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Numerical shock structure and nonlinear corrections for difference schemes in conservation form

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Sixth International Conference on Numerical Methods in Fluid Dynamics

Part of the book series: Lecture Notes in Physics ((LNP,volume 90))

Abstract

In this paper the scalar equation ut + f(u) = 0 is approximated by three-point difference schemes in conservation form with an order of accuracy p equal to one or two. The partial differential equations approximated by the schemes with (p + 1)-th order accuracy are derived and their schock structures are analytically obtained and found to be close to the numerical shock profiles. By using these results, correction terms are proposed for second order schemes.

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Author information

Authors and Affiliations

  1. Ecole Nationale Supérieure d'Arts et Métiers, 75013, Paris

    Alain Lerat

  2. Laboratoire de Mécaniíque Théorique, Univeriité P. et M. Curie, Paris

    Alain Lerat

Authors
  1. Alain Lerat
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Editor information

H. Cabannes M. Holt V. Rusanov

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© 1979 Springer-Verlag

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Lerat, A. (1979). Numerical shock structure and nonlinear corrections for difference schemes in conservation form. In: Cabannes, H., Holt, M., Rusanov, V. (eds) Sixth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 90. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3540091157_187

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  • DOI: https://doi.org/10.1007/3540091157_187

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09115-8

  • Online ISBN: 978-3-540-35521-2

  • eBook Packages: Springer Book Archive

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