Elliptic relaxation for near wall turbulence models
Elliptic relaxation for near wall turbulence models
Elliptic relaxation for near wall turbulence models
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The ϕ − f model<br />
A changes of variable is applied to the original model:<br />
Leading to:<br />
Dϕ<br />
Dt<br />
= f − P ϕ<br />
k<br />
L 2 ∇ 2 f − f = 1<br />
T (C1 − 1)<br />
f = f + 2ν(∇ϕ∇k)<br />
k<br />
2 νt ∂ϕ ∂k<br />
+<br />
k σk ∂xj ∂xj<br />
<br />
ϕ − 2<br />
<br />
3<br />
− C2<br />
+ ν∇ 2 ϕ (2)<br />
+ ∂<br />
∂xj<br />
P<br />
k<br />
νt<br />
σk<br />
− 2ν<br />
k<br />
∂ϕ<br />
∂xj<br />
∂ϕ<br />
∂xj<br />
<br />
∂k<br />
∂xj<br />
(3)<br />
− ν∇ 2 ϕ<br />
Far from the <strong>wall</strong> the last two terms are negligible, ensuring<br />
the correct behaviour.<br />
(4)<br />
<strong>Elliptic</strong> <strong>relaxation</strong> <strong>for</strong> <strong>near</strong> <strong>wall</strong> <strong>turbulence</strong> <strong>models</strong> – p. 14/22