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

Ping Lin, Jian-Guo Liu, Xiliang Lu

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    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.
    Original languageEnglish
    Pages (from-to)398-419
    Number of pages22
    JournalSIAM Journal on Scientific Computing
    Volume31
    Issue number1
    DOIs
    Publication statusPublished - 2008

    Keywords

    • Navier-Stokes equations
    • Approximate projection
    • Constrained dynamical system
    • Iterative penalty method
    • Long time solution
    • Sequential regularization

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