CALCULATION OF COMPRESSIBLE BOUNDARY-LAYERS BY A HYBRID FINITE-ELEMENT METHOD

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).