Vortex Flows and Related Numerical Methods II
ESAIM: Proceedings,
Vol. 1, 1996, pp. 577-585
A Spectral Method for Unbounded Flow in a
Cylindrical Coordinate System
Xungang Shi and Lixin Wu
State Key Laboratory for Turbulence Research
Dept. of Mechanics,
Peking University,
Beijing, 100871, P.R. of China
Abstract
Fourier expansions in the radial direction for unbounded flows expressed
in a cylindrical coordinate system are proposed. By appropriate coordinate
mapping and periodic extension in the r direction, periodic
boundary conditions required by Fourier expansions and infinite
differentiability demanded by spectral convergence are established.
Appropriate zero factors for the general Fourier expansions are given at
the axis and at infinity in order to remove the numerical singularity at
r=0 and to satisfy all the boundary conditions. The effectiveness
of these expansions are demonstrated by the simulation of steady
axisymmetrical vortex rings in ideal fluid and the numerical simulation of
the head-on collision of two coaxial, equal and opposite vortex rings.
Vortex Flows and Related
Numerical Methods II
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