NIFS-636

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Author(s):

A. Kageyama and S. Kida

Title:

A Spectral Method in Spherical Coordinates with Coordinate Singularity at the Origin

Date of publication:

Apr. 2000

Key words:

spectral method, coordinate singularity, spherical coordinates, pole condition

Abstract:

A new spectral method in the spherical coordinate system with a coordinate singularity at the origin is proposed. An analytical condition of all spectral modes is satisfied exactly at the origin. Dependent functions are expanded in terms of Chebyshev polynomials of even order in radial direction. Unnecessarily increased resolution near the origin as well as the restriction of severe time step are avoided automatically. Numerical accuracy is confirmed by applying it to a free decay of magnetic field in spherical geometry. This method is applicable to quadratic nonlinear problems.

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