On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond

zbMath1422.76125arXiv1808.10711MaRDI QIDQ5228102

Philipp W. Schroeder, Alexander Linke, Nicolas R. Gauger

Publication date: 9 August 2019

Full work available at URL: https://arxiv.org/abs/1808.10711

zbMATH Keywords

discontinuous Galerkin methodhigh-order methodsmaterial derivativehigh Reynolds number flowsincompressible Navier-Stokesstructure-preserving algorithmspressure-robust methods(generalised) Beltrami flowsdivergence-free \(H\)(div) finite elementsHelmholtz-Hodge projector

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Boundary-layer theory, separation and reattachment, higher-order effects (76D10) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Viscous vortex flows (76D17)

Related Items (26)

Analysis and computation of a pressure-robust method for the rotation form of the incompressible Navier-Stokes equations with high-order finite elements ⋮ Pressure-Robustness in the Context of Optimal Control ⋮ An Arbitrary Order and Pointwise Divergence-Free Finite Element Scheme for the Incompressible 3D Navier–Stokes Equations ⋮ HHO methods for the incompressible Navier-Stokes and the incompressible Euler equations ⋮ Helmholtz's decomposition for compressible flows and its application to computational aeroacoustics ⋮ An Augmented Lagrangian Preconditioner for the Magnetohydrodynamics Equations at High Reynolds and Coupling Numbers ⋮ A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem ⋮ An EMA-conserving, pressure-robust and Re-semi-robust method with A robust reconstruction method for Navier–Stokes ⋮ The virtual element method ⋮ A lowest-degree conservative finite element scheme for incompressible Stokes problems on general triangulations ⋮ Preconditioners for Computing Multiple Solutions in Three-Dimensional Fluid Topology Optimization ⋮ Pressure-robust enriched Galerkin methods for the Stokes equations ⋮ Monolithic multigrid for implicit Runge-Kutta discretizations of incompressible fluid flow ⋮ Pressure Robust Weak Galerkin Finite Element Methods for Stokes Problems ⋮ On the Significance of Pressure-Robustness for the Space Discretization of Incompressible High Reynolds Number Flows ⋮ Pressure-robustness in quasi-optimal a priori estimates for the Stokes problem ⋮ A pressure-robust virtual element method for the Stokes problem ⋮ Locking-free and gradient-robust \(H(\operatorname{div})\)-conforming HDG methods for linear elasticity ⋮ A Pressure-Robust Discretization of Oseen's Equation Using Stabilization in the Vorticity Equation ⋮ A Reynolds-robust preconditioner for the Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations ⋮ Pressure-robust error estimate of optimal order for the Stokes equations: domains with re-entrant edges and anisotropic mesh grading ⋮ The Stokes complex for virtual elements with application to Navier-Stokes flows ⋮ A low-degree strictly conservative finite element method for incompressible flows on general triangulations ⋮ Guaranteed upper bounds for the velocity error of pressure-robust Stokes discretisations ⋮ An introduction to second order divergence-free VEM for fluidodynamics ⋮ Numerical Analysis of a Discontinuous Galerkin Method for the Borrvall--Petersson Topology Optimization Problem

Uses Software

• NGSolve

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Isogeometric divergence-conforming B-splines for the unsteady Navier-Stokes equations
• On the parameter choice in grad-div stabilization for the Stokes equations
• Well balanced finite volume methods for nearly hydrostatic flows
• New connections between finite element formulations of the Navier-Stokes equations
• Mathematical aspects of discontinuous Galerkin methods.
• Grad-div stabilization and subgrid pressure models for the incompressible Navier-Stokes equations
• Stabilizing poor mass conservation in incompressible flow problems with large irrotational forcing and application to thermal convection
• A finite element exterior calculus framework for the rotating shallow-water equations
• On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime
• Max-norm estimates for Stokes and Navier-Stokes approximations in convex polyhedra
• On the rotation and skew-symmetric forms for incompressible flow simulations
• A stable finite element for the Stokes equations
• Two classes of mixed finite element methods
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
• Analysis of the grad-div stabilization for the time-dependent Navier-Stokes equations with inf-sup stable finite elements
• A divergence-free velocity reconstruction for incompressible flows
• Mathematical tools for the study of the incompressible Navier-Stokes equations and related models
• Pressure separation -- a technique for improving the velocity error in finite element discretisations of the Navier-Stokes equations
• Theory and practice of finite elements.
• The analogue of grad-div stabilization in DG methods for incompressible flows: limiting behavior and extension to tensor-product meshes
• Towards pressure-robust mixed methods for the incompressible Navier-Stokes equations
• Pressure-induced locking in mixed methods for time-dependent (Navier-)Stokes equations
• Pressure-robustness and discrete Helmholtz projectors in mixed finite element methods for the incompressible Navier-Stokes equations
• A discontinuous skeletal method for the viscosity-dependent Stokes problem
• Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier-Stokes equations
• Pressure-robust analysis of divergence-free and conforming FEM for evolutionary incompressible Navier-Stokes flows
• Mixed finite elements for numerical weather prediction
• Continuous interior penalty finite element method for the time-dependent Navier-Stokes equations: space discretization and convergence
• A note on discontinuous Galerkin divergence-free solutions of the Navier-Stokes equations
• Robust Arbitrary Order Mixed Finite Element Methods for the Incompressible Stokes Equations with pressure independent velocity errors
• Finite Element Methods for Incompressible Flow Problems
• A Connection Between Scott–Vogelius and Grad-Div Stabilized Taylor–Hood FE Approximations of the Navier–Stokes Equations
• Stable finite-element calculation of incompressible flows using the rotation form of convection
• IsoGeometric Analysis: Stable elements for the 2D Stokes equation
• On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 2: Implementation
• On stabilized finite element methods for the Stokes problem in the small time step limit
• Local projection FEM stabilization for the time‐dependent incompressible <scp>N</scp>avier–<scp>S</scp>tokes problem
• Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
• Experiments with several elements for viscous incompressible flows
• Are fem solutions of incompressible flows really incompressible? (or how simple flows can cause headaches!)
• Exact fully 3D Navier–Stokes solutions for benchmarking
• Spurious velocities in the steady flow of an incompressible fluid subjected to external forces
• On Really Locking-Free Mixed Finite Element Methods for the Transient Incompressible Stokes Equations
• Arbitrary Order Finite Volume Well-Balanced Schemes for the Euler Equations with Gravity
• Quasi-optimality of a pressure-robust nonconforming finite element method for the Stokes-problem
• A new family of stable mixed finite elements for the 3D Stokes equations
• Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
• Mixed Finite Element Methods and Applications
• ISOGEOMETRIC DIVERGENCE-CONFORMING B-SPLINES FOR THE STEADY NAVIER–STOKES EQUATIONS
• On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows
• The Navier-Stokes Equations
• Spectral/hp Element Methods for Computational Fluid Dynamics

This page was built for publication: On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond