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

摘要

A new highly accurate algorithm for the solution of the Falkner-Skan equationof boundary layer theory is presented. The algorithm, based on a Maclaurinseries representation, finds its coefficients from recurrence. In addition,Wynn-epsilon convergence acceleration and continuous analytical continuationenable an accurate evaluation. The most accurate skin friction coefficients(shooting angle) to date are presented along with comparisons to past andpresent values found in the literature. The algorithm, coded in FORTRAN, usesneither enhanced precision arithmetic beyond quadruple precision nor computeralgebra to achieve results in a timely fashion. Key Words: Falkner-Skan flow; Blasius flow; Wynn-epsilon acceleration;Romberg acceleration; Continuous analytical continuation