Elliptic relaxation for near wall turbulence models

Elliptic relaxation approach
Starting from the Reynolds-stress equation:
with
Duiui
Dt
+ εuiuj
k = Pij + ℘ij + ∂
∂xk
℘ij = −
νTkl
Πij + εij − uiuj
∂uiuj
∂xl
ε
k
+ ν ∂2 uiuj
∂x 2 k
To solve ℘ij a non-homogeneous elliptic equation is
derived. By integrating the pressure equation and assuming
that the two point correlation Ψij can be approximated as
Ψij(x, x ′ ) = Ψij(x ′ , x ′ ) exp(−r/L) (Durbin,1993)
Elliptic relaxation for near wall turbulence models – p. 6/22