Highly Accurate Solutions of the Blasius and Falkner-Skan Boundary Layer Equations via Convergence Acceleration

Abstract

A new highly accurate algorithm for the solution of the Falkner-Skan equation of boundary layer theory is presented. The algorithm, based on a Maclaurin series representation, finds its coefficients from recurrence. In addition, Wynn-epsilon convergence acceleration and continuous analytical continuation enable an accurate evaluation. The most accurate skin friction coefficients (shooting angle) to date are presented along with comparisons to past and present values found in the literature. The algorithm, coded in FORTRAN, uses neither enhanced precision arithmetic beyond quadruple precision nor computer algebra to achieve results in a timely fashion. Key Words: Falkner-Skan flow; Blasius flow; Wynn-epsilon acceleration; Romberg acceleration; Continuous analytical continuation