A Hybridizable Discontinuous Galerkin Method for the Navier–Stokes Equations with Pointwise Divergence-Free Velocity Field
Journal of Scientific Computing
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Rhebergen, S., & Wells, G. (2018). A Hybridizable Discontinuous Galerkin Method for the Navier–Stokes Equations with Pointwise Divergence-Free Velocity Field. Journal of Scientific Computing, 76 (3), 1484-1501. https://doi.org/10.1007/s10915-018-0671-4
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.
External DOI: https://doi.org/10.1007/s10915-018-0671-4
This record's URL: https://www.repository.cam.ac.uk/handle/1810/275178