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Stokes eigenmodes in cubic domain: their symmetry properties

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Abstract

This paper is dedicated to a detailed analysis of the symmetry properties of the cubical Stokes eigenmodes and to the numerical verification of its predictions. These modes are computed numerically by using two different Stokes solvers, the Projection-Diffusion Chebyshev spectral method and a lattice Boltzmann approach. They distribute themselves into 10 symmetry families, 2 families of singlets, 2 families of doublets and 6 families of triplets. The existence of the singlets, doublets and triplets is directly related to the fact that two different bases can be constructed for describing the cyclic-permutation state operator. The singlets and doublets are associated with one of these bases, and they are therefore generated together, the triplets being associated with the other basis.

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Correspondence to G. Labrosse.

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Communicated by Tim Colonius.

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Labrosse, G., Leriche, E. & Lallemand, P. Stokes eigenmodes in cubic domain: their symmetry properties. Theor. Comput. Fluid Dyn. 28, 335–356 (2014). https://doi.org/10.1007/s00162-014-0318-5

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