A Hybridizable Discontinuous Galerkin Method for the Navier–Stokes Equations with Pointwise Divergence-Free Velocity Field
Accepted version
Peer-reviewed
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Repository DOI
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Authors
Rhebergen, S https://orcid.org/0000-0001-6036-0356
Wells, GN https://orcid.org/0000-0001-5291-7951
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., vol. 34 (2012), pp. A889--A913]. 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.
Description
Keywords
Navier-Stokes equations, Hybridized methods, Discontinuous Galerkin, Finite element methods, Solenoidal
Journal Title
Journal of Scientific Computing
Conference Name
Journal ISSN
0885-7474
1573-7691
1573-7691
Volume Title
76
Publisher
Springer Science and Business Media LLC