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A Legendre spectral element method for eigenvalues in hydrodynamic stability
Authors
A.A. Hill
Amili
+20 more
B. Straughan
Brown
Davies
Dongarra
Drazin
Gardner
Golub
Greenberg
Greenberg
Greenberg
Haidvogel
Ivansson
Kirchner
Lehoucq
Nield
Nield
Shen
Sneddon
Straughan
Straughan
Publication date
15 August 2006
Publisher
'Elsevier BV'
Doi
Cite
Abstract
A Legendre polynomial-based spectral technique is developed to be applicable to solving eigenvalue problems which arise in linear and nonlinear stability questions in porous media, and other areas of Continuum Mechanics. The matrices produced in the corresponding generalised eigenvalue problem are sparse, reducing the computational and storage costs, where the superimposition of boundary conditions is not needed due to the structure of the method. Several eigenvalue problems are solved using both the Legendre polynomial-based and Chebyshev tau techniques. In each example, the Legendre polynomial-based spectral technique converges to the required accuracy utilising less polynomials than the Chebyshev tau method, and with much greater computational efficiency. © 2005 Elsevier B.V. All rights reserved
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