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

Didier Bresch; Jonas Koko

International Journal of Applied Mathematics and Computer Science (2006)

  • Volume: 16, Issue: 4, page 419-429
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Bresch, Didier, and Koko, Jonas. "Operator-splitting and Lagrange multiplier domain decomposition methods for numerical simulation of two coupled Navier-Stokes fluids." International Journal of Applied Mathematics and Computer Science 16.4 (2006): 419-429. <http://eudml.org/doc/207803>.

@article{Bresch2006,
abstract = {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.},
author = {Bresch, Didier, Koko, Jonas},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {Navier-Stokes flows; duality; domain decomposition; conjugate gradient; Navier-Stokes equations},
language = {eng},
number = {4},
pages = {419-429},
title = {Operator-splitting and Lagrange multiplier domain decomposition methods for numerical simulation of two coupled Navier-Stokes fluids},
url = {http://eudml.org/doc/207803},
volume = {16},
year = {2006},
}

TY - JOUR
AU - Bresch, Didier
AU - Koko, Jonas
TI - Operator-splitting and Lagrange multiplier domain decomposition methods for numerical simulation of two coupled Navier-Stokes fluids
JO - International Journal of Applied Mathematics and Computer Science
PY - 2006
VL - 16
IS - 4
SP - 419
EP - 429
AB - 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.
LA - eng
KW - Navier-Stokes flows; duality; domain decomposition; conjugate gradient; Navier-Stokes equations
UR - http://eudml.org/doc/207803
ER -

References

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  1. 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. Zbl1034.35106
  2. 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. Zbl1129.76327
  3. 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. Zbl1129.76326
  4. 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. Zbl1185.65223
  5. Ciarlet P. (1979): The Finite Element Method for Elliptic Problems. - Amsterdam: North-Holland. 
  6. Daniel J. (1970): The approximate minimization of functionals. - Englewood Cliffs, NJ: Prentice-Hall. 
  7. Du Q. (2001): Optimization based non-overlapping domain decomposition algorithms and their convergence. - SIAM J. Numer. Anal., Vol. 39, No. 3, pp. 1056-1077. Zbl1004.65132
  8. 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. Zbl0964.65142
  9. Ekeland I. and Temam R. (1999): Convex Analysis and Variational Problems. - Philadelphia: SIAM. Zbl0939.49002
  10. 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. 
  11. Glowinski R. and Le Tallec P. (1989): Augmented Lagrangian and Operator-splitting Methods in Nonlinear Mechanics. -Philadelphia: SIAM. Zbl0698.73001
  12. 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. Zbl0368.65053
  13. 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. Zbl0916.76052
  14. 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. Zbl0970.76057
  15. 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. Zbl0941.65123
  16. 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. Zbl1003.76024
  17. 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. Zbl1205.74016
  18. Koko J. (2006): Uzawa conjugate gradient domain decomposition methods for coupled Stokes flows. - J. Sci. Comput., Vol. 26,No. 2, pp.195-215. Zbl1203.76116
  19. Lewandowski R. (1997): Analyse Mathematique et Oceanographie. - Paris: Masson. 
  20. 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. Zbl0805.76011
  21. Luenberger D. (1989): Linear and Nonlinear Programming. - Reading, MA: Addison Wesley. Zbl1134.90040
  22. 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. Zbl0875.65049
  23. 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. Zbl1035.76051
  24. 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. 
  25. Polak E. (1971): Computational Methods in Optimization. - New York: Academic Press. 
  26. Quarteroni A. and Valli A. (1999): Domain decomposition methods for partial differential equations. - Oxford: Oxford University Press. Zbl0931.65118
  27. 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. 

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