Numerical Algorithms

, Volume 38, Issue 1–3, pp 155–172 | Cite as

Application of the least-squares spectral element method using Chebyshev polynomials to solve the incompressible Navier-Stokes equations

  • Michael M. J. Proot
  • Marc I. Gerritsma
Section II: Spectral Methods
  • 139 Downloads

Abstract

In this paper the extension of the Legendre least-squares spectral element formulation to Chebyshev polynomials will be explained. The new method will be applied to the incompressible Navier-Stokes equations and numerical results, obtained for the lid-driven cavity flow at Reynolds numbers varying between 1000 and 7500, will be compared with the commonly used benchmark results. The new results reveal that the least-squares spectral element formulations based on the Legendre and Chebyshev Gauss-Lobatto Lagrange interpolating polynomials are equally accurate.

Keywords

Navier-Stokes equations least-squares spectral element method Chebyshev polynomials 

AMS subject classification

41A50 65K10 65N35 65Y20 76D05 

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Copyright information

© Springer 2005

Authors and Affiliations

  • Michael M. J. Proot
    • 1
  • Marc I. Gerritsma
    • 1
  1. 1.Aerospace EngineeringDelft University of TechnologyDelftThe Netherlands

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