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

L. Fatone; P. Gervasio; A. Quarteroni

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2001)

  • 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 - Modélisation Mathématique et Analyse Numérique 35.3 (2001): 549-574. <http://eudml.org/doc/194062>.

@article{Fatone2001,
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 - Modélisation Mathématique et Analyse Numérique},
keywords = {Navier-Stokes equations; domain decomposition methods; iterative schemes; convergence analysis; domain decomposition; subdomain splitting; convergence},
language = {eng},
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/194062},
volume = {35},
year = {2001},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2001
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/194062
ER -

References

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  1. [1] C. Bernardi and Y. Maday, Approximations spectrales de problèmes aux limites elliptiques. Springer-Verlag, Paris (1992). Zbl0773.47032MR1208043
  2. [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. [3] L. Fatone, Homogeneous and heterogeneous models for incompressible flows. Ph.D. thesis, Università degli Studi di Milano (1999). 
  4. [4] L. Fatone, P. Gervasio and A. Quarteroni, Multimodels for incompressible flows. J. Math. Fluid Mech. 2 (2000) 126–150. Zbl0962.76021
  5. [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. [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. [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. [12] A. Quarteroni and A. Valli, Domain decomposition methods for partial differential equations. Oxford Science Publications, Oxford (1999). Zbl0931.65118MR1857663
  13. [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. [14] R. Temam, Navier-Stokes equations. Theory and numerical analysis. 3rd edn., North-Holland, Amsterdam (1984). Zbl0568.35002
  15. [15] R. Temam, Navier-Stokes equations and nonlinear functional analysis. SIAM, Philadelphia (1988). Zbl0833.35110MR1318914
  16. [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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