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Galerkin-Laguerre Spectral Solution of Self-Similar Boundary Layer Problems

Published online by Cambridge University Press:  20 August 2015

F. Auteri  and
L. Quartapelle
F. Auteri*
Affiliation:
Politecnico di Milano, Dipartimento di Ingegneria Aerospaziale, Via La Masa 34, 20156 Milano, Italy
L. Quartapelle
Affiliation:
Politecnico di Milano, Dipartimento di Ingegneria Aerospaziale, Via La Masa 34, 20156 Milano, Italy
*
Corresponding author.Email address:auteri@aero.polimi.it
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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.

Keywords

34L1634L3065L6076E05Laguerre polynomialssemi-infinite intervalboundary layer theoryFalkner-Skan equationCooke equationOrr-Sommerfeld equationlinear stability of parallel flows
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 5 , November 2012 , pp. 1329 - 1358
Copyright
Copyright © Global Science Press Limited 2012

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