Acta Mathematicae Applicatae Sinica

, Volume 18, Issue 4, pp 529–536 | Cite as

Convergence of a Stochastic Method for the Modeling of Polymeric Fluids

  • Weinan E*
  • Tie-jun Li
  • Ping-wen Zhang**
Original Papers


We present a convergence analysis of a stochastic method for numerical modeling of complex fluids using Brownian configuration fields (BCF) for shear flows. The analysis takes into account the special structure of the stochastic partial differential equations for shear flows. We establish the optimal rate of convergence. We also analyze the nature of the error by providing its leading order asymptotics.


Brownian Configuration Fields (BCF) convergence analysis dumbbell model 

2000 MR Subject Classification

74S99 60H35 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bird, R.B., Hassager, O., Armstrong, R.C., Curtiss, C.F. Dynamics of polymeric liquids, Vol.2: Kinetic theory. (2nd ed.), Wiley-Interscience, New York (1987)Google Scholar
  2. 2.
    Doi, M., Edwards, S.F. The theory of polymer dynamics. Oxford University Press, New York (1986)Google Scholar
  3. 3.
    Feng, J., Leal, L.G. Simulating complex flows of liquid crystalline polymers using the Doi theory. J. Rheol., 41, 1317–1335 (1997)CrossRefGoogle Scholar
  4. 4.
    Fishman, G.S. Monte Carlo: concepts, algorithms, and applications. Springer-Verlag, Heidelberg, New York (1995)Google Scholar
  5. 5.
    De Gennes, P.G. Scaling concepts in polymer physics. Cornell Univ. Press, Ithaca, London (1979)Google Scholar
  6. 6.
    Hulsen, M.A., van Heel, A.P.G., van den Brule, B.H.A.A. Simulation of viscoelastic flows using Brownian configuration fields. J. Non-Newtonian Fluid Mech., 70, 79–101 (1997)CrossRefGoogle Scholar
  7. 7.
    Kloeden, P.E., Platen, E. Numerical solution of stochastic differential equations. Springer-Verlag, Heidelberg, New York (1995)Google Scholar
  8. 8.
    Laso, M., Öttinger, H.C. Calculation of viscoelastic flow using molecular models: the CONNFFESSIT approach. J. Non-Newtonian Fluid Mech., 47, 1–20 (1993)zbMATHCrossRefGoogle Scholar
  9. 9.
    Liu, T.W. Flexible polymer chain dynamics and rheological properties in the steady flows. J. Chem. Phys., 90, 5826–5842 (1989)CrossRefGoogle Scholar
  10. 10.
    Milstein, G.N. Numerical integration of stochastic differential equations. Kluwer Academic Publishers, Dordrecht, London, Norwell, New York (1995) (Translated from Russian)Google Scholar
  11. 11.
    Nayak, R. Molecular simulation of liquid crystal polymer flow: a wavelet-finite element analysis. Ph D Thesis, MIT (1998)Google Scholar
  12. 12.
    Oksendal, B. Stochastic differential equations: an introduction with applications. (4th ed.), Springer- Verlag, Heidelberg, New York (1998)Google Scholar
  13. 13.
    Öttinger, H.C. Stochastic processes in polymeric liquids. Springer-Verlag, Heidelberg, New York (1996)Google Scholar
  14. 14.
    Varadhan, S.R.S. Large deviation and applications. SIAM Press, Philadelphia (1984)Google Scholar
  15. 15.
    Suen, J.K.C., Joo, Y.L., Armstrong, R.C. Molecular orientation effects in viscoelasticity. Annu. Rev. Fluid Mech., 34, 417–444 (2002)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  1. 1.Department of Mathematics and PACMPrinceton UniversityPrinceton, NJUSA
  2. 2.Key Laboratory of Pure and Applied Mathematics, School of Mathematical SciencesPeking UniversityBeijingChina

Personalised recommendations