA Journal 33(9), 1995, pp. 1561-1568.
  • SA-comp: P. R. Spalart, “Trends in Turbulence Treatments”, AIAA 2000-2306.
  • SA-QCR2000: P. R. Spalart, “Strategies for Turbulence Modelling and Simulation”, Int. J. Heat and Fluid Flow 21, 2000, pp. 252-263.
  • SA-noft2-Edwards: J. R. Edwards and S. Chandra, AIAA Journal 34(4), 1996, pp. 756-763.

Shear Stress Transport (SST)

Select it with KIND_TURB_MODEL= SST. The model solves two equations: the turbulent kinetic energy k (TKE in the output) and the specific dissipation rate omega (DISSIPATION). The TMR SST page gives the equations of every variant.

SST_OPTIONS keywords

The keywords fall into four groups. SU2 has only the “m” forms of SST (see below).

Version (at most one):

Keyword Effect TMR name
V2003m 2003 version, “m” form. This is the default when no version is given. SST-2003m
V1994m Original 1994 version, “m” form. SSTm

Production term (at most one): what SU2 uses in place of the strain rate magnitude S in the production of k.

Keyword Effect TMR name
VORTICITY Uses the vorticity magnitude. SST-Vm
KATO-LAUNDER Replaces S² in production by SΩ, the product of strain-rate and vorticity magnitudes. SST-KLm
UQ Uses a perturbed Reynolds stress tensor, for uncertainty quantification. See the UQ tutorial and the options UQ_COMPONENT (default 1), UQ_DELTA_B (1.0), UQ_URLX (0.1), UQ_PERMUTE (NO). none

Compressibility correction (at most one, only with SOLVER= RANS):

Keyword Effect
COMPRESSIBILITY-WILCOX Wilcox dilatation-dissipation correction. Active where the turbulent Mach number sqrt(2k)/a is above 0.25.
COMPRESSIBILITY-SARKAR Sarkar correction: dilatation dissipation plus a pressure-dilatation term. Same threshold.

With the SST hybrid RANS/LES variants (HYBRID_RANSLES= SST_*, PR #2150), SU2 stops with an error if you set one of these corrections. See Hybrid RANS-LES.

Other modifiers (combine with anything):

Keyword Effect TMR name
SUSTAINING Controlled decay: keeps k and omega from decaying below their free-stream values. SST-sust
DIMENSIONLESS_LIMIT Sets the lower limits of k and omega relative to their free-stream values (see below). none
NONE No effect. none

SU2 stops with an error if you give two versions, two production keywords or two compressibility keywords.

Examples:

TMR name Setting
SST-2003m SST_OPTIONS= V2003m (or leave the option out)
SSTm SST_OPTIONS= V1994m
SST-Vm SST_OPTIONS= V1994m, VORTICITY
SST-KLm SST_OPTIONS= V1994m, KATO-LAUNDER
SST-sust-m SST_OPTIONS= V1994m, SUSTAINING

Original papers:

  • SST (1994): F. R. Menter, “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications”, AIAA Journal 32(8), 1994, pp. 1598-1605.
  • SST-2003: F. R. Menter, M. Kuntz and R. Langtry, “Ten Years of Industrial Experience with the SST Turbulence Model”, Turbulence, Heat and Mass Transfer 4, 2003, pp. 625-632.
  • SST-V: F. R. Menter, “Improved Two-Equation k-omega Turbulence Models for Aerodynamic Flows”, NASA TM 103975, 1992.
  • SST-KL: M. Kato and B. E. Launder, 9th Symposium on Turbulent Shear Flows, Kyoto, 1993, paper 10-4.
  • SST-sust: P. R. Spalart and C. L. Rumsey, “Effective Inflow Conditions for Turbulence Models in Aerodynamic Calculations”, AIAA Journal 45(10), 2007, pp. 2544-2553.

What SU2 does differently from the literature

This section lists where SU2 departs from the TMR definitions, or where the SU2 defaults differ from what the TMR calls “standard”.

SA

  • The default is SA-noft2, not standard SA. The TMR calls the version with the ft2 term “standard”. SU2 leaves ft2 out unless you add WITHFT2. The TMR notes that SA-noft2 gives almost the same results for most practical problems.
  • Limiting of the modified vorticity. In all variants except Edwards, SU2 limits the modified vorticity S-hat as in note 1(c) of Allmaras et al. (2012), and keeps it above 1e-10. In SA-neg, where nu-tilde is negative, S-hat is the vorticity.
  • Rotation correction with SA-neg. With ROTATION, SU2 takes the absolute value of the production term where nu-tilde is negative. The correction constant is 2.
  • Compressibility correction. COMPRESSIBILITY uses C5 = 3.5. SU2 computes the speed of sound from the ideal-gas relation sqrt(gamma p / rho), whatever the fluid model. In axisymmetric runs it adds the matching axisymmetric term. SU2 does not stop you from using it with INC_RANS (to be reviewed: check whether the result makes sense there).
  • QCR2000. SU2 adds the QCR term (constant 0.3) to the stress tensor, scaled by the fraction of eddy viscosity in the total viscosity. It is available only with SA.
  • Rough walls. SU2 applies the Aupoix-Spalart roughness correction when a wall has a roughness height. See Wall Treatment.

