On Numerical Methods for a Boundary Layer on a Body of Revolution

Abstract

Abstract The flow of a viscous incompressible uid past a body of revolution with aparabolic profile when the stream is parallel to its axis falls into a class of problems that exhibit boundary layers. This problem does not have solutions in closed form, and is modeled by boundary-layer equations. Using a self-similar approach based on a Blasius series expansion (up to two terms), the boundary-layer equations can be reduced to a Blasius-type problem consisting of a system of three 3rd order ordinary differential equations on a semi-infinite interval. Numerical methods need to be employed to attain the solutions of these equations and their derivatives, which are required for the computation of the velocity components, on a finite domain with accuracy independent of the viscosity v, which can take arbitrary values from the interval (0; 1]. Numerical methods for which the accuracy of the velocity components depend on the number of mesh points N, used to solve the Blasius-type problem, and do not depend on the viscosity v, are referred to as robust methods. To construct a robust numerical method we reduce the original problem on a semi-infinite axis to a problem on the finite interval [0;K], where K = K(N) = lnN. Employing numerical experiments, we justify that the constructed numerical method is parameter robust.