An application of one-sided Jacobi polynomials for spectral modeling of vector fields in polar coordinates

DOI10.1016/j.jcp.2009.06.017zbMath1175.65120OpenAlexW2050361351MaRDI QIDQ843456

T. Sakai, Larry G. Redekopp

Publication date: 12 October 2009

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2009.06.017

zbMATH Keywords

numerical examplesJacobi polynomialspolar coordinatesspectral methodsvector functionscoordinate singularityevolution equations of hyperbolic-typeFourier exponentialsinternal Kelvin and Poincaré wavesradial expansion functionstau-methodvector field equations

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Spectral methods applied to problems in fluid mechanics (76M22) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) First-order hyperbolic equations (35L02)

Related Items (7)

An optimal Galerkin scheme to solve the kinematic dynamo eigenvalue problem in a full sphere ⋮ Tensor calculus in polar coordinates using Jacobi polynomials ⋮ Tensor calculus in spherical coordinates using Jacobi polynomials. I: Mathematical analysis and derivations ⋮ Orthogonality for a class of generalised Jacobi polynomial P^α,β_ν(x) ⋮ A weakly nonlinear evolution model for long internal waves in a large lake ⋮ Elliptical instability of the Moore–Saffman model for a trailing wingtip vortex ⋮ Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan-Shepp ridge polynomials, Chebyshev-Fourier series, cylindrical Robert functions, Bessel-Fourier expansions, square-to-disk conformal mapping and radial basis functions

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