Prandtl's one-equation model

 Turbulence RANS-based turbulence models Linear eddy viscosity models Nonlinear eddy viscosity models Explicit nonlinear constitutive relation v2-f models $\overline{\upsilon^2}-f$ model $\zeta-f$ model Reynolds stress model (RSM) Large eddy simulation (LES) Detached eddy simulation (DES) Direct numerical simulation (DNS) Turbulence near-wall modeling Turbulence free-stream boundary conditions

Kinematic Eddy Viscosity $\nu _t = k^{{1 \over 2}} l = C_D {{k^2 } \over \varepsilon }$

Model ${{\partial k} \over {\partial t}} + U_j {{\partial k} \over {\partial x_j }} = \tau _{ij} {{\partial U_i } \over {\partial x_j }} - C_D {{k^{{3 \over 2}} } \over l} + {\partial \over {\partial x_j }}\left[ {\left( {\nu + {{\nu _T } \over {\sigma _k }}} \right){{\partial k} \over {\partial x_j }}} \right]$

Closure Coefficients and Auxilary Relations $\varepsilon = C_D {{k^{{3 \over 2}} } \over l}$ $C_D = 0.08$ $\sigma _k = 1$

where $\tau _{ij} = 2\nu _T S_{ij} - {2 \over 3}k\delta _{ij}$ $l$ is the turbulent length scale