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

作　　者：F.Auteri L.Quartapelle 

机构地区：[1]Politecnico di Milano,Dipartimento di Ingegneria Aerospaziale,Via La Masa 34,20156Milano,Italy

出　　处：《Communications in Computational Physics》2012年第10期1329-1358,共30页计算物理通讯（英文）

摘　　要：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.

关 键 词：Laguerre polynomials semi-infinite interval boundary layer theory Falkner-Skan equation Cooke equation Orr-Sommerfeld equation linear stability of parallel flows 

分 类 号：O17[理学—数学]