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

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.

References in corpus (1)

• Analysis of a hybridized/interface stabilized finite element method for the Stokes equations

Cited by in corpus (32)

• An embedded--hybridized discontinuous Galerkin finite element method for the Stokes equations
• Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier-Stokes equations
• A Conservative Finite Element Method for the Incompressible Euler Equations with Variable Density
• Arbitrary Lagrangian-Eulerian hybridizable discontinuous Galerkin methods for incompressible flow with moving boundaries and interfaces
• HDGlab: An open-source implementation of the hybridisable discontinuous Galerkin method in MATLAB
• A Multilevel Approach for Trace System in HDG Discretizations
• A pressure-robust embedded discontinuous Galerkin method for the Stokes problem by reconstruction operators
• An exactly mass conserving space-time embedded-hybridized discontinuous Galerkin method for the Navier-Stokes equations on moving domains
• LEoPart: a particle library for FEniCS
• High-order arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for the incompressible Navier-Stokes equations
• A locally conservative and energy-stable finite element for the Navier--Stokes problem on time-dependent domains
• Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity
• Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier--Stokes equations
• Curl-Flow: Boundary-Respecting Pointwise Incompressible Velocity Interpolation for Grid-Based Fluids
• On fixed-point, Krylov, and $2\times 2$ block preconditioners for nonsymmetric problems
• Fluid-structure interaction with $H(\text{div})$-conforming finite elements
• Hybridizable discontinuous Galerkin methods for the coupled Stokes--Biot problem
• Preconditioning for a pressure-robust HDG discretization of the Stokes equations
• Analysis of pressure-robust embedded-hybridized discontinuous Galerkin methods for the Stokes problem under minimal regularity
• A hybridizable discontinuous Galerkin method for the coupled Navier-Stokes and Darcy problem
• A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem
• A Hybridized Discontinuous Galerkin Method for A Linear Degenerate Elliptic Equation Arising from Two-Phase Mixtures
• A Divergence-Conforming Hybridized Discontinuous Galerkin Method for the Incompressible Reynolds Averaged Navier-Stokes Equations
• A polyhedral discrete de Rham numerical scheme for the Yang-Mills equations
• Convergence to weak solutions of a space-time hybridized discontinuous Galerkin method for the incompressible Navier--Stokes equations
• A conforming sliding mesh technique for an embedded-hybridized discontinuous Galerkin discretization for fluid-rigid body interaction
• An interface-tracking space-time hybridizable/embedded discontinuous Galerkin method for nonlinear free-surface flows
• Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity for incompressible flows. Part II
• Preconditioning of a hybridized discontinuous Galerkin finite element method for the Stokes equations
• A New Global Divergence Free and Pressure-Robust HDG Method for Tangential Boundary Control of Stokes Equations
• Analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains
• Constrained particle-mesh projections in a hybridized discontinuous Galerkin framework with applications to advection-dominated flows