A finite element/Monte-Carlo method for polymer dilute solutions

Computing and Visualization in Science

Volumn 4, Issue 2, 2001, Pages 93-98

  Bonvin, John ^a   Picasso, Marco ^a  

^a EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SCIENCE; VISUALIZATION;

DILUTE SOLUTION; MOMENTUM EQUATION; NUMERICAL RESULTS; OLDROYD-B; POLYMER CHAINS; STOCHASTIC DIFFERENTIAL EQUATIONS;

POLYMERS;

EID: 33748566160     PISSN: 14329360     EISSN: 14330369     Source Type: Journal    
DOI: 10.1007/s007910100060     Document Type: Article

References (28)

1. Baaijens, F.P.T.: Mixed finite element methods for viscoelastic flow analysis: a review. J. Non-Newtonian Fluid Mech. 79, 361-385 (1998)
2. Baranger, J., Sandri, D.: Finite element approximation of viscoelastic fluid flow. Numer. Math. 63, 13-27 (1992)
3. Behr, M., Franca, L., Tezduyar, T.: Stabilized finite element methods for the velocity-pressure-stress formulation of incompressible flows. Comput. Meth. Appl. Mech. Eng. 104, 31-48 (1993)
4. Bird, R., Armstrong, R., Hassager, O.: Dynamics of polymeric liquids. Vol. 1. New York: John Wiley & Sons 1987
5. Bird, R., Curtiss, C., Armstrong, R., Hassager, O.: Dynamics of polymeric liquids. Vol. 2. New York: John Wiley & Sons 1987
6. Bonvin, J.C.: Numerical Simulation of Viscoelastic Fluids with Mesoscopic Models. PhD thesis. Département de Mathématiques, École Polytechnique Fédérale de Lausanne. 2000
7. Bonvin, J.C., Picasso, M.: Variance Reduction Methods for CONNFFESSIT-like Simulations. J. Non-Newtonian Fluid Mech. 84, 191-215 (1999)
8. Bonvin, J.C., Picasso, M., Stenberg, R.: GLS and EVSS methods for a three fields Stokes problem arising from viscoelastic flows. Comp. Meth. Appl. Mech. Eng. 190, 3893-3914 (2001)
9. Ciarlet, P.G.: The Finite Element method for elliptic problems. London: Academic Press 1990
10. Fortin, M., Guénette, R., Pierre, R.: Numerical analysis of the modified EVSS method. Comp. Meth. Appl. Mech. Eng. 143, 79-95 (1997)
11. Fortin, M., Pierre, R.: On the convergence of the mixed method of Crochet and Marchal for viscoelastic flows. Comput. Meth. Appl. Mech. Eng. 73, 341-350 (1989)
12. Franca, L., Stenberg, R.: Error analysis of some GLS methods for elasticity equations. Siam. J. Numer. Anal. 28(6), 1680-1697 (1991)
13. Guillopé, C., Saut, J.-C.: Existence results for the flow of viscoelastic fluids with a differential constitutive law. Nonlinear Anal. 15, 849-869 (1990)
14. Halin, P., Lielens, G., Keunings, R., Legat, V.: The Lagrangian Particle Method for Macroscopic and Micro-Macro Viscoelastic Flow Computations. Comp. Meth. Appl. Mech. Eng. 180, 345-364 (1999)
15. Hulsen, M.A., Heel, A.P.G. van, Brule, B.H.A.A. van den: Simulation of Viscoelastic Flows using Brownian Configuration Fields. J. Non- Newtonian Fluid Mech. 70, 79-101 (1997)
16. Jourdain, B., Lebris, C., Lelièvre, T.: Modèle micro-macro pour un flot non newtonien de cisaillement : analyse et analyse numérique. in preparation (2000)
17. Kloeden, P.E., Platen, E.: Numerical solution of stochastic differential equations. Berlin, Heidelberg, New York: Springer 1992
18. Laso, M., Öttinger, H.C.: Calculation of viscoelastic flow using molecular models. J. Non-Newtonian Fluid Mech. 47, 1-20 (1993)
19. Najib, K., Sandri, D.: On a decoupled algorithm for solving a finite element problem for the approximation of viscoelastic fluid flow. Numer. Math. 72(2), 223-238 (1995)
20. Öttinger, H.C.: Stochastic processes in polymeric fluids. Berlin, Heidelberg, New York: Springer 1996
21. Picasso, M., Rappaz, J.: Existence, a priori and a posteriori error estimates for a nonlinear three fields Stokes problem arising from viscoelastic flows. Accepted in RAIRO Modél. Math. Anal. Num. (2001)
22. Pironneau, O.: The Finite Element method for fluids. Chichester: John Wiley 1990
23. Quinzani, L.M., Armstrong, R.C., Brown, R.A.: Birefringence and Laser-Doppler Velocimetry studies of viscoelastic flow through a planar contraction. J. Non-Newtonian Fluid Mech. 52, 1-36 (1994)
24. Renardy, M.: Existence of slow steady flows of viscoelastic fluids with differential constitutive equations. ZAMM 65, 449-451 (1985)
25. Ruas, V.: Finite element methods for the three-field Stokes system. RAIRO Modél. Math. Anal. Num. 30, 489-525 (1996)
26. Sandri, D.: Analysis of a three-fields approximation of the Stokes problem. RAIRO Modél. Math. Anal. Num. 27, 817-841 (1993)
27. Sequeira, A., Baia, M.: A finite element approximation for the steady solution of a second-grade fluid model. J. Comp. Appl. Math. 111(2), 281-295 (1999)
28. Talay, D.: Discretization of stochastic differential equations and rough estimate of the expectations of functionals. RAIRO Modél. Math. Anal. Num. 20, 141-179 (1986)