Application of the least-squares spectral element method using Chebyshev polynomials to solve the incompressible Navier-Stokes equations
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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.
KeywordsNavier-Stokes equations least-squares spectral element method Chebyshev polynomials
AMS subject classification41A50 65K10 65N35 65Y20 76D05
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- C. Bernardi and Y. Maday,Approximations spectrale de problèmes aux limites élliptiques (Springer-Verlag, 1992).Google Scholar
- W. Couzy, Spectral element discretization of the unsteady Navier-Stokes equations and its iterative solution on parallel computers, PhD thesis, École Polytechnique Fédérale de Lausanne (1995).Google Scholar
- R.D. Henderson, Adaptive spectral element methods for turbulence and transition, in:High-order Methods for Computational Physics, Leccture Notes in Computer Science, Vol. 9, (Springer, New York, 1999) pp. 225–324.Google Scholar
- B-N. Jiang,The Least-Squares Finite Element Method, Theory and Applications in Computational Fluid Dynamics and Electromagnetics (Springer, 1998).Google Scholar
- G.E. Karniadakis and S.J. Sherwin,Spectral/hp Element Methods for CFD (Oxford University Press, 1999).Google Scholar
- Y. Maday and A.T. Patera, Spectral element methods for the incompressible Navier-Stokes equations, in:State-of-the-Art Surveys in Computational Mechanics, eds. A.K. Noorr and J.T. Oden (1989). pp. 71–143.Google Scholar
- J.C. Mason and D.C. Handscomb,Chebyshev Polynomials (Chapman and Hall/CRC, 2003).Google Scholar
- M.M.J. Proot, The least-squares spectral element method, PhD thesis, Delft University of Technology (2003).Google Scholar
- M.M.J. Proot and M.I. Gerritsma, A least-squares spectral element formulation for the Stokes problem, J. Sci. Comput. 17(1–3) (2002) 311–322.Google Scholar