A finite element-differential method for compressible turbulent boundary-layer flows

The applicability of a finite element differential method to the computation of steady two dimensional compressible turbulent boundary layer flows is investigated. The turbulence model chosen for the Reynolds shear stress and turbulent heat flux is the k-sigma two equation model. Calculations are extended up to the wall and the exact values of the dependent variables at the wall are used as boundary conditions. A number of well justified transformations are carried out and the assumed solutions at a longitudinal station are represented by classical cubic spline functions. In essence, the method converts the governing partial differential equations into a system of ordinary differential equations by a weighted residuals method and invokes an ordinary differential equation solver for the numerical integration of the reduced initial value problem. The accuracy and efficiency of the numerical method are investigated for low speed as well as supersonic flows over a flat plate.