Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-25T16:46:20.866Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  15 April 2002

L. Fatone ,
P. Gervasio  and
A. Quarteroni
L. Fatone
Affiliation:
Department of Mathematics, Politecnico di Milano, 20133 Milano Italy. (fatone@mate.polimi.it)
P. Gervasio
Affiliation:
Department of Mathematics, University of Brescia, 25100 Brescia Italy. (gervasio@ing.unibs.it)
A. Quarteroni
Affiliation:
Department of Mathematics, Politecnico di Milano, 20133 Milano Italy. (fatone@mate.polimi.it) Department of Mathematics, EPFL, 1015 Lausanne, Switzerland. (Alfio.Quarteroni@epfl.ch)
Get access

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.

Keywords

Navier-Stokes equationsdomain decomposition methodsiterative schemesconvergence analysis.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 3 , May 2001 , pp. 549 - 574
Copyright
© EDP Sciences, SMAI, 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

C. Bernardi and Y. Maday, Approximations spectrales de problèmes aux limites elliptiques. Springer-Verlag, Paris (1992).
Bjørstad, P. and Widlund, O.B., Iterative methods for the solution of elliptic problems on regions partitioned into substructures. SIAM J. Numer. Anal. 23 (1986) 1097-1120. CrossRef
L. Fatone, Homogeneous and heterogeneous models for incompressible flows. Ph.D. thesis, Università degli Studi di Milano (1999).
Fatone, L., Gervasio, P. and Quarteroni, A., Multimodels for incompressible flows. J. Math. Fluid Mech. 2 (2000) 126-150. CrossRef
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).
Feistauer, M. and Schwab, C., On coupled problems for viscous flow in exterior domains. Math. Models Methods Appl. Sci. 8 (1998) 657-684. CrossRef
M. Feistauer and C. Schwab, Coupled problems for viscous incompressible flow in exterior domains. In Applied nonlinear analysis. Kluwer/Plenum, New York (1999) 97-116.
Kovasznay, L.I.G., Laminar flow behind two-dimensional grid. Proc. Cambridge Phil. Soc. 44 (1948) 58-62. CrossRef
Y. Maday and A.T. Patera, Spectral element methods for the incompressible Navier-Stokes equations. In State-of-the-art surveys on computational mechanics. A.K. Noor and J. T. Oden Eds., The American Society of Mechanical Engineers, New York (1989).
Quarteroni, A., Sacchi La, G.ndriani, and A. Valli, Coupling of viscous and inviscid incompressible Stokes equations. Numer. Math. 59 (1991) 831-859. CrossRef
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.
A. Quarteroni and A. Valli, Domain decomposition methods for partial differential equations. Oxford Science Publications, Oxford (1999).
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).
R. Temam, Navier-Stokes equations. Theory and numerical analysis. 3rd edn., North-Holland, Amsterdam (1984).
R. Temam, Navier-Stokes equations and nonlinear functional analysis. SIAM, Philadelphia (1988).
van der Vorst, H.A., 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. CrossRef