Prandtl's one-equation model

**Turbulence modeling**
	Turbulence
	RANS-based turbulence models Linear eddy viscosity models Algebraic models Cebeci-Smith model ; Baldwin-Lomax model ; Johnson-King model ; A roughness-dependent model ; ; One equation models Prandtl's one-equation model ; Baldwin-Barth model ; Spalart-Allmaras model ; ; Two equation models k-epsilon models Standard k-epsilon model ; Realisable k-epsilon model ; RNG k-epsilon model ; Near-wall treatment ; ; k-omega models Wilcox's k-omega model ; Wilcox's modified k-omega model ; SST k-omega model ; Near-wall treatment ; ; Realisability issues Kato-Launder modification ; Durbin's realizability constraint ; Yap correction ; Realisability and Schwarz' inequality ; ; ; ; Nonlinear eddy viscosity models Explicit nonlinear constitutive relation Cubic k-epsilon ; EARSM ; ; v2-f models model ; model ; ; ; Reynolds stress model (RSM) ;
	Large eddy simulation (LES) Smagorinsky-Lilly model ; Dynamic subgrid-scale model ; RNG-LES model ; Wall-adapting local eddy-viscosity (WALE) model ; Kinetic energy subgrid-scale model ; Near-wall treatment for LES models ;
	Detached eddy simulation (DES)
	Direct numerical simulation (DNS)
	Turbulence near-wall modeling
	Turbulence free-stream boundary conditions Turbulence intensity ; Turbulence length scale ;

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Revision as of 09:34, 12 June 2007

Kinematic Eddy Viscosity

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

Model

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