Symbolic-numeric stability investigations of Jameson's schemes for the thin-layer Navier-Stokes equations

  • Authors:

  • V. G. Ganzha;E. V. Vorozhtsov;J. Boers;J. A. van Hulzen

  • Affiliations:

  • Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk 630090, Russia and GH-Universität, Kassel;Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk 630090, Russia;Department of Computer Sciences, University of Twente, P. O. Box 217, 7500AE Enschede, The Netherlands;Department of Computer Sciences, University of Twente, P. O. Box 217, 7500AE Enschede, The Netherlands

  • Venue:
  • ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
  • Year:
  • 1994

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Abstract

The Navier-Stokes equations governing the three-dimensional flows of viscous, compressible, heat-conducting gas and augmented by turbulence modeling present the most realistic model for gas flows around the elements of aircraft configurations. We study the stability of one of the Jameson's schemes of 1981, which approximates the set of five Navier-Stokes equations completed by the turbulence model of Baldwin and Lomax. The analysis procedure implements the check-up of the necessary von Neumann stability criterion. It is shown with the aid of the proposed symbolic-numeric strategy that the physical viscosity terms in the Navier-Stokes equations have a dominant effect on the sizes of the stability region in comparison with the heat conduction terms. It turns out that the consideration of turbulence with the aid of eddy viscosity model of Baldwin and Lomax has an insignificant effect on the size of the necessary stability region.