A new domain decomposition method for the compressible euler equations using smith factorization

Victorita Dolean; Fŕed́eric Nata

doi:10.1007/978-3-540-75199-1_40

A new domain decomposition method for the compressible euler equations using smith factorization

Victorita Dolean^*, Fŕed́eric Nata

^*Corresponding author for this work

Mathematics And Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

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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 [1]. 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, ⋯).

Original language	English
Title of host publication	Domain Decomposition Methods in Science and Engineering XVII
Publisher	Springer
Pages	331-338
Number of pages	8
Volume	60
ISBN (Print)	9783540751984
DOIs	https://doi.org/10.1007/978-3-540-75199-1_40
Publication status	Published - 1 Dec 2008
Event	17th International Conference on Domain Decomposition Methods - St. Wolfgang /Strobl, Austria Duration: 3 Jul 2006 → 7 Jul 2006

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	60
ISSN (Print)	1439-7358

Conference

Conference	17th International Conference on Domain Decomposition Methods
Country/Territory	Austria
City	St. Wolfgang /Strobl
Period	3/07/06 → 7/07/06

Keywords

Mach number
Euler equation
domain decomposition
domain decomposition method

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10.1007/978-3-540-75199-1_40

Dolean-Nata-DD2006-A-new-domain-decomposition-method-compressible-euler-equations-smith-factorizationAccepted author manuscript, 218 KB

Cite this

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title = "A new domain decomposition method for the compressible euler equations using smith factorization",

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 [1]. 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, ⋯).",

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author = "Victorita Dolean and F{\'r}e{\'d}eric Nata",

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Dolean, V & Nata, F 2008, A new domain decomposition method for the compressible euler equations using smith factorization. in Domain Decomposition Methods in Science and Engineering XVII. vol. 60, Lecture Notes in Computational Science and Engineering, vol. 60, Springer, pp. 331-338, 17th International Conference on Domain Decomposition Methods, St. Wolfgang /Strobl, Austria, 3/07/06. https://doi.org/10.1007/978-3-540-75199-1_40

A new domain decomposition method for the compressible euler equations using smith factorization. / Dolean, Victorita; Nata, Fŕed́eric.
Domain Decomposition Methods in Science and Engineering XVII. Vol. 60 Springer, 2008. p. 331-338 (Lecture Notes in Computational Science and Engineering; Vol. 60).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - A new domain decomposition method for the compressible euler equations using smith factorization

AU - Dolean, Victorita

AU - Nata, Fŕed́eric

PY - 2008/12/1

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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 [1]. 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 [1]. 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 - Mach number

KW - Euler equation

KW - domain decomposition

KW - domain decomposition method

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VL - 60

T3 - Lecture Notes in Computational Science and Engineering

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BT - Domain Decomposition Methods in Science and Engineering XVII

PB - Springer

T2 - 17th International Conference on Domain Decomposition Methods

Y2 - 3 July 2006 through 7 July 2006

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A new domain decomposition method for the compressible euler equations using smith factorization

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