An application of homotopy analysis to the viscous flow past a circular cylinder
type: Item
instance of: scholarly article
title: An application of homotopy analysis to the viscous flow past a circular cylinder
zbMATH Open document ID: 1417.76033
DOI: 10.1155/2009/524307
author: E. O. Ifidon
published in: Journal of Applied Mathematics
publication date: 2009-11-10T00:00:00Z
review text: Summary: We consider the application of a new analytic method based on homotopy analysis to the solution of the steady flow of a viscous incompressible fluid past a fixed circular cylinder. The solutions obtained using this method produce some interesting results. For instance, an analytic verification of the critical Reynolds number \(R_{d}\) for which a standing vortex first appears behind the cylinder is given for the first time and found to be \(R_{d}\preccurlyeq 2.4\). Since these values of the critical Reynolds number are beyond the range of validity of Oseen theory, no analytic verification of this value had previously been given. As a check on the accuracy of the solutions, the calculated drag coefficients at 6th-order approximation are found to agree reasonably well with experimental measurements for \(R_{d}\simeq 30\) which is considerably larger than the \(R_{d}\simeq 1\) results currently available using other analytic techniques. This buttresses the usefulness of the homotopy analysis method (HAM) as an important tool in solving highly nonlinear problems.
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 65N99
Mathematics Subject Classification ID: 76D09
zbMATH DE Number: 5628312
Wikidata QID: Q58648639
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2009/524307
OpenAlex ID: W1986855885
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description: scientific article; zbMATH DE number 5628312