A Chebyshev Method for the Solution of Boundary Value Problems
Abstract
An expansion procedure using the Chebyshev polynomials as base functions is proposed. The method yields more accurate results than either of the Galerkin or tau methods as indicated from solving the OrrSommerfeld equation for both the plane Poiseuille flow and the Blasius velocity profile. The Chebyshev approximation is also applied to resolve the radial dependence of the flow field for a circular cylinder or a sphere in a uniform flow.
 Publication:

Journal of Computational Physics
 Pub Date:
 March 1984
 DOI:
 10.1016/00219991(84)900706
 Bibcode:
 1984JCoPh..53..443Z
 Keywords:

 Boundary Value Problems;
 Chebyshev Approximation;
 Computational Fluid Dynamics;
 Flow Stability;
 Galerkin Method;
 Uniform Flow;
 Accuracy;
 Blasius Equation;
 Circular Cylinders;
 Flow Distribution;
 Incompressible Flow;
 Laminar Flow;
 NavierStokes Equation;
 OrrSommerfeld Equations;
 Fluid Mechanics and Heat Transfer