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Time-dependent non-uniform grids for parabolic equations

  • P. Orlandi
Contributed Papers
Part of the Lecture Notes in Physics book series (LNP, volume 218)

Abstract

A method based on a time dependent coordinate transformation has been applied to solve Burgers' equation. The numerical solution has been compared to the analytical solution of Lighthill [1]. The numerical results agree completely with the analytical ones. They have been obtained with very large time steps because a fast implicit non-iterative algorithm has been employed for the time discretization. The number of grid points in the space discretization is very low because the coordinate transformation gives a steady shock in the “new” coordinate.

Keywords

Grid Point Coordinate Transformation Error Distribution Mesh Point Implicit Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    M.J. Lighthill, “Surveys in Mechanics” (G.K. Batchelor and R.M. Davis, Eds.), p. 250, Academic Press, New Yrok & London, 1956.Google Scholar
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    T.H. Chong, SIAM J. Numer. Anal., 15 (1978), 835.CrossRefGoogle Scholar
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    B.L. Lohar and P.C. Jain, J. of Comp. Physics, 39 (1981), 433.CrossRefGoogle Scholar
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    P. Orlandi and J.H. Ferziger, AIAA J., 19 (1981), 1408.Google Scholar
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    W.R. Briley and H. McDonald, Lecture Notes in Physics, vol. 35, 105–110, Springer Verlag, New York, 1975.Google Scholar
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    R.M. Beam and R.F. Warming, AIAA J., 16 (1978), 393.Google Scholar
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    P. Orlandi, “Direct Simulation of Burgulence”, Proceedings of CTAC-83, J. Noye and C. Pletcher, North-Holland Publ. Company, p. 641, 1983.Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • P. Orlandi
    • 1
  1. 1.Dipartimento di Meccanica e AeronauticaUniversità degli Studi di Roma “La Sapienza”Italy

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