Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
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
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.
Opis fizyczny
  • IMAGLMC CNRS UMR 5523, BP 53, F-38041 Grenoble cedex, France
  • LIMOS, Université Blaise Pascal - CNRS UMR 6158 ISIMA, Campus des Cézezeaux, BP 10125, 63173 Aubière cedex, France
  • Bernardi C., Chacon T., Lewandowski R. and Murat F. (2002) A model for two coupled turbulent fluids I: Analysis of the system. - Nonlinear Partial Differential Equationsand Their Applications, Coll`ge de France Seminar, Vol. XIV (Paris,19971998), pp. 69-102, Stud. Math. Appl., Vol. 31, Amsterdam: North-Holland.
  • 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.
  • Lewandowski R. (1997): Analyse Mathematique et Oceanographie. - Paris: Masson.
  • Lions J.L., Temam R. and Wang S. (1993): Models for the coupled atmosphere and ocean. (CAO I,II). - Comput. Mech. Adv., Vol. 1, No. 1, pp. 120.
  • Luenberger D. (1989): Linear and Nonlinear Programming. - Reading, MA: Addison Wesley.
  • Marchuk G.I. (1990): Splitting and alternating direction methods,In: Handbook of Numerical AnalysisVol. I, (Ciarlet P.G. and Lions J.L., Eds.). - Amsterdam: North-Holland,pp. 197-462.
  • Miglio E., Quarteroni A. and Saleri F. (2003): Coupling of free-surface and ground water flows. - Comput. Fluids,Vol. 32, No. 1, pp. 73-83.
  • Pan T.W., Joseph D.D. and Glowinski R. (2005): Simulating the dynamics of fluid-ellipsoid interactions. - Comput. Struct.,Vol. 83, No. 6-7, pp. 463-478.
  • Polak E. (1971): Computational Methods in Optimization. - New York: Academic Press.
  • Quarteroni A. and Valli A. (1999): Domain decomposition methods for partial differential equations. - Oxford: Oxford University Press.
  • Suquet P.M. (1988): Discontinuities and plasticity, In: Non-smooth Mechanicsand Applications, (Moreau J.J. and Panagiotopoulos P.D., Eds.). -CISM courses and lectures, New-York: Springer, No. 302, pp. 279-340.
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.