A comparison of time-discretization/linearization approaches for the incompressible Navier-Stokes equations

DOI10.1016/j.cma.2005.10.007zbMath1124.76041OpenAlexW1976778931MaRDI QIDQ2382798

Joachim Rang, Volker John, Gunar Matthies

Publication date: 4 October 2007

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

Full work available at URL: https://doi.org/10.1016/j.cma.2005.10.007

zbMATH Keywords

Rosenbrock methodsfixed point iterationimplicit theta-scheme

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items

A spectral deferred correction method for incompressible flow with variable viscosity, Robust stabilised finite element solvers for generalised Newtonian fluid flows, A PROJECTION-BASED VARIATIONAL MULTISCALE METHOD FOR LARGE-EDDY SIMULATION WITH APPLICATION TO NON-ISOTHERMAL FREE CONVECTION PROBLEMS, Numerical studies of finite element variational multiscale methods for turbulent flow simulations, Numerical methods for nonlinear second-order hyperbolic partial differential equations. II: Rothe's techniques for 1-D problems, On the efficiency of a matrix-free linearly implicit time integration strategy for high-order discontinuous Galerkin solutions of incompressible turbulent flows, Perturbation index of linear partial differential-algebraic equations with a hyperbolic part, A numerical investigation of velocity-pressure reduced order models for incompressible flows, A variational multiscale method for turbulent flow simulation with adaptive large scale space, A new linearly extrapolated Crank-Nicolson time-stepping scheme for the Navier-Stokes equations, High-order matrix-free incompressible flow solvers with GPU acceleration and low-order refined preconditioners, On adaptive grad-div parameter selection, Time filtered second order backward Euler method for EMAC formulation of Navier-Stokes equations, Rosenbrock-Wanner and W-methods for the Navier-Stokes equations, Numerical investigation of the sharp-interface limit of the Navier–Stokes–Cahn–Hilliard equations, Stability and convergence of the numerical solution for the species equation of a model for PEMFCs, Adaptive time step control for the incompressible Navier-Stokes equations, Application of the rosenbrock methods to the solution of unsteady 3D incompressible Navier-Stokes equations, Pressure corrected implicit \(\theta \)-schemes for the incompressible Navier-Stokes equations, On the impact of the scheme for solving the higher dimensional equation in coupled population balance systems, A New Stiffly Accurate Rosenbrock-Wanner Method for Solving the Incompressible Navier-Stokes Equations, An analysis of the Prothero-Robinson example for constructing new DIRK and ROW methods, Finite element LES and VMS methods on tetrahedral meshes, Implicit time discretization schemes for mixed least-squares finite element formulations, Projection methods for incompressible flow problems with WENO finite difference schemes, Adaptive time step control for higher order variational time discretizations applied to convection-diffusion-reaction equations, Numerical implementation of the Crank-Nicolson/Adams-Bashforth scheme for the time-dependent Navier-Stokes equations, A robust and accurate adaptive approximation method for a diffuse-interface model of binary-fluid flows, Semi‐implicit schemes for transient Navier–Stokes equations and eddy viscosity models, A local projection stabilization/continuous Galerkin-Petrov method for incompressible flow problems, Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal Equation, Improved traditional Rosenbrock-Wanner methods for stiff ODEs and DAEs

Uses Software

• MooNMD
• ROS3P
• RODAS
• FEATFLOW

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rosenbrock methods for differential-algebraic systems with solution- dependent singular matrix multiplying the derivative
• MooNMD -- a program package based on mapped finite element methods
• Efficient solvers for incompressible flow problems. An algorithmic and computational approach
• An analysis of the time integration algorithms for the finite element solutions of incompressible Navier--Stokes equations based on a stabilised formulation.
• Large eddy simulation of turbulent incompressible flows. Analytical and numerical results for a class of LES models.
• Adaptive multilevel solution of nonlinear parabolic PDE systems. Theory, algorithm, and applications
• The inf-sup condition for the mapped \(Q_k-P_{k-1}^{\text{disc}}\) element in arbitrary space dimensions
• On the efficiency of linearization schemes and coupled multigrid methods in the simulation of a 3D flow around a cylinder
• Finite-Element Approximation of the Nonstationary Navier–Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization
• Structure of the set of stationary solutions of the navier‐stokes equations
• Stability of the Fractional Step $\Theta $-Scheme for the Nonstationary Navier–Stokes Equations
• Higher-order finite element discretizations in a benchmark problem for incompressible flows
• Reference values for drag and lift of a two‐dimensional time‐dependent flow around a cylinder
• Higher order finite element methods and multigrid solvers in a benchmark problem for the 3D Navier-Stokes equations
• A Flexible Inner-Outer Preconditioned GMRES Algorithm
• Numerical Solution of the Navier-Stokes Equations
• ROS3P -- An accurate third-order Rosenbrock solver designed for parabolic problems