In this paper, we review the so-called Toepfer algorithm that allows us to find a non-iterative numerical solution of the Blasius problem, by solving a related initial value problem and applying a scaling transformation. Moreover, we remark that the applicability of this algorithm can be extended to any given problem, provided that the governing equation and the initial conditions are invariant under a scaling group of point transformations and that the asymptotic boundary condition is non-homogeneous. Then, we describe an iterative extension of Toepfer's algorithm that can be applied to a general class of problems. Finally, we solve the Falkner-Skan model, for values of the parameter where multiple solutions are admitted, and report original numerical results, in particular data related to the famous reverse flow solutions by Stewartson. The numerical data obtained by the extended algorithm are in good agreement with those obtained in previous studies.

Blasius Problem and Falkner-Skan model: Topfer's Algorithm and its Extension

FAZIO, Riccardo
2013-01-01

Abstract

In this paper, we review the so-called Toepfer algorithm that allows us to find a non-iterative numerical solution of the Blasius problem, by solving a related initial value problem and applying a scaling transformation. Moreover, we remark that the applicability of this algorithm can be extended to any given problem, provided that the governing equation and the initial conditions are invariant under a scaling group of point transformations and that the asymptotic boundary condition is non-homogeneous. Then, we describe an iterative extension of Toepfer's algorithm that can be applied to a general class of problems. Finally, we solve the Falkner-Skan model, for values of the parameter where multiple solutions are admitted, and report original numerical results, in particular data related to the famous reverse flow solutions by Stewartson. The numerical data obtained by the extended algorithm are in good agreement with those obtained in previous studies.
2013
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/2431821
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