A hybridizable discontinuous Galerkin method for the Navier--Stokes equations with pointwise divergence-free velocity field

04/25/2017

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by   Sander Rhebergen, et al.

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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 proposed here builds on the method presented by Labeur and Wells [SIAM J. Sci. Comput., vol. 34 (2012), pp. A889--A913]. We show that with simple modifications of the function spaces in the method of Labeur and Wells that it is possible to formulate a simple method with pointwise divergence-free velocity fields, and which is both momentum conserving and energy stable. Theoretical results are verified by two- and three-dimensional numerical examples and for different orders of polynomial approximation.