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Computational issues related to iterative coupling of subsurface and channel flows. (English) Zbl 1150.76028
The authors consider iterative solution techniques for the coupling of Darcy and Stokes flow based on efficient solvers for the discrete Stokes and Darcy problems. After a short introduction into the problem and a discussion of iterative techniques used numerical examples are given in order to compare different techniques. The paper ends with a discussion of pros and cons of the techniques tested.
76M10Finite element methods (fluid mechanics)
65N22Solution of discretized equations (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
76D07Stokes and related (Oseen, etc.) flows
76S05Flows in porous media; filtration; seepage
65F10Iterative methods for linear systems
[1]1. Axelsson, O.: Iterative solution methods. Cambridge: Cambridge University Press 1994
[2]2. Beavers, G.S., Joseph, D.D.: Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207 (1967) · doi:10.1017/S0022112067001375
[3]3. Discacciati, M., Miglio, E., Quarteroni, A.: Mathematical and numerical models for coupling surface and groundwater flows. Appl. Numer. Math. 43, 57–74 (2002) · Zbl 1023.76048 · doi:10.1016/S0168-9274(02)00125-3
[4]4. Discacciati, M., Quarteroni, A.: Analysis of a domain decomposition method for the coupling of Stokes and Darcy equations. In: Brezzi, F. et al. (eds.): Numerical mathematics and advanced applications. ENUMATH 2001. Milan: Springer 2003, pp. 3–20
[5]5. Discacciati, M., Quarteroni, A.: Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations. Comput. Vis. Sci. 6, 93–103 (2004)
[6]6. Discacciati, M.: Domain decomposition methods for the coupling of surface and groundwater flows. PhD Thesis, Ecole Polytechnique Federale de Lausanne 2004
[7]7. Graham, I., Hagger, M.J.: Unstructured additive Schwarz-conjugate gradient method for elliptic problems with highly discontinuous coefficients. SIAM J. Sci. Comput. 20, 2041–2066 (1999) · Zbl 0943.65147 · doi:10.1137/S1064827596305593
[8]8. Jäger, W., Mikelić, A.: On the interface boundary condition of Beavers, Joseph and Saffman. SIAM J. Appl. Math. 60, 1111–1127 (2000) · Zbl 0969.76088 · doi:10.1137/S003613999833678X
[9]9. Layton, W., Schieweck, F., Yotov, I.: Coupling fluid flow with porous media flow. SIAM J. Numer. Anal. 40, 2195–2218 (2003) · Zbl 1037.76014 · doi:10.1137/S0036142901392766
[10]10. Miglio, E., Quarteroni, A., Saleri, F.: Coupling of free surface and groundwater flows. Comput. & Fluids 32, 73–83 (2003) · Zbl 1035.76051 · doi:10.1016/S0045-7930(01)00102-5
[11]11. Payne, L.E., Straughan, B.: Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modelling questions. J. Math. Pures Appl. (9) 77, 317–354 (1998)
[12]12. Porta, P.: Heterogeneous domain decomposition methods for coupled flow problems. PhD Thesis, University of Augsburg 2004
[13]13. Quarteroni, A., Valli, A.: Domain decomposition methods for partial differential equations. Oxford: Oxford University Press 1999
[14]14. Saffman, P.: On the boundary condition at the surface of a porous medium. Stud. Appl. Math. 50, 93–101 (1971)
[15]15. Salinger, A.G., Aris, R., Derby, J.J.: Finite element formulations for large-scale, coupled flows in adjacent porous and open fluid domains. Internat. J. Numer. Methods Fluids 18, 1185–1209 (1994) · Zbl 0807.76039 · doi:10.1002/fld.1650181205
[16]16. Stüben K.: Algebraic multigrid (AMG): experiences and comparisons. Appl. Math. Comput. 13, 419–451 (1983) · Zbl 0533.65064 · doi:10.1016/0096-3003(83)90023-1