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A Spectral Method for Unbounded Domains

✍ Scribed by T. Matsushima; P.S. Marcus

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
522 KB
Volume
137
Category
Article
ISSN
0021-9991

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✦ Synopsis

A spectral method for an unbounded domain is presented. Rational basis functions, which are algebraically mapped Legendre functions, are used for expansion in the radial direction of polar coordinates (r, ) or (r, , z). They satisfy the pole condition exactly at the coordinate singularity and their behavior as r Ǟ ȍ is suitable for expanding smooth functions which decay algebraically or exponentially as r Ǟ ȍ. The method is not stiff when it is applied to initial value problems despite the presence of the coordinate singularity. Solenoidal vector fields are treated efficiently by the toroidal and poloidal decomposition which reduces the number of dependent variables from 3 to 2. Examples include the computation of vortex dynamics in two and three dimensions.

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