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We introduce a hybridizable discontinuous Galerkin method for theincompressible Navier--Stokes equations for which the approximate velocityfield is pointwise divergence-free. The method builds on the method presentedby Labeur and Wells [SIAM J. Sci. Comput., vol. 34 (2012), pp. A889--A913]. Weshow that with modifications of the function spaces in the method of Labeur andWells it is possible to formulate a simple method with pointwisedivergence-free velocity fields which is momentum conserving, energy stable,and pressure-robust. Theoretical results are supported by two- andthree-dimensional numerical examples and for different orders of polynomialapproximation.

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