The falkneer-skan equation: Numerical solutions within group invariance theory

Fazio, Riccardo

doi:10.1007/bf02575722

Cited by 36 publications

(47 citation statements)

References 18 publications

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“…It is an initial value method even if we solve a different model for each iteration when the governing differential equation is not invariant under every scaling group of point transformation. Its versatility has been shown by solving several problems of interest: free boundary problems [33,23,28,29], a hyperbolic moving boundary problem [25], the Homann and the Hiemenz flows governed by the Falkner-Skan equation in [26], one-dimensional parabolic moving boundary problems [30], two variants of the Blasius problem [32], namely: a boundary layer problem over moving surfaces, studied first by Klemp and Acrivos [38], and a boundary layer problem with slip boundary condition, that has found application to the study of gas and liquid flows at the micro-scale regime [18,40], parabolic problems on unbounded domains [34] and, recently, see the preprints: [22] parabolic moving boundary problems, and [21] an interesting problem in boundary layer theory: the so-called Sakiadis problem [45,46].…”

Section: Discussionmentioning

confidence: 99%

Blasius problem and Falkner–Skan model: Töpfer’s algorithm and its extension

Fazio

2013

Computers & Fluids

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a b s t r a c tIn this paper, we review the so-called Töpfer 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 Töpfer'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.

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Section: Discussionmentioning

confidence: 99%

Blasius problem and Falkner–Skan model: Töpfer’s algorithm and its extension

Fazio

2013

Computers & Fluids

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“…On the other hand, free BVPs governed by the most general second order differential equation, in normal form, can be solved iteratively by extending a scaling group via the introduction of a numerical parameter so as to recover the original problem as the introduced parameter goes to one, see Fazio [25,26,33,41]. The extension of this iterative TM to problems in boundary layer theory has been considered in [42,43,44,45]. Moreover, a further extension to the sequence of free BVPs obtained by a semi-discretization of parabolic moving boundary problems was repoted in [46].…”

Section: Resultsmentioning

confidence: 99%

Blood Response to Mercury Exposure in Athletic Horse From Messina, Italy

Fazio

Cicero

Piccione

et al. 2020

Journal of Equine Veterinary Science

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“…Now, it is a simple matter to show that the linear system defined by (52) has the unique solution α 1 = α 2 = α 3 = 0. However, as a last word on this topic we can mention an iterative extension of our transformation method that has been developed in [13,14] and successfully applied to the Falkner-Skan model [13,16].…”

Section: Discussionmentioning

confidence: 99%

The non-iterative transformation method

Fazio

2019

International Journal of Non-Linear Mechanics

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The Blasius flow is the idealized flow of a viscous fluid past an infinitesimally thick, semi-infinite flat plate. The definition of a noniterative transformation method for the celebrated Blasius problem is due to Töpfer and dates more than a century ago. Here we define a non-iterative transformation method for Blasius equation with a moving wall, a slip flow condition or a surface gasification. The defined method allows us to deal with classes of problems in boundary layer theory that, depending on a parameter, admit multiple or no solutions. This approach is particularly convenient when the main interest is on the behaviour of the considered models with respect to the involved parameter. The obtained numerical results are found to be in good agreement with those available in literature.

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The falkneer-skan equation: Numerical solutions within group invariance theory

Cited by 36 publications

References 18 publications

Blasius problem and Falkner–Skan model: Töpfer’s algorithm and its extension

Blasius problem and Falkner–Skan model: Töpfer’s algorithm and its extension

Blood Response to Mercury Exposure in Athletic Horse From Messina, Italy

The non-iterative transformation method

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