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

Abstract

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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, ...).

How to cite

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Dolean, 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 -

References

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