Double Fourier series on a sphere: Applications to elliptic and vorticity equations

DOI10.1006/jcph.1999.6385zbMath0961.76062OpenAlexW2024531971MaRDI QIDQ1971403

Hyeong-Bin Cheong

Publication date: 5 June 2001

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

Full work available at URL: https://doi.org/10.1006/jcph.1999.6385

zbMATH Keywords

double Fourier seriesorthogonal basis functionsPoisson equationvorticity equationsine seriesrotating Rossby-Haurwitz wavesspherical harmonics filters

Mathematics Subject Classification ID

Spectral methods applied to problems in fluid mechanics (76M22) General theory of rotating fluids (76U05)

Related Items

A semi-Lagrangian double Fourier method for the shallow water equations on the sphere., Interpolation on the cubed sphere with spherical harmonics, Fourth-Order Time-Stepping For Stiff PDEs On The Sphere, A generalization of the Riesz-Fischer theorem and linear summability methods, Further study on the high-order double-Fourier-series spectral filtering on a sphere., An efficient implementation of a high-order filter for a cubed-sphere spectral element model, Application of double Fourier series to the shallow water equations on a sphere, Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations, Computing with Functions in Spherical and Polar Geometries I. The Sphere, A performance comparison of associated Legendre projections, Fast direct solvers for Poisson equation on 2D polar and spherical geometries, Use of a double Fourier series for three-dimensional shape representation, A new series representation derived for periodic functions that can be represented by the Fourier series, A fast solver of the shallow water equations on a sphere using a combined compact difference scheme., High-order harmonic spectral filter with the double Fourier series on a sphere, An optimization of the icosahedral grid modified by spring dynamics.

Uses Software

• Mathematica
• chammp

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The spectral element method for the shallow water equations on the sphere
• Multigrid methods for two- and three-dimensional Poisson-type equations on the sphere
• Computation of spherical harmonic expansion coefficients via FFT's
• Spectral algorithms for vector elliptic equations in a spherical gap
• A test of a modified algorithm for computing spherical harmonic coefficients using an FFT
• A standard test set for numerical approximations to the shallow water equations in spherical geometry
• Fast shallow-water equation solvers in latitude-longitude coordinates
• The direct solution of the discrete Poisson equation on the surface of a sphere
• Spectral transform solutions to the shallow water test set
• On the Spectral Approximation of Discrete Scalar and Vector Functions on the Sphere