Multimodels for incompressible flows: iterative solutions for the Navier-Stokes/Oseen coupling

L. Fatone; P. Gervasio; A. Quarteroni

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 35, Issue: 3, page 549-574
  • ISSN: 0764-583X

Abstract

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In a recent paper [4] we have proposed and analysed a suitable mathematical model which describes the coupling of the Navier-Stokes with the Oseen equations. In this paper we propose a numerical solution of the coupled problem by subdomain splitting. After a preliminary analysis, we prove a convergence result for an iterative algorithm that alternates the solution of the Navier-Stokes problem to the one of the Oseen problem.

How to cite

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Fatone, L., Gervasio, P., and Quarteroni, A.. "Multimodels for incompressible flows: iterative solutions for the Navier-Stokes/Oseen coupling." ESAIM: Mathematical Modelling and Numerical Analysis 35.3 (2010): 549-574. <http://eudml.org/doc/197606>.

@article{Fatone2010,
abstract = { In a recent paper [4] we have proposed and analysed a suitable mathematical model which describes the coupling of the Navier-Stokes with the Oseen equations. In this paper we propose a numerical solution of the coupled problem by subdomain splitting. After a preliminary analysis, we prove a convergence result for an iterative algorithm that alternates the solution of the Navier-Stokes problem to the one of the Oseen problem. },
author = {Fatone, L., Gervasio, P., Quarteroni, A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Navier-Stokes equations; domain decomposition methods; iterative schemes; convergence analysis.; domain decomposition; subdomain splitting; convergence},
language = {eng},
month = {3},
number = {3},
pages = {549-574},
publisher = {EDP Sciences},
title = {Multimodels for incompressible flows: iterative solutions for the Navier-Stokes/Oseen coupling},
url = {http://eudml.org/doc/197606},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Fatone, L.
AU - Gervasio, P.
AU - Quarteroni, A.
TI - Multimodels for incompressible flows: iterative solutions for the Navier-Stokes/Oseen coupling
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 3
SP - 549
EP - 574
AB - In a recent paper [4] we have proposed and analysed a suitable mathematical model which describes the coupling of the Navier-Stokes with the Oseen equations. In this paper we propose a numerical solution of the coupled problem by subdomain splitting. After a preliminary analysis, we prove a convergence result for an iterative algorithm that alternates the solution of the Navier-Stokes problem to the one of the Oseen problem.
LA - eng
KW - Navier-Stokes equations; domain decomposition methods; iterative schemes; convergence analysis.; domain decomposition; subdomain splitting; convergence
UR - http://eudml.org/doc/197606
ER -

References

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  11. A. Quarteroni and A. Valli, Theory and application of Steklov-Poincaré operators for boundary-value problems. In Applied and Industrial Mathematics, R. Spigler Ed., Kluwer Academic Publisher, Dordest (1991) 179-203.  
  12. A. Quarteroni and A. Valli, Domain decomposition methods for partial differential equations. Oxford Science Publications, Oxford (1999).  
  13. K. Schenk and F.K. Hebeker, Coupling of two dimensional viscous and inviscid incompressible Stokes equations. Technical Report Preprint 93-68 (SFB 359), Heidelberg University (1993).  
  14. R. Temam, Navier-Stokes equations. Theory and numerical analysis. 3rd edn., North-Holland, Amsterdam (1984).  
  15. R. Temam, Navier-Stokes equations and nonlinear functional analysis. SIAM, Philadelphia (1988).  
  16. H.A. van der Vorst, Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Statist. Comput.13 (1992) 631-644.  

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