Summary
We develop a method for the coupling of a generalized Stokes problem and a problem with vanishing viscosity for an incompressible flow in a bounded region in two dimensions. Correct transmission conditions are derived, and an iterative procedure involving the successive resolution of two subproblems is suggested.
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References
Zeidler, E.: “Vorlesungen iiber nichtlineare Funktionalanalysis II: Monotone Operatoren”, B. G. Teubner Leipzig 1977.
Temam, R.: “Navier-Stokes equations: theory and numerical analysis”, North Holland, Amsterdam, Oxford 1984.
Glowinski, R.: “Numerical methods for nonlinear variational problems”, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo 1984.
Girault, V. and Raviart, P.-A.: “Finite element methods for the Navier-Stokes equations”, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo 1986.
Hackbusch, W.: “Theorie und Numerik elliptischer Differentialgleichungen”, B. G. Teubner Stuttgart 1986.
Dautray, R., and Lions, J.-L.: “Mathematical analysis and numerical methods for science and technology, volume 2”, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo 1988.
Cahouet, J.: “On some difficulties occurring in the simulation of incompressible fluid flows by domain decomposition”, In: Chan, T. et al (eds.): Domain decomposition methods for partial differential equations, vol. I. SIAM, Philadelphia (1988), pp. 313–332.
Dinh, Q.V., Glowinski, R., Periaux, J., and Terrasson, G.: “On the coupling of viscous and inviscid models for incompressible fluid flows via domain decomposition”, In: Chan, T. et al (eds.): Domain decomposition methods for partial differential equations, vol. I. SIAM, Philadelphia (1988), pp. 350–369.
Brezzi, F., Canuto, C., and Russo, A.: “A self-adaptive formulation for the Euler/Navier-Stokes coupling”, Comp. Meth. A.pl. Mech. Eng., 73 (1989) pp. 317–330.
Pasciak, J.E.: “Two domain decomposition techniques for Stokes problems”, In: Chan, T. et al (eds.): Domain decomposition methods for partial differential equations, vol. II. SIAM, Philadelphia (1989), pp. 419–430.
Quarteroni, A.: “Domain decomposition algorithms for the Stokes equations”, In: Chan, T. et al (eds.): Domain decomposition methods for partial differential equations, vol. 11. SIAM, Philadelphia (1989), pp. 431–442.
Castaldi, F., Quarteroni, A.: “On the coupling of hyperbolic and parabolic systems: analytical and numerical approach”, Appl. Numer. Math., 6 (1989) pp. 3–31.
Gastaldi, F., Quarteroni, A. and Sacchi Landriani, G.: “On the coupling of two dimensional hyperbolic and elliptic equations: analytical and numerical approach”, In: Chan, T. et al (eds.): Domain decomposition methods for partial differential equations, vol. III. SIAM, Philadelphia (1990), pp. 22–63.
Quarteroni, A.: “Domain decomposition and parallel processing for the numerical solution of partial differential equations”, Mathematics for Industry, 1 (1991) pp. 75–118.
Quarteroni, A., Sacchi Landriani, G., and Valli, A.: “Coupling of viscous and inviscid Stokes equations via a domain decomposition method for finite elements”, Numer. Math., 59 (1991) pp. 831–859.
Quarteroni, A., Valli, A.: “Domain decomposition for a generalized Stokes problem”, In: Manley, J. et al (eds.): Proceedings of the third European conference on mathematics in industry, Kluwer, Dortrecht, B.G.Teubner, Stuttgart (1991), pp. 59–74.
Quarteroni, A., Pasquarelli, F., and Valli, A.: “Heterogeneous domain decomposition: principles, algorithms, applications”, Preprint Nr. 40/P, Milano 1991.
Heywood, J. G., Rannacher, R., and Turek, S.: “Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations”, Preprint Nr. 681, SFB 123, Universität Heidelberg 1992.
Hebeker, F.-K., and Wilde, P.: “On missing boundary conditions with unsteady incompressible Navier-Stokes flow”, Math. Meth. in the Appl. Sci., 15 (1992) pp. 421–432.
Borchers, W.: “A Fourier spectral method for incompressible viscous flows past obstacles”, In: Hirschel, E.H. et al (eds.): Flow simulation with high-performance computers I, Vieweg, Braunschweig (1993).
Frati, A., Pasquarelli, F., and Quarteroni, A.: “Spectral approximation to advection-diffusion problems by the fictitious interface method”, J. Comp. Phys., 107 (1993) pp. 201–212.
Schenk, K., and Hebeker, F.-K.: “Coupling of two dimensional viscous and inviscid incompressible Stokes equations”, Preprint, Universität Heidelberg Dezember 1993.
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© 1994 Springer Fachmedien Wiesbaden
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Schenk, K., Hebeker, F.K. (1994). Coupling of Two Dimensional Viscous and Inviscid Incompressible Stokes Equations. In: Hebeker, FK., Rannacher, R., Wittum, G. (eds) Numerical methods for the Navier-Stokes equations. Notes on Numerical Fluid Mechanics (NNFM), vol 47. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14007-8_24
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DOI: https://doi.org/10.1007/978-3-663-14007-8_24
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-07647-4
Online ISBN: 978-3-663-14007-8
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