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Fundamental Stokes eigenmodes in the square: which expansion is more accurate, Chebyshev or Reid-Harris?

Authors
  • Leriche, E.1
  • Labrosse, G.1
  • 1 Ecole Polytechnique Fédérale de Lausanne, Laboratoire d'Ingénierie Numérique, Institut des Sciences de l'Energie, Faculté des Sciences et Techniques de l'Ingénieur, Ecublens, CH-1015, Switzerland , Ecublens
Type
Published Article
Journal
Numerical Algorithms
Publisher
Springer US
Publication Date
Mar 01, 2005
Volume
38
Issue
1-3
Pages
111–131
Identifiers
DOI: 10.1007/BF02810619
Source
Springer Nature
Keywords
License
Yellow

Abstract

The well-known Reid-Harris expansions, applied to the stream function formulation, and the projection-diffusion Chebyshev Stokes solver, in primitive variables, are used to compute the fundamental Stokes eigenmodes of each of the symmetry families characterizing the Stokes solutions in the square. The numerical accuracy of both methods, applied with several discretizations, are compared, for both the eigenvalues and the main features of the corresponding eigenmodes. The Chebyshev approach is by far the most efficient, even though the associated solver does not provide a divergence free velocity but asymptotically.

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