Long time numerical solutyion of the Navier-Stokes equations based on a sequential regularization formulation

Ping Lin National University of Singapore Jian-Guo Liu University of Maryland Xiliang Lu National University of Singapore

Numerical Analysis and Scientific Computing mathscidoc:1702.25036

SIAM Journal on Scientific Computing, 31, (1), 398–419, 2008.1
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.
Navier–Stokes equations, sequential regularization, iterative penalty method, long time solution, constrained dynamical system, approximate projection
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@inproceedings{ping2008long,
  title={Long time numerical solutyion of the Navier-Stokes equations based on a sequential regularization formulation},
  author={Ping Lin, Jian-Guo Liu, and Xiliang Lu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209004811741359350},
  booktitle={SIAM Journal on Scientific Computing},
  volume={31},
  number={1},
  pages={398–419},
  year={2008},
}
Ping Lin, Jian-Guo Liu, and Xiliang Lu. Long time numerical solutyion of the Navier-Stokes equations based on a sequential regularization formulation. 2008. Vol. 31. In SIAM Journal on Scientific Computing. pp.398–419. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209004811741359350.
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