Computation of high speed turbulent boundary-layer flows using the k-epsilon turbulence model

The applicability of a finite element-differential method to the computation of steady two-dimensional low-speed, transonic, and supersonic turbulent boundary-layer flows is investigated. The turbulence model chosen for the Reynolds shear stress and turbulent heat flux is the k-epsilon two-equation model. Calculations are extended up to the wall, and the exact values of the dependent variables at the wall are used asboundary conditions. A number of transformations are carried out and the assumed solutions at a longitudinal station are represented by complete 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 results of the computations reveal that the method is highly accurate and efficient. Furthermore, the accuracy and applicability of the k-epsilon turbulence model are examined by comparing results of the computations with experimental data. The agreement is very good.