Commun. Comput. Phys., 12 (2012), pp. 1329-1358.


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

F. Auteri 1*, L. Quartapelle 1

1 Politecnico di Milano, Dipartimento di Ingegneria Aerospaziale, Via La Masa 34, 20156 Milano, Italy.

Received 13 April 2011; Accepted (in revised version) 23 September 2011
Available online 8 May 2012
doi:10.4208/cicp.130411.230911a

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.

AMS subject classifications: 34L16, 34L30, 65L60, 76E05

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Key words: Laguerre polynomials, semi-infinite interval, boundary layer theory, Falkner-Skan equation, Cooke equation, Orr-Sommerfeld equation, linear stability of parallel flows.

*Corresponding author.
Email: auteri@aero.polimi.it (F. Auteri)
 

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