A numerical method for the solution of the Falkner-Skan Equation

A new Reliable Numerical Algorithm Based on the First Kind of Bessel Functions to Solve Prandtl–Blasius Laminar Viscous Flow over a Semi-Infinite Flat Plate

“…Now, we have an approximation functionf N (η) for f (η). As mentioned before, in the Blasius equation, f (0) plays an important role, and Asaithambi [33] found the value of this point to fourteen decimal positions as 0.33205733621519. In Table 1, we represent values of f (0) by different orders of approximation in the BFC method and compare the convergency of them with the results of Liao [36] and Parand and Taghavi [48].…”

“…Later, Howarth [32] solved the Blasius problem numerically and found f (0) = 0.332057. Asaithambi [33] found this number correct to nine decimal positions as 0.332057336. In 2008, Boyd [34] reported 0.33205733621519630 as f (0) in the Blasius equation.…”

Numerical solution of the Falkner Skan Equation by using shooting techniques

“…The Falkner-Skan equation constitutesathirdorder, nonlinear twopoint boundary-valueproblem,no exactanalyticalsolutionisknown.Inthecase of = 0,the Falkner-Skan equationreducestothewell-known Blasiusequationwhichisperhapsoneofthemostfamousequationsoffluiddynamicsandrepresentstheproblemof anincompressiblefluidthatpassesona semi-infinityflatplate.Inthecaseofacceleratingflows( >0),thevelocity profileshavenopointsofinflection,whereasinthecaseofdeceleratedflows [4], [5], [6] ( <0).Physicallyrelevantsolutions existonlyfor-0.19884< ≤ 2 [2].…”

Numerical solution of the Falkner-Skan equation using third-order and high-order-compact finite difference schemes

“…A raft of computational approaches and methodologies have been presented for the solution of the FS equation, see for example Hartree (1937), Asaithambii (1997), Asaithambi (1998Asaithambi ( , 2004bAsaithambi ( , 2005, Abbasbandy (2007), Alizadeh et al (2009) and Zhang and Chen (2009). The most widely used and 'classical' approach to numerical solution is to reduce the boundary value problem to an initial value problem via a shooting method (see Cebeci and Bradshaw (1977); Cebeci and Keller (1971) for a thorough discussion).…”