A hybridizable discontinuous Galerkin method for the Navier--Stokes equations with pointwise divergence-free velocity field
Numerical Analysis
2023-07-04 v2 Computational Engineering, Finance, and Science
Fluid Dynamics
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.
Keywords
Cite
@article{arxiv.1704.07569,
title = {A hybridizable discontinuous Galerkin method for the Navier--Stokes equations with pointwise divergence-free velocity field},
author = {Sander Rhebergen and Garth N. Wells},
journal= {arXiv preprint arXiv:1704.07569},
year = {2023}
}