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Upwind and High-Resolution Schemes pp 1–7Cite as

ICASE and the History of High-Resolution Schemes

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Abstract

The need for high-resolution schemes is a direct consequence of the nonlinear properties of hyperbolic systems of conservation laws such as the Euler equations of inviscid compressible flow. Due to the nonlinearity of these equations, any compression wave, no matter how smooth initially, will evolve into a shock discontinuity, while the interaction of shock waves in turn may create shear and entropy discontinuities. When attempting to compute a solution with such features on a grid of discrete meshes, we have the choice of representing these as actual discontinuities — as in “shock fitting” [1, 2], “jump recovery” [3], or “sub-cell resolution” [4], or spreading them artificially, as in “shock capturing” [5, 6]. In the latter technique the goal is to automatically represent any discontinuity by a sharp but oscillation-free transition, with most of the jump realized within one to three meshes, without compromising accuracy away from such jumps. The term “high resolution” appeared first in an article by A. Harten [7], who attributed it to P. R. Woodward.

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Authors
  1. Bram van Leer
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Editors and Affiliations

  1. Program in Computational Science & Engineering, Florida State University, Tallahassee, FL, 32306-3075, USA

    M. Yousuff Hussaini

  2. Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109-2118, USA

    Bram van Leer

  3. ICASE, NASA Langley Research Center, Mail Stop 132C, Hampton, VA, 23681-0001, USA

    John Van Rosendale

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© 1997 Springer-Verlag Berlin Heidelberg

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van Leer, B. (1997). ICASE and the History of High-Resolution Schemes. In: Hussaini, M.Y., van Leer, B., Van Rosendale, J. (eds) Upwind and High-Resolution Schemes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60543-7_1

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  • DOI: https://doi.org/10.1007/978-3-642-60543-7_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64452-8

  • Online ISBN: 978-3-642-60543-7

  • eBook Packages: Springer Book Archive

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