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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  2. P. Bjørstad and O.B. Widlund, Iterative methods for the solution of elliptic problems on regions partitioned into substructures. SIAM J. Numer. Anal.23 (1986) 1097-1120.  Zbl0615.65113
  3. L. Fatone, Homogeneous and heterogeneous models for incompressible flows. Ph.D. thesis, Università degli Studi di Milano (1999).  
  4. L. Fatone, P. Gervasio and A. Quarteroni, Multimodels for incompressible flows. J. Math. Fluid Mech.2 (2000) 126-150.  Zbl0962.76021
  5. M. Feistauer and C. Schwab, Coupling of an interior Navier-Stokes problem with an exterior Oseen problem. Technical Report Research 98-01, ETH, Zurich (1998).  Zbl0991.35061
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  10. A. Quarteroni, G. Sacchi Landriani, and A. Valli, Coupling of viscous and inviscid incompressible Stokes equations. Numer. Math.59 (1991) 831-859.  Zbl0738.76044
  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.  Zbl0723.65098
  12. A. Quarteroni and A. Valli, Domain decomposition methods for partial differential equations. Oxford Science Publications, Oxford (1999).  Zbl0931.65118
  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).  Zbl0872.76024
  14. R. Temam, Navier-Stokes equations. Theory and numerical analysis. 3rd edn., North-Holland, Amsterdam (1984).  Zbl0568.35002
  15. R. Temam, Navier-Stokes equations and nonlinear functional analysis. SIAM, Philadelphia (1988).  Zbl0522.35002
  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.  Zbl0761.65023

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