1997
DOI: 10.1006/jcph.1997.5747
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A Spectral Model for Two-Dimensional Incompressible Fluid Flow in a Circular Basin

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Cited by 33 publications
(42 citation statements)
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“…For rectangular blocks, Cheybyshev polynomials are used along each axis; for a spherical shell (i.e., where the center is excised), spherical harmonics in angles and Chebyshev polynomials in radius are employed; and for an open cylinder (i.e., with the region near the axis excised), Chebyshev polynomials and a Fourier series. For full spheres and filled cylinders, multidimensional basis functions respecting the continuity conditions at the origin/ axis are employed [74,75]. For more details see [72].…”
Section: A Evolution Codementioning
confidence: 99%
“…For rectangular blocks, Cheybyshev polynomials are used along each axis; for a spherical shell (i.e., where the center is excised), spherical harmonics in angles and Chebyshev polynomials in radius are employed; and for an open cylinder (i.e., with the region near the axis excised), Chebyshev polynomials and a Fourier series. For full spheres and filled cylinders, multidimensional basis functions respecting the continuity conditions at the origin/ axis are employed [74,75]. For more details see [72].…”
Section: A Evolution Codementioning
confidence: 99%
“…We also considered a second basis, basis B, which is essentially the basis proposed by Matsushima and Marcus [29] and Verkley [34], and satisfies the full pole condition; see [22] for more details.…”
Section: Discrete Spaces and Approximation Resultsmentioning
confidence: 99%
“…: 34) where the discretisation matrices are as in (3.11) and I q is the N D × N D identity matrix. Equation (3.32) can be written in tensor product matrix form also:…”
Section: Quadrature Hypothesis 2 (Qh2) the Quadrature Rule Satisfiesmentioning
confidence: 99%
“…This is, effectively, the basis proposed by Matsushima and Marcus [29] and Verkley [34], except that, as above, we ensure that the functions are zero at r = 1 and that they are π-periodic in θ:…”
Section: Implementation Of the Numerical Methodsmentioning
confidence: 99%