Elliptic relaxation for near wall turbulence models

The ϕ − f model
Instead of solving v 2 , a transport equation is solved for the
ratio ϕ = v 2 /k (Laurence et al., 2004):
D(υ 2 /k)
Dt
= f − (υ2 /k)
k
P + ∂
∂xk
ν + νt
σ (υ 2 /k)
ν + νt
σ (υ 2 /k)
Where X is the "cross diffusion" term from the
transformation:
X = 2
∂(υ
k
2 /k) ∂k
∂xk ∂xk
∂(υ2
/k)
+ X
∂xk
Elliptic relaxation for near wall turbulence models – p. 12/22