Long Time Numerical Solution of the Navier-Stokes Equations Based on a Sequential Regularization Formulation

Authors:
Ping Lin;Jian-Guo Liu;Xiliang Lu
Affiliations:
plin@maths.dundee.ac.uk;jliu@math.umd.edu;lu_xiliang@hotmail.com
Venue:
SIAM Journal on Scientific Computing
Year:
2008

Citing 0
Cited 2

An efficient numerical method for the equations of steady and unsteady flows of homogeneous incompressible Newtonian fluid

Journal of Computational Physics
Energy law preserving C0 finite element schemes for phase field models in two-phase flow computations

Journal of Computational Physics

Quantified Score

Hi-index	0.01

Visualization

Abstract

The sequential regularization method is a reformulation of the unsteady Navier-Stokes equations from the viewpoint of constrained dynamical systems or the approximate Helmholtz-Hodge projection. In this paper we study the long time behavior of the sequential regularization formulation. We give a uniform-in-time estimate between the solution of the reformulated system and that of the Navier-Stokes equations. We also conduct an error analysis for the temporal discrete system and show that the error bound is independent of time. A couple of long time flow examples are computed to demonstrate this method.