# A new domain decomposition method for the compressible Euler equations

Victorita Dolean; Frédéric Nataf

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

- Volume: 40, Issue: 4, page 689-703
- ISSN: 0764-583X

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topDolean, Victorita, and Nataf, Frédéric. "A new domain decomposition method for the compressible Euler equations." ESAIM: Mathematical Modelling and Numerical Analysis 40.4 (2006): 689-703. <http://eudml.org/doc/249735>.

@article{Dolean2006,

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. I325 (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, ...).
},

author = {Dolean, Victorita, Nataf, Frédéric},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Smith factorization; domain decomposition method; Euler equations.; Euler equations},

language = {eng},

month = {11},

number = {4},

pages = {689-703},

publisher = {EDP Sciences},

title = {A new domain decomposition method for the compressible Euler equations},

url = {http://eudml.org/doc/249735},

volume = {40},

year = {2006},

}

TY - JOUR

AU - Dolean, Victorita

AU - Nataf, Frédéric

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

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2006/11//

PB - EDP Sciences

VL - 40

IS - 4

SP - 689

EP - 703

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. I325 (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, ...).

LA - eng

KW - Smith factorization; domain decomposition method; Euler equations.; Euler equations

UR - http://eudml.org/doc/249735

ER -

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