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Compact differencing schemes for advective problems

  • Richard S. Hirsh
  • Ralph E. Ferguson
Contributed Papers
Part of the Lecture Notes in Physics book series (LNP, volume 141)

Abstract

Compact differencing techniques have been shown to be applicable to simple first order advection equations. A second-order accurate compact upwind scheme has been derived which is identically equivalent to Keller's box method. Two fourth order compact analogs of Lax-Wendroff methods have also been shown. The accuracy of any of these compact methods is superior to a standard second-order method, even for one quarter of the nodes in the case of the fourth-order schemes.

Keywords

Upwind Scheme Compact Scheme Order Upwind Compact Method Compact Difference 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

  1. 1.
    Hirsh, R. S., “Higher Order Accurate Difference Solutions of Fluid Mechanics Problems by a Compact Differencing Technique,” J. Comp. Phys., 19, 90–109, 1975.CrossRefGoogle Scholar
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    Ciment, M. and Leventhal, S. H., ”Higher Order Compact Implicit Schemes for the Wave Equation,” Math. Comp., 29, 985–994, 1975.Google Scholar
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    Bontoux, P., Forestier, B. and Roux, B., “Analysis of Higher Order Methods for the Numerical Simulation of Confined Flows,” Paper presented at the Sixth International Conference on Numerical Methods in Fluid Dynamics, June 20–25, 1978, Tbilisi, U.S.S.R.Google Scholar
  4. 4.
    Leventhal, S. H., “A Two-Dimensional Operator Compact Implicit Method for Parabolic Equations,” Paper presented at SIAM 1979 Fall Meeting, November 12–14, 1979, Denver, Colorado.Google Scholar
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    Keller, H. B., “A New Difference Scheme for Parabolic Problems,” in J. Bramble (ed.), Numerical Solutions of Partial Differential Equations, Vol. II, Academic Press, New York, 1970.Google Scholar
  6. 6.
    Gottlieb, D. and Turkel, E., “Dissipative Two-Four Methods for Time Dependent Problems,” ICASE Report No. 75-22, October 1975.Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Richard S. Hirsh
    • 1
  • Ralph E. Ferguson
    • 1
  1. 1.JAYCORDel Mar

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