화학공학소재연구정보센터
홈 로그인 로그아웃 연락처 사이트맵
Korea-Australia Rheology Journal, Vol.14, No.4, 161-174, December, 2002
Export Citation
Computation of viscoelastic flow using neural networks and stochastic simulation
D. Tran-Canh, and T. Tran-Cong†
  • Faculty of Engineering and Surveying, University of Southern Queensland, Toowoomba, QLD 4350, Australia
E-mail:
A new technique for numerical calculation of viscoelastic flow based on the combination of Neural Networks (NN) and Brownian Dynamics simulation or Stochastic Simulation Technique (SST) is presented in this paper. This method uses a “universal approximator” based on neural network methodology in combination with the kinetic theory of polymeric liquid in which the stress is computed from the molecular configuration rather than from closed form constitutive equations. Thus the new method obviates not only the need for a rheological constitutive equation to describe the fluid (as in the original Calculation Of Non-Newtonian Flows: Finite Elements & Stochastic Simulation Techniques (CONNFFESSIT) idea) but also any kind of finite element-type discretisation of the domain and its boundary for numerical solution of the governing PDE's. As an illustration of the method, the time development of the planar Couette flow is studied for two molecular kinetic models with finite extensibility, namely the Finitely Extensible Nonlinear Elastic (FENE) and FENE-Peterlin (FENE-P) models.
Keywords:Brownian dynamics;neural networks;molecular models;stochastic simulation;viscoelastic flow;diffusion equation;Fokker-Plank equation;Brownian simulation;CONNFFESSIT
  1. Beatson RK, Light WA, IMA J. Numer. Anal., 17, 343 (1997) 
  2. Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P, Comput. Meth. Appl. Mech. Eng., 139, 347 (1996) 
  3. Bird RB, Curtiss CF, Armstrong RC, Hassager O, Dynamics of Polymeric Liquids, Vol. 2, John Wiley & Sons, New York (1987)
  4. Bonvin J, Picasso M, J. Non-Newton. Fluid Mech., 84(2-3), 191 (1999) 
  5. Carlson RE, Foley TA, Comput. Math. Appl., 21(9), 29 (1991) 
  6. Camahan B, Luther HA, Wilkes JO, Applied Numerical Methods, John Wiley & Sons, New York (1969)
  7. Chow AW, Fuller CG, J. Non-Newton. Fluid Mech., 17, 125 (1985) 
  8. Constantinides A, Mostoufi N, Numerical Methods for Chemical Engineers with Matlab Application, Prentice Hall PTR, New Jersey (1999)
  9. Conti M, Turchetti C, Neural Parallel Scientific Comput., 2, 299 (1994)
  10. Duchon J, RAIRO Anal. Numer., 10, 5 (1976)
  11. Fan XJ, J. Non-Newton. Fluid Mech., 17, 125 (1985) 
  12. Feigl K, Laso M, Ottinger HC, Macromolecules, 28(9), 3261 (1995) 
  13. Fixman M, J. Chem. Phys., 69(4), 1527 (1978) 
  14. Fixman M, J. Chem. Phys., 69(4), 1538 (1978) 
  15. Franke R, Math. Comput., 48, 181 (1982)
  16. Gardiner CW, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, Springer-Verlag, Berlin (1990)
  17. Gihman II, Skorohod AV, The Theory of Stochastic Processes III, Springer-Verlag, Berlin (1974)
  18. Hardy RL, J. Geophys. Res., 176, 1095 (1971)
  19. Haykin S, Neural Networks: A Comprehensive Foundation, Prentice Hall, New Jersey (1999)
  20. He S, Reif K, Unbehauen R, Neural Networks, 13, 385 (2000) 
  21. Herrchen M, Ottinger HC, J. Non-Newton. Fluid Mech., 68(1), 17 (1997) 
  22. Hulsen MA, vanHeel APG, vandenBrule BHAA, J. Non-Newton. Fluid Mech., 70(1-2), 79 (1997) 
  23. Kansa EJ, Comput. Math. Appl., 19(8-9), 147 (1990) 
  24. Keunings R, J. Non-Newton. Fluid Mech., 68(1), 85 (1997) 
  25. Kloeden PE, Platen E, Schurz H, Numerical Solution of SDE through Computer Experiments, Springer, Berlin (1997)
  26. Kloeden PE, Platen E, Numerical Solution of Stochastic Differential Equations, Springer, Berlin (1997)
  27. Laso M, Ottinger HC, J. Non-Newton. Fluid Mech., 47, 1 (1993) 
  28. Laso M, Picasso M, Ottinger HC, AIChE J., 43(4), 877 (1997) 
  29. Laso M, Picasso M, Ottinger HC, Calculation of Flows with Large Elongation Components: CONNFFESSIT Calculation of the Flow of a FENE Fluid in a Planar 10:1 Contraction. In: Nguyen, T.Q. and Kausch, H.H., Flexible Polymer Chains Dynamics in Elongational Flow: Theory and Experiment, Chapter 6, 101-136, Springer, Berlin (1999)
  30. Mai-Duy N, Tran-Cong T, Neural Networks, 14, 185 (2001) 
  31. Mochimaru Y, J. Non-Newton. Fluid Mech., 12, 135 (1983) 
  32. Onate E, Idelsohn S, Zienkiewicz OC, Taylor L, Int. J. Numer. Methods Eng., 39, 3839 (1996) 
  33. Orr MJL, Matlab Routines for Subset Selection and Ridge Regression in Linear Network, http://www.cns.ed.ac.uk/~mjo (1997)
  34. Orr MJL, Regularisation in the Selection of Radial Basis Function Centres, http://www.cns.ed.ac.uk/~mjo (1999)
  35. Ottinger HC, Stochastic Processes in Polymeric Fluids: Tools and Examples for Developing Simulation Algorithms, Springer, Berlin (1996)
  36. Ottinger HC, vandenBrule BHAA, Hulsen MA, J. Non-Newton. Fluid Mech., 70(3), 255 (1997) 
  37. Park J, Sandberg IW, Neural Comput., 3, 246 (1991)
  38. Smith GD, Numerical Solution Partial Differential Equations: Finite Difference Methods, Clarendon, Oxford (1978)
  39. Tran-Canh D, Tran-Cong T, Eng. Anal. Boundary Elements, 26, 15 (2002) 
  40. Zerroukat M, Power H, Chen CS, Int. J. Numer. Methods Eng., 42, 1263 (1998)