Journal of Scientific Computing

, Volume 66, Issue 1, pp 275–295

# Towards Optimized Schwarz Methods for the Navier–Stokes Equations

• Eric Blayo
• David Cherel
• Antoine Rousseau
Article

## Abstract

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.

## Keywords

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

## Notes

### Acknowledgments

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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