A spectral method for unbounded flow in a cylindrical coordinate system

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.