On the accuracy of the rotation form in simulations of the Navier-Stokes equations

DOI10.1016/j.jcp.2009.01.027zbMath1161.76030OpenAlexW2059413295MaRDI QIDQ1017605

William J. Layton, Leo G. Rebholz, Monika Neda, Maxim A. Olshanskii, Carolina Cardoso Manica

Publication date: 12 May 2009

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2009.01.027

zbMATH Keywords

finite element methodpressure-velocity couplingBernoulli pressurelinear grad-div stabilization

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items (70)

Analysis and computation of a pressure-robust method for the rotation form of the incompressible Navier-Stokes equations with high-order finite elements ⋮ A unified framework of continuous and discontinuous Galerkin methods for solving the incompressible Navier-Stokes equation ⋮ Small-scale divergence penalization for incompressible flow problems via time relaxation ⋮ On the regularized modeling of density currents ⋮ On the grad-div stabilization for the steady Oseen and Navier-Stokes equations ⋮ A new kinetic-energy-preserving method based on the convective rotational form ⋮ A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations. I: Periodic domains ⋮ Analysis of a conforming finite element method for the Boussinesq problem with temperature-dependent parameters ⋮ Natural vorticity boundary conditions on solid walls ⋮ Numerical analysis and computational comparisons of the NS-alpha and NS-omega regularizations ⋮ Sensitivity analysis of the grad-div stabilization parameter in finite element simulations of incompressible flow ⋮ Stability in 3d of a sparse Grad-div approximation of the Navier-Stokes equations ⋮ On the determination of the grad-div criterion ⋮ Modular grad-div stabilization for the incompressible non-isothermal fluid flows ⋮ Stabilised finite element methods for the Oseen problem on anisotropic quadrilateral meshes ⋮ New connections between finite element formulations of the Navier-Stokes equations ⋮ A connection between coupled and penalty projection timestepping schemes with FE spatial discretization for the Navier-Stokes equations ⋮ Global in time analysis and sensitivity analysis for the reduced NS-\(\alpha\) model of incompressible flow ⋮ On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows ⋮ Consistency of the full and reduced order models for evolve‐filter‐relax regularization of convection‐dominated, marginally‐resolved flows ⋮ On augmented finite element formulations for the Navier-Stokes equations with vorticity and variable viscosity ⋮ A grad‐div stabilized method using the Jacobi iteration for the thermally coupled incompressible magnetohydrodynamic system ⋮ A sparse grad-div stabilized algorithm for the incompressible magnetohydrodynamics equations ⋮ Stabilized isogeometric collocation methods for scalar transport and incompressible fluid flow ⋮ \(H(\operatorname{div})\) conforming methods for the rotation form of the incompressible fluid equations ⋮ A stabilized implicit fractional-step method for the time-dependent Navier-Stokes equations using equal-order pairs ⋮ A parallel grad-div stabilized finite element algorithm for the Stokes equations with damping ⋮ A deconvolution enhancement of the Navier-Stokes-\({\alpha}{\beta}\) model ⋮ New subgrid artificial viscosity Galerkin methods for the Navier-Stokes equations ⋮ Variational multiscale modeling with discretely divergence-free subscales ⋮ Enforcing energy, helicity and strong mass conservation in finite element computations for incompressible Navier-Stokes simulations ⋮ On the parameter choice in grad-div stabilization for the Stokes equations ⋮ Error analysis and iterative solvers for Navier-Stokes projection methods with standard and sparse grad-div stabilization ⋮ Approximation of coupled Stokes-Darcy flow in an axisymmetric domain ⋮ A finite element solver and energy stable coupling for 3D and 1D fluid models ⋮ On a reduced sparsity stabilization of Grad-div type for incompressible flow problems ⋮ Grad-div stabilization and subgrid pressure models for the incompressible Navier-Stokes equations ⋮ A numerical study of the Navier-Stokes-\(\alpha \beta \) model ⋮ Discretizations in isogeometric analysis of Navier-Stokes flow ⋮ Rotational pressure-correction method for the Stokes/Darcy model based on the modular grad-div stabilization ⋮ Optimal vorticity accuracy in an efficient velocity-vorticity method for the 2D Navier-Stokes equations ⋮ Assessment of a vorticity based solver for the Navier-Stokes equations ⋮ Unconditional Long Time $\text{H}^1$-Stability of a Velocity-Vorticity-Temperature Scheme for the $2\text{D}$-Boussinesq System ⋮ Energy stability analysis of some fully discrete numerical schemes for incompressible Navier-Stokes equations on staggered grids ⋮ Supraconservative Finite-Volume Methods for the Euler Equations of Subsonic Compressible Flow ⋮ Regularity conditions for suitable weak solutions of the Navier-Stokes system from its rotation form ⋮ Grad-div Stabilized Finite Element Schemes for the Fluid-Fluid Interaction Model ⋮ Theory for the rotational deconvolution model of turbulence with fractional regularization ⋮ Stabilizing poor mass conservation in incompressible flow problems with large irrotational forcing and application to thermal convection ⋮ On the convergence rate of grad-div stabilized Taylor-Hood to Scott-Vogelius solutions for incompressible flow problems ⋮ Velocity-vorticity-helicity formulation and a solver for the Navier-Stokes equations ⋮ Convergence analysis of the Navier–Stokes alpha model ⋮ A divergence-free reconstruction of the nonconforming virtual element method for the Stokes problem ⋮ Longer time accuracy for incompressible Navier-Stokes simulations with the EMAC formulation ⋮ Convergence analysis and computational testing of the finite element discretization of the Navier-Stokes alpha model ⋮ Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations ⋮ Numerical simulations of fluid pressure in the human eye ⋮ Modular nonlinear filter stabilization of methods for higher Reynolds numbers flow ⋮ Time relaxation algorithm for flow ensembles ⋮ On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime ⋮ Analysis of second order time filtered backward Euler method for MHD equations ⋮ Numerical analysis of a BDF2 modular grad-div stabilization method for the Navier-Stokes equations ⋮ Pressure-robustness and discrete Helmholtz projectors in mixed finite element methods for the incompressible Navier-Stokes equations ⋮ Fully discrete approximations to the time-dependent Navier-Stokes equations with a projection method in time and grad-div stabilization ⋮ New numerical method for the rotation form of the Oseen problem with corner singularity ⋮ The reduced order NS-αmodel for incompressible flow: theory, numerical analysis and benchmark testing ⋮ Full and reduced order model consistency of the nonlinearity discretization in incompressible flows ⋮ Convergence of second-order in time numerical discretizations for the evolution Navier-Stokes equations ⋮ Numerical study of the Navier–Stokes-αdeconvolution model with pointwise mass conservation ⋮ High order algebraic splitting for magnetohydrodynamics simulation

