Year: 2012
Communications in Computational Physics, Vol. 12 (2012), Iss. 5 : pp. 1329–1358
Abstract
In this work the Laguerre basis for the biharmonic equation introduced by Jie Shen is employed in the spectral solution of self-similar problems of the boundary layer theory. An original Petrov-Galerkin formulation of the Falkner-Skan equation is presented which is based on a judiciously chosen special basis function to capture the asymptotic behaviour of the unknown. A spectral method of remarkable simplicity is obtained for computing Falkner-Skan-Cooke boundary layer flows. The accuracy and efficiency of the Laguerre spectral approximation is illustrated by determining the linear stability of nonseparated and separated flows according to the Orr-Sommerfeld equation. The pentadiagonal matrices representing the derivative operators are explicitly provided in an Appendix to aid an immediate implementation of the spectral solution algorithms.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.130411.230911a
Communications in Computational Physics, Vol. 12 (2012), Iss. 5 : pp. 1329–1358
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
-
Finite difference schemes on quasi-uniform grids for BVPs on infinite intervals
Fazio, Riccardo | Jannelli, AlessandraJournal of Computational and Applied Mathematics, Vol. 269 (2014), Iss. P.14
https://doi.org/10.1016/j.cam.2014.02.036 [Citations: 22] -
The iterative transformation method
Fazio, Riccardo
International Journal of Non-Linear Mechanics, Vol. 116 (2019), Iss. P.181
https://doi.org/10.1016/j.ijnonlinmec.2019.06.011 [Citations: 5] -
Revisiting Blasius Flow by Fixed Point Method
Xu, Ding | Xu, Jinglei | Xie, GongnanAbstract and Applied Analysis, Vol. 2014 (2014), Iss. P.1
https://doi.org/10.1155/2014/953151 [Citations: 0] -
Blasius problem and Falkner–Skan model: Töpfer’s algorithm and its extension
Fazio, Riccardo
Computers & Fluids, Vol. 73 (2013), Iss. P.202
https://doi.org/10.1016/j.compfluid.2012.12.012 [Citations: 21] -
Barycentric rational collocation method for semi-infinite domain problems
Li, Jin
AIMS Mathematics, Vol. 8 (2023), Iss. 4 P.8756
https://doi.org/10.3934/math.2023439 [Citations: 2] -
Application of fixed point method to obtain semi-analytical solution to Blasius flow and its variation
Xu, Ding | Guo, XinApplied Mathematics and Computation, Vol. 224 (2013), Iss. P.791
https://doi.org/10.1016/j.amc.2013.08.066 [Citations: 7] -
Existence and Uniqueness of BVPs Defined on Semi-Infinite Intervals: Insight from the Iterative Transformation Method
Fazio, Riccardo
Mathematical and Computational Applications, Vol. 26 (2021), Iss. 1 P.18
https://doi.org/10.3390/mca26010018 [Citations: 0]