Viscous turbulent flows over high-lift airfoils are investigated by using u
nsteady, incompressible, and compressible Reynolds-averaged Navier-Stokes e
quations under a parallel computing environment. Compressibility effects ca
n be significant in the leading-edge region of high-lift airfoils with a hi
ghly loaded element. Thus, both the Incompressible and compressible computa
tions are performed to study the compressibility effects. The compressible
code involves an upwind-differenced scheme for the convective terms and a l
ower-upper symmetric Gauss-Seidel scheme for temporal integration. The inco
mpressible code with a pseudocompressibility method also adopts the same sc
hemes as the compressible code. Both codes are parallel processed by using
message passing interface programming method and show good parallel speedup
s. Three two equation turbulence models (the standard k-epsilon, the k-omeg
a, and the k-omega shear stress transport model) are carefully evaluated by
computing the flows over single-element and multielement airfoils. The com
pressible and incompressible codes are validated by predicting the flow aro
und the RAE 2822 transonic airfoil and NACA 4412 airfoil, respectively. In
addition, both the incompressible and compressible codes using the Chimera
overlapping grid scheme are used to compute the how over the NLR 7301 airfo
il with Rap and the NASA GAW-1 high-lift airfoil. Compressibility effects o
n surface pressure coefficients, velocity profiles, and skin friction coeff
icients are numerically simulated.