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

Publication ,  Journal Article
Lin, P; Liu, JG; Lu, X
Published in: SIAM Journal on Scientific Computing
January 1, 2008

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. © 2008 Society for Industrial and Applied Mathematics.

Duke Scholars

Published In

SIAM Journal on Scientific Computing

DOI

ISSN

1064-8275

Publication Date

January 1, 2008

Volume

31

Issue

1

Start / End Page

398 / 419

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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Lin, P., Liu, J. G., & Lu, X. (2008). Long time numerical solution of the Navier-Stokes equations based on a sequential regularization formulation. SIAM Journal on Scientific Computing, 31(1), 398–419. https://doi.org/10.1137/060673722
Lin, P., J. G. Liu, and X. Lu. “Long time numerical solution of the Navier-Stokes equations based on a sequential regularization formulation.” SIAM Journal on Scientific Computing 31, no. 1 (January 1, 2008): 398–419. https://doi.org/10.1137/060673722.
Lin P, Liu JG, Lu X. Long time numerical solution of the Navier-Stokes equations based on a sequential regularization formulation. SIAM Journal on Scientific Computing. 2008 Jan 1;31(1):398–419.
Lin, P., et al. “Long time numerical solution of the Navier-Stokes equations based on a sequential regularization formulation.” SIAM Journal on Scientific Computing, vol. 31, no. 1, Jan. 2008, pp. 398–419. Scopus, doi:10.1137/060673722.
Lin P, Liu JG, Lu X. Long time numerical solution of the Navier-Stokes equations based on a sequential regularization formulation. SIAM Journal on Scientific Computing. 2008 Jan 1;31(1):398–419.

Published In

SIAM Journal on Scientific Computing

DOI

ISSN

1064-8275

Publication Date

January 1, 2008

Volume

31

Issue

1

Start / End Page

398 / 419

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics