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On the Advantage of Well-Balanced Schemes for Moving-Water Equilibria of the Shallow Water Equations

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Abstract

This note aims at demonstrating the advantage of moving-water well-balanced schemes over still-water well-balanced schemes for the shallow water equations. We concentrate on numerical examples with solutions near a moving-water equilibrium. For such examples, still-water well-balanced methods are not capable of capturing the small perturbations of the moving-water equilibrium and may generate significant spurious oscillations, unless an extremely refined mesh is used. On the other hand, moving-water well-balanced methods perform well in these tests. The numerical examples in this note clearly demonstrate the importance of utilizing moving-water well-balanced methods for solutions near a moving-water equilibrium.

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References

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Authors and Affiliations

  1. Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA

    Yulong Xing

  2. Department of Mathematics, University of Tennessee, Knoxville, TN, 37996, USA

    Yulong Xing

  3. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Chi-Wang Shu

  4. Institute for Geometry and Applied Mathematics, RWTH Aachen University, 52056, Aachen, Germany

    Sebastian Noelle

Authors
  1. Yulong Xing
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  2. Chi-Wang Shu
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  3. Sebastian Noelle
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Corresponding author

Correspondence to Yulong Xing.

Additional information

C.-W. Shu’s research is supported by AFOSR grant FA9550-09-1-0126 and NSF grant DMS-0809086. S. Noelle’s research is supported by DFG grant GK 775.

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Xing, Y., Shu, CW. & Noelle, S. On the Advantage of Well-Balanced Schemes for Moving-Water Equilibria of the Shallow Water Equations. J Sci Comput 48, 339–349 (2011). https://doi.org/10.1007/s10915-010-9377-y

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  • DOI: https://doi.org/10.1007/s10915-010-9377-y

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