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2006 | 16 | 4 | 419-429

Tytuł artykułu

Operator-splitting and Lagrange multiplier domain decomposition methods for numerical simulation of two coupled Navier-Stokes fluids

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
We present a numerical simulation of two coupled Navier-Stokes flows, using ope-rator-split-ting and optimization-based non-overlapping domain decomposition methods. The model problem consists of two Navier-Stokes fluids coupled, through a common interface, by a nonlinear transmission condition. Numerical experiments are carried out with two coupled fluids; one with an initial linear profile and the other in rest. As expected, the transmission condition generates a recirculation within the fluid in rest.

Rocznik

Tom

16

Numer

4

Strony

419-429

Opis fizyczny

Daty

wydano
2006
otrzymano
2006-03-17
poprawiono
2006-08-15

Twórcy

  • IMAGLMC CNRS UMR 5523, BP 53, F-38041 Grenoble cedex, France
autor
  • LIMOS, Université Blaise Pascal - CNRS UMR 6158 ISIMA, Campus des Cézezeaux, BP 10125, 63173 Aubière cedex, France

Bibliografia

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  • Bernardi C., Chacon T., Lewandowski R. and Murat F. (2003): A model for two coupled turbulent fluids II:Numerical analysis of a spectral discretization. - SIAM J. Numer. Anal.Vol. 40, No. 6, pp. 2368-2394.
  • Bernardi C., Chacon-Rebello T., Gomez-Marmol, Lewandowski R. and Murat F. (2004): A model for two coupled turbulent fluids III: Numerical approximation by finiteelements. - Numer. Math., Vol. 98, No. 1, pp. 33-66.
  • Bresch D. and Koko J. (2004): An optimization-based domain decomposition method for nonlinear wall laws in coupled systems. - Math. Models Meth. Appl. Sci., Vol. 14, No. 7, pp. 1085-1101.
  • Ciarlet P. (1979): The Finite Element Method for Elliptic Problems. - Amsterdam: North-Holland.
  • Daniel J. (1970): The approximate minimization of functionals. - Englewood Cliffs, NJ: Prentice-Hall.
  • Du Q. (2001): Optimization based non-overlapping domain decomposition algorithms and their convergence. - SIAM J. Numer. Anal., Vol. 39, No. 3, pp. 1056-1077.
  • Du Q. and Gunzburger M.D. (2000): A gradient method approach to optimization-based multidisciplinary simulations and nonverlapping domain decomposition algorithms. - SIAM J. Numer. Anal., Vol. 37,No. 5, pp. 1513-1541.
  • Ekeland I. and Temam R. (1999): Convex Analysis and Variational Problems. - Philadelphia: SIAM.
  • Glowinski R. (2003): Numerical Methods for Fluids, In: Handbook of Numerical Analysis,Vol. IX, (Ciarlet P.G. and Lions J.L., Eds.), Amsterdam: North-Holland.
  • Glowinski R. and Le Tallec P. (1989): Augmented Lagrangian and Operator-splitting Methods in Nonlinear Mechanics. -Philadelphia: SIAM.
  • Glowinski R. and Marocco A. (1975): Sur l'approximation par éléments finis d'ordre un, et la résolution par pénalisation-dualité, d'une classe de problèmes de Dirichlet non linéaires, RAIRO Anal. Num., Vol. 2, No. 2, pp. 41-76.
  • Glowinski R., Pan T.-W. and Periaux J. (1998): Distributed Lagrange multiplier methods for incompressible viscous flow around moving rigid bodies. - Comput. Meth. Appl. Mech. Eng., Vol. 151, No. 1-2, pp. 181-194.
  • Glowinski R., Pan T.W., Hesla T.I., Joseph D.D. and Periaux J. (2000): A distributed Lagrange multiplier fictitious domain method for the simulation of flow around moving rigid bodies: application to particulate flow. - Comput. Methods Appl. Mech. Eng., Vol. 184, No. 2-4, pp. 241-267.
  • Gunzburger M.D. and Peterson J. (1999): An optimization based domain decomposition method for partial differential equations. - Comp. Math. Appl., Vol. 37, No. 10, pp. 77-93.
  • Gunzburger M.D. and Lee H.K. (2000): An optimization-based domain decomposition method for Navier-Stokes equations. - SIAM J. Numer. Anal., Vol. 37, No. 5, pp. 1455-1480.
  • Koko J. (2002): An optimization based domain decomposition method for a bonded structure. - Math. Models Meth. Appl. Sci.,Vol. 12, No. 6, pp. 857-870.
  • Koko J. (2006): Uzawa conjugate gradient domain decomposition methods for coupled Stokes flows. - J. Sci. Comput., Vol. 26,No. 2, pp.195-215.
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Bibliografia

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