An implicit spectral solver for the compressible Navier-Stokes equations in complex domains

  • Renzo Arina
  • Fabrizio Ramella
3. Numerical Methods for Aerodynamic Design d) Euler/Navier-Stokes Equations
Part of the Lecture Notes in Physics book series (LNP, volume 453)


A spectral collocation method for the compressible Navier-Stokes equations written in generalized coordinates is presented. The method is combined with an implicit time integration technique based on nonlinear Krylov methods (GMRES) with a finite volume preconditioning.


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  1. 1.
    Arina R., Canuto C. (1993): “A Self-Adaptive Domain Decomposition for the Viscous/Inviscid Coupling. I — Burgers Equation”, J. Comput. Phys., Vol. 105, pp. 290–300CrossRefGoogle Scholar
  2. 2.
    Arina R., Canuto C. (1994): “A χ-Formulation of the Viscous-Inviscid Domain Decomposition for the Euler/Navier-Stokes Equations”, in Proc. of the 7th Int. Conf. Domain Decomposition Methods in Scientific and Engineering Computing, ed. by D. Keyes and J. Xu (Contemporary Mathematics, AMS)Google Scholar
  3. 3.
    Canuto C., Hussaini M.Y., Quarteroni A., Zang T.A. (1987): “Spectral Methods in Fluid Dynamics”, Springer-VerlagGoogle Scholar
  4. 4.
    Coutanceau M., Bouard R. (1977): “Experimental Determination of the Main Features of the Viscous Flow in the Wake of a Circular Cylinder in Uniform Translation. Part I. Steady Flow”, J. Fluid Mech., Vol. 79-2, pp. 231–256Google Scholar
  5. 5.
    Brown P.N., Saad Y. (1990): “Hybrid Krylov Methods for Nonlinear Systems of Equations”, SIAM J. Sci. Stat. Comput., Vol.11, 3, pp 450–481CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Renzo Arina
    • 1
  • Fabrizio Ramella
    • 1
  1. 1.Dipartimento di Ingegneria AerospazialePolitecnico di TorinoTorinoItaly

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