Long-term rigorous numerical integration of navier-stokes equation by newton-gmres iteration

Issue Date

9-2013

Abstract

The recent result of an orbit continuation algorithm has provided a rigorous method for long-term numerical integration of an orbit on the unstable manifold of a periodic solution. This algorithm is matrix-free and employs a combination of the Newton-Raphson method and the Krylov subspace method. Moreover, the algorithm adopts a multiple shooting method to address the problem of orbital instability due to long-term numerical integration. The algorithm is described through computing the extension of unstable manifold of a recomputed Nagata's lower-branch steady solution of plane Couette flow, which is an example of an exact coherent state that has recently been studied in subcritical transition to turbulence.

Source or Periodical Title

Transactions of Nanjing University of Aeronautics and Astronautics

ISSN

1005-1120

Volume

30

Issue

3

Page

248-251

Document Type

Article

Language

English

Subject

General minimal residual (GMRES), Long-term numerical integration, Multiple shooting, Newton-Raphson iteration, Unstable manifold

Digital Copy

yes

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