A Hybridizable Discontinuous Galerkin Method for the Navier-Stokes Equations with Pointwise Divergence-Free Velocity Field

作者：Rhebergen Sander^*; Wells Garth N

来源：Journal of Scientific Computing, 2018, 76(3): 1484-1501.

DOI：10.1007/s10915-018-0671-4

• Navier-Stokes equations
• Hybridized methods
• Discontinuous Galerkin
• Finite element methods
• Solenoidal

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 34(2):A889-A913, 2012). 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.

• 出版日期2018-9