The Falkner-Skan equation: Numerical solutions within group invariance theory
type: Item
instance of: scholarly article
title: The Falkner-Skan equation: Numerical solutions within group invariance theory
zbMATH Open document ID: 0835.76023
DOI: 10.1007/BF02575722
author: Riccardo Fazio
published in: Calcolo
publication date: 1996-04-15T00:00:00Z
review text: A model describing the flow of a fluid past a wedge is considered. The governing differential equation is the classical Falkner-Skan equation with relevant boundary conditions. In this problem, a boundary condition at infinity is imposed which is not suitable for numerical treatment. In order to overcome this difficulty, a free boundary formulation of the problem is introduced. The author devises an iterative transformation method that reduces the free boundary formulation to a sequence of initial value problems. Moreover, as far as the value of the wall shear stress is concerned, the author proposes a numerical test on convergence. The usefulness of this approach is illustrated by considering the wall shear stress for the classical Homann and Hiemenz flows. Numerical results obtained are compared with those reported in literature.
Mathematics Subject Classification ID: 76D10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 65L10
zbMATH DE Number: 817319
zbMATH Keywords: flow past wedge
zbMATH Keywords: Homann flow
zbMATH Keywords: Hiemenz flow
zbMATH Keywords: Falkner-Skan equation
zbMATH Keywords: boundary condition at infinity
zbMATH Keywords: free boundary formulation
zbMATH Keywords: iterative transformation method
zbMATH Keywords: initial value problems
zbMATH Keywords: wall shear stress
zbMATH Keywords: convergence
reviewed by: Karel Najzar
describes a project that uses: IMSL Numerical Libraries
MaRDI profile type: Publication
cites work: Exact shooting and eigenparameter problems
cites work: Finite difference solutions of boundary-layer type equations
cites work: Q3259280
cites work: On a differential equation of boundary-layer theory
cites work: Reverse flow solutions of the Falkner‐Skan equation for λ > 1
cites work: Q4479744
cites work: A noniterative transformation method applied to two-point boundary-value problems
cites work: Q4035547
cites work: The Blasius problem formulated as a free boundary value problem
cites work: Q3241447
cites work: An approximation theory for boundary value problems on infinite intervals
cites work: On the Transformation of a Class of Boundary Value Problems into Initial Value Problems for Ordinary Differential Equations
cites work: Transformation of boundary value problems into initial value problems
cites work: Boundary Value Problems on Semi-Infinite Intervals and Their Numerical Solution
cites work: A Theory for the Approximation of Solutions of Boundary Value Problems on Infinite Intervals
cites work: Analysis of Boundary Value Problems on Infinite Intervals
cites work: Q5632263
cites work: Computational methods in engineering boundary value problems
cites work: Chebyshev solution of laminar boundary layer flow
cites work: An estimate of the error due to the truncated boundary in the numerical solution of the Blasius equation
cites work: Q3681199
cites work: On the first differential approximation method in the theory of difference schemes for hyperbolic systems of equations
cites work: Q4403232
cites work: On the differential equations of the simplest boundary-layer problems
description: scientific article; zbMATH DE number 817319