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A hybridizable discontinuous Galerkin method for the Navier-Stokes equations with pointwise divergence-free velocity field. (English) Zbl 1397.76077

Summary: 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 R. J. Labeur and the second author [SIAM J. Sci. Comput. 34, No. 2, A889–A913 (2012; Zbl 1391.76344)]. 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.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations

Citations:

Zbl 1391.76344

Software:

NGSolve
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References:

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