### Abstract

In this work we design a new domain decomposition method for the Euler equations in 2 dimensions. The starting point is the equivalence with a third order scalar equation to whom we can apply an algorithm inspired from the Robin-Robin preconditioner for the convection-diffusion equation [Achdou and Nataf, C. R. Acad. Sci. Paris Sér. I 325 (1997) 1211-1216]. Afterwards we translate it into an algorithm for the initial system and prove that at the continuous level and for a decomposition into 2 sub-domains, it converges in 2 iterations. This property cannot be conserved strictly at discrete level and for arbitrary domain decompositions but we still have numerical results which confirm a very good stability with respect to the various parameters of the problem (mesh size, Mach number, ...).

Language | English |
---|---|

Pages | 689-703 |

Number of pages | 15 |

Journal | Mathematical Modelling and Numerical Analysis |

Volume | 40 |

Issue number | 4 |

DOIs | |

Publication status | Published - 31 Aug 2006 |

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### Keywords

- domain decomposition method
- Euler equations
- Smith factorization

### Cite this

*Mathematical Modelling and Numerical Analysis*,

*40*(4), 689-703. https://doi.org/10.1051/m2an:2006026

}

*Mathematical Modelling and Numerical Analysis*, vol. 40, no. 4, pp. 689-703. https://doi.org/10.1051/m2an:2006026

**A new domain decomposition method for the compressible Euler equations.** / Dolean, Victorita; Nataf, Frédéric.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A new domain decomposition method for the compressible Euler equations

AU - Dolean, Victorita

AU - Nataf, Frédéric

PY - 2006/8/31

Y1 - 2006/8/31

N2 - In this work we design a new domain decomposition method for the Euler equations in 2 dimensions. The starting point is the equivalence with a third order scalar equation to whom we can apply an algorithm inspired from the Robin-Robin preconditioner for the convection-diffusion equation [Achdou and Nataf, C. R. Acad. Sci. Paris Sér. I 325 (1997) 1211-1216]. Afterwards we translate it into an algorithm for the initial system and prove that at the continuous level and for a decomposition into 2 sub-domains, it converges in 2 iterations. This property cannot be conserved strictly at discrete level and for arbitrary domain decompositions but we still have numerical results which confirm a very good stability with respect to the various parameters of the problem (mesh size, Mach number, ...).

AB - In this work we design a new domain decomposition method for the Euler equations in 2 dimensions. The starting point is the equivalence with a third order scalar equation to whom we can apply an algorithm inspired from the Robin-Robin preconditioner for the convection-diffusion equation [Achdou and Nataf, C. R. Acad. Sci. Paris Sér. I 325 (1997) 1211-1216]. Afterwards we translate it into an algorithm for the initial system and prove that at the continuous level and for a decomposition into 2 sub-domains, it converges in 2 iterations. This property cannot be conserved strictly at discrete level and for arbitrary domain decompositions but we still have numerical results which confirm a very good stability with respect to the various parameters of the problem (mesh size, Mach number, ...).

KW - domain decomposition method

KW - Euler equations

KW - Smith factorization

UR - http://www.scopus.com/inward/record.url?scp=33751538838&partnerID=8YFLogxK

U2 - 10.1051/m2an:2006026

DO - 10.1051/m2an:2006026

M3 - Article

VL - 40

SP - 689

EP - 703

JO - ESAIM: Mathematical Modelling and Numerical Analysis

T2 - ESAIM: Mathematical Modelling and Numerical Analysis

JF - ESAIM: Mathematical Modelling and Numerical Analysis

SN - 0764-583X

IS - 4

ER -