Advertisement

Stability analysis for a family of space one dimensional convection diffusion difference schemes

  • Seiichiro Nagoya
  • Teruo Ushijima
Article

Abstract

This paper concerns theL 2-stability analysis for a family of finite difference schemes for the initial value problem of space 1 dimensional linear constant coefficient convection diffusion equation. The space difference operators of the schemes have the order of accuracy greater than or equal to 2. In this paper we say that the scheme satisfies the von Neumann condition if the maximum of the absolute value of the amplification coefficient of the scheme is less than or equal to 1. The problem is to characterize, in terms of the space mesh and the time mesh, the scheme which satisfies the von Neumann condition. To investigate the toughness of the scheme in the computation of the modes in a range of relatively shorter wave length in the relevant discrete problem, the concept of ε-stability is introduced, and characterized in this paper. The principal aim of the paper is to give the proof of the characterization.

Key words

von Neumann condition convection diffusion equation five point upwinding difference operator ε-stability 

References

  1. [1]
    Tetuya Kawamura, Hideo Takami and Kunio Kuwahara, New higher-order upwind scheme for incompressible Navier-Stokes equations. Proc. 9th Intern. Confer. Numerical Methods in Fluid Dynamics, Lecture Note in Phys.218, Springer, 1985, 291–295.Google Scholar
  2. [2]
    B.P. Leonard, A stable and accurate convective modeling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Engrg., 1979, 59–98.Google Scholar
  3. [3]
    Robert D Richtmyer and K. W. Morton, Difference Methods for Initial-Value Problems. Interscience Publishers, New York, 1967.MATHGoogle Scholar
  4. [4]
    Patrick J. Roache, Computational Fluid Dynamics. Hermosa Publishers Inc., New York, 1976.Google Scholar
  5. [5]
    Akio Tomiyama and Ryoichi Takahashi, Numerical stability and numerical oscillation of higher order difference methods for computational fluid dynamics (in Japanese). J. Atomic Energy Soc. Japan,32 (1990), 999–1008.Google Scholar

Copyright information

© JJIAM Publishing Committee 1995

Authors and Affiliations

  • Seiichiro Nagoya
    • 1
    • 2
  • Teruo Ushijima
    • 1
  1. 1.Department of Computer Science and Information MathematicsThe University of Electro-CommunicationsChofu-shi, TokyoJapan
  2. 2.ARK Information Systems, Inc.Chiyoda-ku, TokyoJapan

Personalised recommendations