SST

  • SST is always the “m” form. SU2 does not include the turbulent kinetic energy in the viscous stress tensor of the mean flow equations. The production of k is mu_t S^2 (or the vorticity or Kato-Launder form). The unmodified keywords V1994 and V2003 are not available.
  • Exception: UQ. With UQ, SU2 uses the perturbed Reynolds stress tensor, which includes k, both in the mean flow equations and in the production of k.
  • V1994m is consistent with the TMR since SU2 v8. Before, SU2 dropped k from the stress tensor but kept a divergence term in the production (issue #1551, now closed). Pull request #2062, merged in July 2023, removed that term and made V2003m the default.
  • 1994 versus 2003. As in the TMR: 1994 uses the vorticity in the eddy viscosity limiter, a production limiter of 20 and the unlimited production in the omega equation; 2003 uses the strain rate, a limiter of 10 and the limited production in the omega equation. The 2003 version also uses its own values of the constants gamma_1 = 5/9 and gamma_2 = 0.44.
  • Sustaining terms. The TMR adds the sustaining terms to the sources. SU2 instead takes the larger of the production and the sustaining term, for k and for omega. Where production is larger, the model is unchanged. The ambient values are the free-stream k and omega that SU2 computes from FREESTREAM_TURBULENCEINTENSITY and FREESTREAM_TURB2LAMVISCRATIO (see below). The TMR recommends specific ambient values; SU2 does not set them for you.
  • Compressibility corrections replace the production keyword. In the code, COMPRESSIBILITY-WILCOX and COMPRESSIBILITY-SARKAR overwrite the production setting. If you combine them with VORTICITY, KATO-LAUNDER or UQ, SU2 gives no error, but the production uses the strain rate. The start-up message shows only the compressibility correction. With UQ, the mean flow stress tensor is still perturbed. Do not combine the two groups.
  • Lower limits of k and omega. By default SU2 keeps k above 1e-10 and omega above 1e-4 (in the non-dimensional units of the solver). With DIMENSIONLESS_LIMIT, the limits become LOWER_LIMIT_K_FACTOR (default 1e-15) times the free-stream k and LOWER_LIMIT_OMEGA_FACTOR (default 1e-05) times the free-stream omega.
  • No curvature correction. SST-RC and similar variants are not implemented.

Free-stream and inlet values

SU2 starts the whole field from the free-stream values of the turbulence variables, and uses them at far-field boundaries.

SA.

Option Default Meaning
FREESTREAM_NU_FACTOR 3.0 Free-stream nu-tilde divided by the free-stream kinematic viscosity.
ENGINE_NU_FACTOR 3.0 Same ratio at engine and actuator disk boundaries.

With BCM, SU2 multiplies the free-stream, inlet and engine values (not the actuator disk value) by 0.005. The default free-stream nu-tilde is then 0.015 times the kinematic viscosity.

SST.

Option Default Meaning
FREESTREAM_TURBULENCEINTENSITY 0.05 Turbulence intensity Tu as a fraction (0.05 means 5 %).
FREESTREAM_TURB2LAMVISCRATIO 10.0 Ratio of eddy viscosity to laminar viscosity.

SU2 computes k = 1.5 (Tu U)^2 from the free-stream speed U, and then omega = rho k / (mu × ratio).

The defaults (5 % and 10) are not calibrated inlet conditions. Choose the intensity and length/time scale for the actual flow, and check their decay between the boundary and the body. The TMR gives recommended far-field values for each model, and Setup Guide: Steady RANS for External Aerodynamics discusses the choice.

Inlets. MARKER_INLET_TURBULENT sets values per inlet marker:

  • SA: MARKER_INLET_TURBULENT= (inlet, 3.0). The value is nu-tilde divided by the kinematic viscosity at the inlet, like FREESTREAM_NU_FACTOR. (The SU2 error message calls it a viscosity ratio, but the code uses it as the nu-tilde factor.)
  • SST: MARKER_INLET_TURBULENT= (inlet, 0.05, 10.0): turbulence intensity, then viscosity ratio. SU2 computes k and omega from the inlet velocity, density and viscosity.
  • An inlet not listed in MARKER_INLET_TURBULENT uses the free-stream values of the options above.
  • With an inlet profile file, the file gives nu-tilde (SA) or k and omega (SST) in dimensional units.

Verification and test cases

Verification and validation (V&V) pages, with configs in TestCases/vandv:

Page Models Config
Flat plate SA, SST 1994m and 2003m turb_flatplate_sst.cfg (V1994m)
Bump in channel SST turb_bump_sst.cfg (V1994m)
DSMA661 airfoil wake SA, SST dsma661_sa_config.cfg (SA-noft2), dsma661_sst_config.cfg (V2003m)
30P30N high-lift airfoil SA-noft2 config.cfg
Shock-wave boundary-layer interaction SA-neg, SST-2003m with Wilcox correction config_sa.cfg, config_sst.cfg
Sandia jet SST-2003m, incompressible validation.cfg

Test cases that show the option keywords:

Tutorials:

Known limits

  • Only SA and SST are available. There are no k-epsilon, Reynolds stress or algebraic models.
  • SST has no unmodified (non-“m”) form and no curvature correction.
  • The SST compressibility corrections work only with SOLVER= RANS.
  • Some SA combinations need EXPERIMENTAL. Results with those combinations are not verified against the TMR.
  • FEM_RANS (the high-order finite element solver) does not use these models.
  • RANS models predict a fully turbulent boundary layer. For laminar regions and transition, see Transition Models.

Source review: 22 October 2026, against SU2 docs_site at 41ea6a219a. See the review scope and outstanding validation. Setup recommendations remain draft where indicated.


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