## RANS Turbulence Models in TAU

### One-equation models

TAU name "Turbulence model version" | Long name | Reference
SAO | Spalart-Allmaras model, original version | Spalart, P.R., “Allmaras, S.R., A one-equation turbulence model for aerodynamic flows”, La Recherche Aerospatiale, Vol. 1 (1994), pp. 5-21
SAE | Spalart-Allmaras model with Edwards modification | Edwards, J.R., Chandra, S., "Comparison of Eddy Viscosity-Transport Turbulence Models for Three-Dimensional, Shock-Separated Flowfields", AIAA Journal, Vol. 34 No. 4 (1996), pp. 756-763
SAM | Spalart-Allmaras model, modified version |
SALSA | Strain Adaptive Linear Spalart-Allmaras model | Rung, T., Bunge, U., Schatz, M., Thiele, F., “Restatement of the Spalart-Allmaras Eddy-Viscosity Model in Strain-Adaptive Formulation”, AIAA Journal, Vol. 41 No. 7 (2003), pp. 1396-1399

### Two-equation models

TAU name "Turbulence model version" | Long name | Reference
Wilcox_k-w | Wilcox k-ω model (1988) | Wilcox, D.C., “Reassessment of the Scale-Determining Equation for Advanced Turbulence Models”, AIAA Journal, Vol. 26, No. 11 (1988), pp. 1299-1310
Wilcox_k-w+SST | Wilcox k-ω model (1988) with SST limitiation |
TNT | Kok TNT (turbulent/non-turbulent interaction) k-ω model | Kok, J.C., “Resolving the Dependence on Freestream Values for the k-ω Turbulence Model”, AIAA Journal, Vol. 38 No. 7 (2000), pp.1292-1295
LEA | Linear truncation of Explicit Algebraic Stress k-ω model | Rung, T., Lübcke, H., Franke, M., Xue, L., Thiele, F., Fu, S., „Assessment of Explicit Algebraic Stress Models in Transonic Flows“. In: Proceedings of the 4th International Symposium on Engineering Turbulence Modelling and Measurements, Corsica, France, 1999, pp. 659-668
Menter_BSL | Menter Baseline k-ω model | Menter, F.R., „Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications“, AIAA Journal, Vol. 32 No. 8 (1994), pp. 1598-1605
Menter_SST | Menter SST k-ω model | Original version: Menter, F.R., „Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications“, AIAA Journal, Vol. 32 No. 8 (1994), pp. 1598-1605 Modified SST limitation: Menter, F.R., Kuntz, M., Langtry, R., “Ten Years of Industrial Experience with the SST Turbulence Model”, 4th Internatinal Symposium on Turbulence, Heat and Mass Transfer, Oct. 12-17, 2003, Antalya, Turkey, pp. 625-632
2layer_k_eps |  |

### Two-equation models, nonlinear

TAU name "Turbulence model version" | Long name | Reference
RQEVM | Realizable Quadratic Eddy Viscosity Model (k-ω) |
WJ2D+Wilcox Wilcox, D.C., “Reassessment of the Scale-Determining Equation for Advanced Turbulence Models”, AIAA Journal, Vol. 26, No. 11 (1988), pp. 1299-1310 | Explicit Algebraic Reynolds Stress Model (EARSM) by Wallin&Johannson, 2D formulation, Wilcox (1988) k-ω-equations | EARSM : Wallin, S., Johansson, A.V., „An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows”, Journal of Fluid Mechanics, Vol. 403 (2000), pp. 89-132 Background k-ω model:
WJ3D+TNT | Explicit Algebraic Reynolds Stress Model (EARSM) by Wallin&Johannson, 3D formulation, Kok TNT k-ω-equations | EARSM : Wallin, S., Johansson, A.V., „An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows”, Journal of Fluid Mechanics, Vol. 403 (2000), pp. 89-132 Background k-ω model: Kok, J.C., “Resolving the Dependence on Freestream Values for the k-ω Turbulence Model”, AIAA Journal, Vol. 38 No. 7 (2000), pp.1292-1295
WJ3D+Hellsten | Explicit Algebraic Reynolds Stress Model (EARSM) by Wallin&Johannson, 3D formulation, Hellsten k-ω-equations | Hellsten, A., “New Two-Equation Turbulence Model for Aerodynamic Applications”, Report A-21, Helsinki University of Technology Laboratory of Aerodynamics, Espoo, Finland, 2004

### Differential Reynolds stress models

#### Re-distribution models

TAU name "Turbulence model version" | Long name | Reference
SSG/LRR-w | SSG/LRR-ω model | Eisfeld, B., Brodersen, O., „Advanced Turbulence Modelling and Stress Analysis for the DLR-F6 Configuration”, AIAA-Paper 2005-4727, 2005
Wilcox_RSM | Wilcox stress-ω model | Wilcox, D.C., „Turbulence Modeling for CFD“, DCW Industries, 2nd edition, 1998

#### Diffusion models

TAU name "Turbulence model version" | Long name | Reference
SSGH | Simple Gradient Diffusion Hypothesis | e.g. Wilcox, D.C., „Turbulence Modeling for CFD“, DCW Industries, 2nd edition, 1998
GGDH | Generalized Gradient Diffusion Hypothesis | Daly, B.J., Harlow, F.H., „Transport Equations in Turbulence“, The Pysics of Fluids, Vol. 13 No. 11 (1970), pp. 2634-2649

#### Dissipation model

TAU name "Turbulence model version" | Long name | Reference
isotropic |  | Rotta, J., “Statistische Theorie nichthomogener Turbulenz”, Zeitschrift für Physik, Vol. 129 (1951), pp. 547-572

#### Length scale equations

TAU name "Turbulence model version" | Long name | Reference
Wilcox_omega | ω-equation according to Wilcox (1988) k-ω model | Wilcox, D.C., “Reassessment of the Scale-Determining Equation for Advanced Turbulence Models”, AIAA Journal, Vol. 26, No. 11 (1988), pp. 1299-1310
Kok_TNT-Omega | ω-equation according to TNT k-ω model | Kok, J.C., “Resolving the Dependence on Freestream Values for the k-ω Turbulence Model”, AIAA Journal, Vol. 38 No. 7 (2000), pp.1292-1295
Menter_BSL_omega | ω-equation according to Menter Baseline k-ω model | Menter, F.R., „Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications“, AIAA Journal, Vol. 32 No. 8 (1994), pp. 1598-1605
Hellsten_omega | ω-equation according to Hellsten model (EARSM) | Hellsten, A., “New Two-Equation Turbulence Model for Aerodynamic Applications”, Report A-21, Helsinki University of Technology Laboratory of Aerodynamics, Espoo, Finland, 2004