SST k-omega model
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Contents |
Kinematic Eddy Viscosity
Turbulence Kinetic Energy
![{{\partial k} \over {\partial t}} + U_j {{\partial k} \over {\partial x_j }} = \tau _{ij} {{\partial U_i } \over {\partial x_j }} - \beta ^* k\omega + {\partial \over {\partial x_j }}\left[ {\left( {\nu + \sigma_{k1} \nu _T } \right){{\partial k} \over {\partial x_j }}} \right]](/W/images/math/a/0/6/a068399c3d0288b112c831c476e3d2ab.png)
Specific Dissipation Rate
![{{\partial \omega } \over {\partial t}} + U_j {{\partial \omega } \over {\partial x_j }} = \alpha {\omega \over k}\tau _{ij} {{\partial U_i } \over {\partial x_j }} - \beta \omega ^2 + {\partial \over {\partial x_j }}\left[ {\left( {\nu + \sigma_{\omega 1} \nu _T } \right){{\partial \omega } \over {\partial x_j }}} \right] + 2( 1 - F_1 ) \sigma_{\omega 2} {1 \over \omega} {{\partial k } \over {\partial x_i}} {{\partial \omega } \over {\partial x_i}}](/W/images/math/5/c/7/5c7586a0a5764a6f207d4e5020c98e96.png)
Closure Coefficients and Auxilary Relations
- Failed to parse (syntax error): F_1=\mbox{tanh} \left{ \left{ \mbox{min} \left[ \mbox{max} \left( {\sqrt{k} \over \beta^*\omega y},
- Failed to parse (syntax error): {500 \nu \over y^2 \omega } \right) , {4 \sigma_{\omega 2} k} \over CD_{k\omega} y^2} \right] \right}^4 \right}
References
- Wilcox, D.C. (1988), "Re-assessment of the scale-determining equation for advanced turbulence models", AIAA Journal, vol. 31, pp. 1414-1421.
