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Fundamental Algorithms in Computational Fluid Dynamics pp 181–207Cite as

Introduction to High-Resolution Upwind Schemes

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Abstract

The algorithms described in the two preceding chapters have been used successfully for the computation of many flow fields. However, in some contexts an additional degree of robustness is required. There are many flow problems, especially those involving complex physics, where positivity and monotonicity preservation is critical. For example, in a hypersonic flow, where the Mach number is much greater than unity, strong shock waves arise.

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Notes

  1. 1.

    This is a necessary property of a conservative scheme.

  2. 2.

    Henceforth we drop the bars denoting cell average quantities for convenience.

  3. 3.

    For example, Goodman and Leveque [19] showed that TVD schemes for scalar conservation laws in two dimensions can be no better than first-order accurate.

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Authors and Affiliations

  1. NASA Ames Research Center, MS 258-2, Mountain View, CA, 94035-1000, USA

    Thomas H. Pulliam

  2. Institute for Aerospace Studies, Universtiy of Toronto, 4925 Dufferin St., Toronto, ON, M3H 5T6, Canada

    David W. Zingg

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  1. Thomas H. Pulliam
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  2. David W. Zingg
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Correspondence to Thomas H. Pulliam .

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Pulliam, T.H., Zingg, D.W. (2014). Introduction to High-Resolution Upwind Schemes. In: Fundamental Algorithms in Computational Fluid Dynamics. Scientific Computation. Springer, Cham. https://doi.org/10.1007/978-3-319-05053-9_6

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  • DOI: https://doi.org/10.1007/978-3-319-05053-9_6

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