Numerical solutions of the classical Blasius flat-plate problem. (English) Zbl 1077.76023

This paper presents a numerical study of the nonlinear differential equation \(af'''+ff''=0\), where a prime denotes differentiation with respect to the similarity variable \(\eta\), and \(a\) is a parameter. For \(a=1\) and \(a=2\) this equation is a form of the Blasius relation for the flat-plate flow in fluid mechanics. Several numerical solution are obtained using a Runge-Kutta algorithm for high-order initial value problems for \(1\leq a\leq 2\).


76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76M20 Finite difference methods applied to problems in fluid mechanics
Full Text: DOI


[1] Howarth, L., On the solution of the laminar boundary layer equations, Proc. Roy. Soc. London A, 164, 547-579 (1938) · JFM 64.1452.01
[2] Lock, R. C., The velocity distribution in the laminar boundary layer between parallel streams, Quart. J. Mech. Appl. Math., 4, 42-63 (1951) · Zbl 0042.43002
[3] Lock, R. C., Hydrodynamic stability of the flow in the laminar boundary layer between parallel streams, Proc. Cambridge Phil. Soc., 50, 105-124 (1954) · Zbl 0055.19002
[4] Potter, O. E., Mass transfer between co-current fluid streams and boundary layer solutions, Chem. Eng. Sci., 6, 170-182 (1957)
[5] Abussita, A. M.M., A note on a certain boundary-layer equation, Appl. Math. Comp., 64, 73-77 (1994) · Zbl 0811.34013
[6] Asaithambi, A., A finite-difference method for the Falkner-Skan equation, Appl. Math. Comp., 92, 135-141 (1998) · Zbl 0973.76581
[7] Wang, L., A new algorithm for solving classical Blasius equation, Appl. Math. Comp., 157, 1-9 (2004) · Zbl 1108.65085
[8] Cortell, R., Application of the fourth-order Runge-Kutta method for the solution of high-order general initial value problems, Comput. & Struct., 49, 897-900 (1993) · Zbl 0799.76052
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.