Preliminary results are presented of a finite element/finite differenc
e method (semidiscrete Galerkin or SDG method) used to calculate compr
essible turbulent boundary-layer flow about airfoils, in which the gro
up finite element scheme is applied to the Dorodnitsyn formulation of
the boundary-layer equations. The finite element discretization across
the layer yields a system of first-order ordinary differential equati
ons in the streamwise direction. Linear elements are chosen for comput
ational efficiency, while also providing adequate accuracy. The stream
wise derivatives are solved by an implicit and noniterative finite dif
ference marching scheme. Results are presented for low-speed laminar n
ow past a circular cylinder and past an NACA 0012 airfoil at zero angl
e of attack at a Mach number of 0.5. Also shown are results for compre
ssible flow past a flat plate for a Mach number range of 0-10 and resu
lts for incompressible turbulent flow past a flat plate. All numerical
solutions assume an attached boundary layer. The semidiscrete Galerki
n method promises to be fast, accurate, and computationally efficient.
The resulting computer code can also be applied to any smoothly conne
cted airfoil shape without modification and can be coupled to any exis
ting inviscid flow solver (portability).