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.
|Titolo:||Galerkin-Laguerre Spectral Solution of Self-Similar Boundary Layer Problems|
|Data di pubblicazione:||2012|
|Appare nelle tipologie:||01.1 Articolo in Rivista|
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|Auteri_Quartapelle_CiCP_12_2012_1329_1358.pdf||Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)||Accesso riservato||Accesso riservato|