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

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

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. 

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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

Keywords:   

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