Journal of Scientific Computing

, Volume 66, Issue 1, pp 275–295 | Cite as

Towards Optimized Schwarz Methods for the Navier–Stokes Equations

  • Eric Blayo
  • David Cherel
  • Antoine Rousseau


This paper presents a study of optimized Schwarz domain decomposition methods for Navier–Stokes equations. Once discretized in time, optimal transparent boundary conditions are derived for the resulting Stokes equations, and a series of local approximations for these nonlocal conditions are proposed. Their convergence properties are studied, and numerical simulations are conducted on the test case of the driven cavity with two subdomains. It is shown that conditions involving one or two degrees of freedom can improve the convergence properties of the original algorithm.


Domain decomposition Optimized boundary conditions   Navier–Stokes equations Schwarz alternating method 



This work was supported by the ANR through contract ANR-11-MONU-005 (COMODO) and by the French national programme LEFE/INSU (project CoCoA).


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.LJKUniv. Grenoble AlpesGrenobleFrance
  2. 2.LJKCNRSGrenobleFrance
  3. 3.Inria, Institut de Mathématiques et de Modélisation de MontpellierMontpellierFrance

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