Abstract
A suitable restatement of the Navier-Stokes equations provides a new tool for their numerical approximation. Spectral methods are used in the experiments to show the effectiveness of the technique. The main achievement is the total elimination of spurious modes.
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References
Bernardi, C., and Maday, Y. (1992).Approximations Spectrales de Problèmes aux Limites Elliptiques, Mathematiques and Applications 10, Springer-Verlag, Paris.
Boyd, J. P. (1989).Chebyshev and Fourier Spectral Methods, Lecture Notes in Engineering, Springer, New York.
Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A. (1988).Spectral Methods in Fluid Dynamics, Springer Series in Computational Physics, Springer-Verlag, New York.
Funaro, D. (1992a).Polynomial Approximation of Differential Equations, Lecture Notes in Physics, 8, Springer-Verlag, Heidelberg.
Funaro, D. (1992b). A New Scheme for the Approximation of Advection-Diffusion Equations by Collocation,SIAM J. Numer. Anal. 30, 1664–1676.
Ghia, U., Ghia, K. N., and Shin, C. T. (1982). High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method,J. Comput. Phys. 48, 387–411.
Gottlieb, D., and Orszag, S. A. (1977).Numerical Analysis of Spectral Methods, Theory and Applications, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia.
Gresho P. M. (1991). Some current CFD issues relevant to the incompressible Navier-Stokes equations,Computer Methods in Appl. Mech. and Eng. 87, 201–252.
Jiang, C. B., and Kawahara, M. (1993). The analysis of unsteady incompressible flows by a three-step finite element method,Int. J. for Numerical Methods in Fluids,16, 793–811.
Lions, J. L., and Magenes, E. (1972).Non-Homogeneous Boundary Value Problems and Applications, Springer-Verlag, New York.
Montigny-Rannou, F., and Morchoisne, Y. (1978). A spectral method with staggered grid for incompressible Navier-Stokes Equations,Int. J. for Numerical Methods in Fluids 7, 175–189.
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This work has been partially supported by I.A.N.-CNR, Pavia.
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Boffi, D., Funaro, D. An alternative approach to the analysis and the approximation of the Navier-Stokes equations. J Sci Comput 9, 1–16 (1994). https://doi.org/10.1007/BF01573175
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DOI: https://doi.org/10.1007/BF01573175