Synthetic Inflow Condition for Large Eddy Simulation (Synthetic - KTH

and
2.3 Numerical Method
CHAPTER 2. BACKGROUND
C 2 m ≈ 10.6C 2 s ≈ 0.58 (2.20)
Among the important number of numerical methods simulating the viscous fluid,
some of them will be presented on this section taken from the Ref.[6]. But firstly
we need to define the hypotheses used for external aerodynamics which are the
followings:
• The air is considered as being a perfect gas
• The kinetic viscosity of the air depends only on the temperature. Exemple:
the law of Sutherland
µ
µ∞
� �3/2 T T∞ + S1
=
T∞ T + S1
(2.21)
Where T is the temperature, µ∞ the kinetic viscosity for the reference temperature
T∞ and S1 a constant (110 · 3 ž for air).
• The conductive heat flux −→ q is given by the Fourier law
−→ q = −λ −−→
gradT (2.22)
With these hypotheses, the Navier-Stokes equations are written:
∂ −→ W
∂t
With −→ ⎜
W the vector of the conservative variables ⎜
⎝
+ divF = 0 (2.23)
⎛
ρ
ρu
ρv
ρw
ρE
⎞
⎟ where E is the kinetic
⎟
⎠
energy, F the flux matrice, F equals to F = f − fv where f is the matrice of the
convectiv flux and fv is the matrix of the viscous flux.
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