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A Hybridizable Discontinuous Galerkin Method for the Navier–Stokes Equations with Pointwise Divergence-Free Velocity Field

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Abstract

We introduce a hybridizable discontinuous Galerkin method for the incompressible Navier–Stokes equations for which the approximate velocity field is pointwise divergence-free. The method builds on the method presented by Labeur and Wells (SIAM J Sci Comput 34(2):A889–A913, 2012). We show that with modifications of the function spaces in the method of Labeur and Wells it is possible to formulate a simple method with pointwise divergence-free velocity fields which is momentum conserving, energy stable, and pressure-robust. Theoretical results are supported by two- and three-dimensional numerical examples and for different orders of polynomial approximation.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Waterloo, Waterloo, N2L 3G1, Canada

    Sander Rhebergen

  2. Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK

    Garth N. Wells

Authors
  1. Sander Rhebergen
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  2. Garth N. Wells
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Corresponding author

Correspondence to Sander Rhebergen.

Additional information

SR gratefully acknowledges support from the Natural Sciences and Engineering Research Council of Canada through the Discovery Grant Program (RGPIN-05606-2015) and the Discovery Accelerator Supplement (RGPAS-478018-2015).

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Rhebergen, S., Wells, G.N. A Hybridizable Discontinuous Galerkin Method for the Navier–Stokes Equations with Pointwise Divergence-Free Velocity Field. J Sci Comput 76, 1484–1501 (2018). https://doi.org/10.1007/s10915-018-0671-4

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  • DOI: https://doi.org/10.1007/s10915-018-0671-4

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