Direct Solution of the VorticityStream Function Ordinary Differential Equations by a Chebyshev Approximation
Abstract
A numerical method for solving the coupled vorticitystream function equations in one dimension with an exact noniterative determination of the vorticity boundary values is presented. The onedimensional form considered can represent the Fourier modes of a twodimensional problem. The equations are separated by replacing the derivative specifications for the stream function at the boundary points with equivalent conditions of an integral type for the vorticity. A spectral approximation by means of Chebyshev polynomials is considered. The numerical properties of the algorithm are investigated against a few analytical examples which demonstrate the accuracy of the proposed method.
 Publication:

Journal of Computational Physics
 Pub Date:
 December 1983
 DOI:
 10.1016/00219991(83)900025
 Bibcode:
 1983JCoPh..52..448D
 Keywords:

 Chebyshev Approximation;
 Computational Fluid Dynamics;
 Differential Equations;
 Stream Functions (Fluids);
 Vorticity Equations;
 Boundary Value Problems;
 Matrices (Mathematics);
 Fluid Mechanics and Heat Transfer