An embedded variable step IMEX scheme for the incompressible Navier-Stokes equations

DOI10.1016/j.cma.2020.113661zbMath1506.76069arXiv2002.00074OpenAlexW3004086025MaRDI QIDQ2022016

Victor DeCaria, Michael Schneier

Publication date: 27 April 2021

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.00074

zbMATH Keywords

Navier-Stokessemi-implicitIMEXadaptive timesteppingimplicit/explicitvariable step BE-AB2 scheme

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) 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)

Related Items

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Uses Software

• Matlab
• CUDA
• FEniCS

Cites Work

• Unnamed Item
• High-order time stepping for the Navier-Stokes equations with minimal computational complexity
• Finite element approximation of the Navier-Stokes equations
• Adaptive time step control for the incompressible Navier-Stokes equations
• Stability of two IMEX methods, CNLF and BDF2-AB2, for uncoupling systems of evolution equations
• Grad-div stabilization and subgrid pressure models for the incompressible Navier-Stokes equations
• Numerical methods for solids (Part 3). Numerical methods for fluids (Part 1)
• A second order backward difference method with variable steps for a parabolic problem
• An analysis of the time integration algorithms for the finite element solutions of incompressible Navier--Stokes equations based on a stabilised formulation.
• Time filters increase accuracy of the fully implicit method
• Analysis of the grad-div stabilization for the time-dependent Navier-Stokes equations with inf-sup stable finite elements
• On the large eddy simulation of the Taylor-Green vortex
• Adaptive time step control for higher order variational time discretizations applied to convection-diffusion-reaction equations
• Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term
• An efficient and modular grad-div stabilization
• Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier-Stokes equations
• Stability of Two-Step Methods for Variable Integration Steps
• The Euler implicit/explicit scheme for the 2D time-dependent Navier-Stokes equations with smooth or non-smooth initial data
• Adaptive Time-Stepping for Incompressible Flow Part II: Navier–Stokes Equations
• A Connection Between Scott–Vogelius and Grad-Div Stabilized Taylor–Hood FE Approximations of the Navier–Stokes Equations
• The Convergence of Variable-Stepsize, Variable-Formula, Multistep Methods
• On a Higher Order Accurate Fully Discrete Galerkin Approximation to the Navier-Stokes Equations
• STABILITY OF HIGHER ORDER TRIANGULAR HOOD-TAYLOR METHODS FOR THE STATIONARY STOKES EQUATIONS
• Three-Dimensional Finite Element Methods for the Stokes Problem
• A Second Order BDF Numerical Scheme with Variable Steps for the Cahn--Hilliard Equation
• Goal‐oriented space–time adaptivity in the finite element Galerkin method for the computation of nonstationary incompressible flow
• The Mathematical Theory of Finite Element Methods
• Numerical Solution of the Navier-Stokes Equations