Numerical analysis of a BDF2 modular grad-div stabilization method for the Navier-Stokes equations

DOI10.1007/s10915-020-01165-5zbMath1436.76046arXiv1806.10750OpenAlexW3007244759MaRDI QIDQ2302416

J. A. Fiordilino, Yao Rong

Publication date: 26 February 2020

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.10750

zbMATH Keywords

Navier-Stokes equationsgrad-div stabilizationmodular methodstability and error estimatesTaylor-Hood finite elementsBDF2 time discretization

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Finite difference methods applied to problems in fluid mechanics (76M20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (11)

Analysis and computation of a pressure-robust method for the rotation form of the incompressible Navier-Stokes equations with high-order finite elements ⋮ Numerical analysis of a BDF2 modular grad-div stability method for the Stokes/Darcy equations ⋮ Stability in 3d of a sparse Grad-div approximation of the Navier-Stokes equations ⋮ Modular grad-div stabilization for the incompressible non-isothermal fluid flows ⋮ Numerical analysis of projection methods for the time-dependent Navier-Stokes equations with modular grad-div stabilization ⋮ A grad‐div stabilized method using the Jacobi iteration for the thermally coupled incompressible magnetohydrodynamic system ⋮ Numerical analysis of CNLF modular grad-div stabilization method for time-dependent Navier-Stokes equations ⋮ On the convergence order of the finite element error in the kinetic energy for high Reynolds number incompressible flows ⋮ A modular Grad-div stabilization for the 2D/3D nonstationary incompressible magnetohydrodynamic equations ⋮ A mathematical description of the flow in a spherical lymph node ⋮ Filtered time-stepping method for incompressible Navier-Stokes equations with variable density

Uses Software

• FreeFem++

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• High-order time stepping for the Navier-Stokes equations with minimal computational complexity
• 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
• On the convergence rate of grad-div stabilized Taylor-Hood to Scott-Vogelius solutions for incompressible flow problems
• Grad-div stabilization and subgrid pressure models for the incompressible Navier-Stokes equations
• On the accuracy of the rotation form in simulations of the Navier-Stokes equations
• Two classes of mixed finite element methods
• On the determination of the grad-div criterion
• Preconditioning sparse grad-div/augmented Lagrangian stabilized saddle point systems
• Analysis of the grad-div stabilization for the time-dependent Navier-Stokes equations with inf-sup stable finite elements
• A low-order Galerkin finite element method for the Navier-Stokes equations of steady incompressible flow: a stabilization issue and iterative methods.
• A conservative, second order, unconditionally stable artificial compression method
• An efficient and modular grad-div stabilization
• Grad-div stabilization for the evolutionary Oseen problem with inf-sup stable finite elements
• On a reduced sparsity stabilization of Grad-div type for incompressible flow problems
• 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
• Finite-Element Approximation of the Nonstationary Navier–Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• A Two-Level Method with Backtracking for the Navier--Stokes Equations
• Computer-aided analysis of flow past a surface-mounted obstacle
• Reference values for drag and lift of a two‐dimensional time‐dependent flow around a cylinder
• A partitioned second‐order method for magnetohydrodynamic flows at small magnetic reynolds numbers
• Grad-div stablilization for Stokes equations
• New development in freefem++
• On relaxation times in the Navier-Stokes-Voigt model
• Efficient augmented Lagrangian‐type preconditioning for the Oseen problem using Grad‐Div stabilization
• On Pressure Approximation via Projection Methods for Nonstationary Incompressible Navier–Stokes Equations
• On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows

This page was built for publication: Numerical analysis of a BDF2 modular grad-div stabilization method for the Navier-Stokes equations