Uses Software

• FreeFem++

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the effect of numerical errors in large eddy simulations of turbulent flows
• A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations
• A modified streamline diffusion method for solving the stationary Navier- Stokes equation
• On the rotation and skew-symmetric forms for incompressible flow simulations
• Stabilized finite element schemes for incompressible flow using Scott-Vogelius elements
• Stabilized finite element methods. II: The incompressible Navier-Stokes equations
• Truncation error analysis of the rotational form for the convective terms in the Navier-Stokes equation
• Large eddy simulation of turbulent incompressible flows. Analytical and numerical results for a class of LES models.
• Comparison of conservative and rotational forms in large eddy simulation of turbulent channel flow
• A low-order Galerkin finite element method for the Navier-Stokes equations of steady incompressible flow: a stabilization issue and iterative methods.
• The effect of the formulation of nonlinear terms on aliasing errors in spectral methods
• Stable and unstable formulations of the convection operator in spectral element simulations
• Numerical analysis and computational comparisons of the NS-alpha and NS-omega regularizations
• Stabilized finite element methods for the generalized Oseen problem
• Reduced aliasing formulations of the convective terms within the Navier-Stokes equations for a compressible fluid
• Navier--Stokes Equations in Rotation Form: A Robust Multigrid Solver for the Velocity Problem
• Stable finite-element calculation of incompressible flows using the rotation form of convection
• Time-dependent flow across a step: the slip with friction boundary condition
• An Energy- and Helicity-Conserving Finite Element Scheme for the Navier–Stokes Equations
• An Efficient Solver for the Incompressible Navier–Stokes Equations in Rotation Form
• Grad-div stablilization for Stokes equations
• Local projection type stabilization applied to inf-sup stable discretizations of the Oseen problem
• Spectral Methods
• ARTIFICIAL BOUNDARIES AND FLUX AND PRESSURE CONDITIONS FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

This page was built for publication: On the accuracy of the rotation form in simulations of the Navier-Stokes equations