A spline solution of the incompressible parabolized Navier-Stokes equations in a sheared coordinate stem

A model strong interaction problem for two-dimensional laminar flow is solved numerically. The method makes use of the parabolized vorticity approximation in conjunction with fourth-order accurate polynomial splines to resolve the wall shear layer with a relatively sparse grid. A sheared wall fitted coordinate mapping is used which produces discontinous coefficients in the governing differential equations. These discontinuities are treated in an exact way numerically. The spline-finite difference equations, which result from the discretization, are solved as a coupled system by single line overrelaxation plus a Newton-Raphson iteration to take care of the nonlinearity. Numerical results are presented for six cases consisting of five wall geometries and two Reynolds numbers (10,000 and 100,000). Comparisons are made with potential flow-boundary layer calculations. The method is found to be an efficient way of treating the model strong interaction problem even when thin separated zones are present.