Multimodels for incompressible flows : iterative solutions for the Navier-Stokes / Oseen coupling
ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 3, pp. 549-574.

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.

Classification : 76D05, 65M55, 65M60, 65M70
Mots-clés : Navier-Stokes equations, domain decomposition methods, iterative schemes, convergence analysis 
@article{M2AN_2001__35_3_549_0,
     author = {Fatone, L. and Gervasio, P. and Quarteroni, A.},
     title = {Multimodels for incompressible flows : iterative solutions for the {Navier-Stokes} / {Oseen} coupling},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {549--574},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {3},
     year = {2001},
     mrnumber = {1837084},
     zbl = {1039.76031},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2001__35_3_549_0/}
}
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: Modélisation mathématique et analyse numérique
PY  - 2001
SP  - 549
EP  - 574
VL  - 35
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/M2AN_2001__35_3_549_0/
LA  - en
ID  - M2AN_2001__35_3_549_0
ER  - 
%0 Journal Article
%A Fatone, L.
%A Gervasio, P.
%A Quarteroni, A.
%T Multimodels for incompressible flows : iterative solutions for the Navier-Stokes / Oseen coupling
%J ESAIM: Modélisation mathématique et analyse numérique
%D 2001
%P 549-574
%V 35
%N 3
%I EDP-Sciences
%U http://www.numdam.org/item/M2AN_2001__35_3_549_0/
%G en
%F M2AN_2001__35_3_549_0
Fatone, L.; Gervasio, P.; Quarteroni, A. Multimodels for incompressible flows : iterative solutions for the Navier-Stokes / Oseen coupling. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 3, pp. 549-574. http://www.numdam.org/item/M2AN_2001__35_3_549_0/

[1] C. Bernardi and Y. Maday, Approximations spectrales de problèmes aux limites elliptiques. Springer-Verlag, Paris (1992). | MR | Zbl

[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. | Zbl

[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. | Zbl

[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). | Zbl

[6] M. Feistauer and C. Schwab, On coupled problems for viscous flow in exterior domains. Math. Models Methods Appl. Sci. 8 (1998) 657-684. | Zbl

[7] 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. | Zbl

[8] L.I.G. Kovasznay, Laminar flow behind two-dimensional grid. Proc. Cambridge Phil. Soc. 44 (1948) 58-62. | Zbl

[9] 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). | Zbl

[10] A. Quarteroni, G. Sacchi Landriani, and A. Valli, Coupling of viscous and inviscid incompressible Stokes equations. Numer. Math. 59 (1991) 831-859. | Zbl

[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. | Zbl

[12] A. Quarteroni and A. Valli, Domain decomposition methods for partial differential equations. Oxford Science Publications, Oxford (1999). | MR | Zbl

[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). | Zbl

[14] R. Temam, Navier-Stokes equations. Theory and numerical analysis. 3rd edn., North-Holland, Amsterdam (1984). | Zbl

[15] R. Temam, Navier-Stokes equations and nonlinear functional analysis. SIAM, Philadelphia (1988). | MR | Zbl

[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. | Zbl