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Volume 12, Issue 5
Galerkin-Laguerre Spectral Solution of Self-Similar Boundary Layer Problems

F. Auteri & L. Quartapelle

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

Published online: 2012-12

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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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@Article{CiCP-12-1329, author = {}, title = {Galerkin-Laguerre Spectral Solution of Self-Similar Boundary Layer Problems}, journal = {Communications in Computational Physics}, year = {2012}, volume = {12}, number = {5}, pages = {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. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.130411.230911a}, url = {http://global-sci.org/intro/article_detail/cicp/7337.html} }
TY - JOUR T1 - Galerkin-Laguerre Spectral Solution of Self-Similar Boundary Layer Problems JO - Communications in Computational Physics VL - 5 SP - 1329 EP - 1358 PY - 2012 DA - 2012/12 SN - 12 DO - http://doi.org/10.4208/cicp.130411.230911a UR - https://global-sci.org/intro/article_detail/cicp/7337.html KW - AB -

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. 

F. Auteri & L. Quartapelle. (2020). Galerkin-Laguerre Spectral Solution of Self-Similar Boundary Layer Problems. Communications in Computational Physics. 12 (5). 1329-1358. doi:10.4208/cicp.130411.230911a
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