On the reduction of kinetic theory models related to finitely extensible dumbbells

Journal of Non-Newtonian Fluid Mechanics

Volumn 134, Issue 1-3 SPEC. ISS., 2006, Pages 136-147

  Ammar, Amine ^a   Ryckelynck, David ^b   Chinesta, Francisco ^b   Keunings, R ^c  

^a Univ Joseph Fourier Grenoble 1   (France)

^b CNRS   (France)

^c UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

FENE model; Fokker Planck equation; Karhunen Lo ve decomposition; Kinetic theory; Krylov's subspaces; Model reduction; Non Newtonian fluids; Numerical modelling

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; MATHEMATICAL MODELS; NON NEWTONIAN FLOW; VISCOELASTICITY;

FOKKER-PLANCK EQUATION; KRYLOV SUBSPACES; MODEL REDUCTION;

KINETIC THEORY;

APPROXIMATION THEORY; COMPUTER SIMULATION; KINETIC THEORY; MATHEMATICAL MODELS; NON NEWTONIAN FLOW; VISCOELASTICITY;

EID: 33645105324     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2006.01.007     Document Type: Article

References (16)

1. A. Ammar, F. Chinesta, A particle strategy for solving Fokker-Planck equation governing the fiber orientation distribution in steady recirculating flows involving short fiber suspensions, Lecture Notes on Computational Science and Engineering. Springer 43 (2004) 1-16.
2. B.B. Bird C.F. Curtiss R.C. Armstrong O. Hassager Dynamics of polymeric liquids Kinetic Theory, vol. 2 1987 John Wiley & Sons
3. C.V. Chaubal A. Srinivasan O. Egecioglu L.G. Leal Smoothed particle hydrodynamics techniques for the solution of kinetic theory problems J. Non-Newtonian Fluid Mech. 70 1997 125-154
4. C. Chauviere A. Lozinski Simulation of dilute polymer solutions using a Fokker-Planck equation Comput. Fluids 33 2004 687-696
5. F. Chinesta G. Chaidron A. Poitou On the solution of the Fokker-Planck equations in steady recirculating flows involving short fiber suspensions J. Non-Newtonian Fluid Mech. 113 2-3 2004 97-125
6. R. Jendrejack J. de Pablo M. Graham A method for multiscale simulation of flowing complex fluids J. Non-Newtonian Fluid Mech. 108 2002 123-142
7. R. Keunings On the Peterlin approximation for finitely extensible dumbells J. Non-Newtonian Fluid Mech. 68 1997 85-100
8. R. Keunings Micro-macro methods for the multiscale simulation viscoelastic flow using molecular models of kinetic theory D.M. Binding K. Walters Rheology Reviews 2004 British Society of Rheology 67-98
9. A. Lozinski C. Chauviere A fast solver for Fokker-Planck equation applied to viscoelastic flows calculations: 2D FENE model J. Comput. Phys. 189 2003 607-625
10. M.A. Martinez E. Cueto I. Alfaro M. Doblar F. Chinesta Updated Lagrangian free surface flow simulations with the natural neighbour Galerkin methods Int. J. Numer. Meth. Eng. 60 2004 2105-2129
11. M.A. Martinez E. Cueto M. Doblar F. Chinesta Natural element meshless simulation of injection processes involving short fiber suspensions J. Non-Newtonian Fluid Mech. 115 2003 51-78
12. H.C. Öttinger, M. Laso, Smart polymers in finite element calculation, International Congress on Rheology, Brussel, Belgium, 1992.
13. D. Ryckelynck A priori hyperreduction method: An adaptive approach J. Comput. Phys. 202 2005 346-366
14. D. Ryckelynck F. Chinesta E. Cueto A. Ammar On the a priori model reduction: Overview and recent developments Arch. Comput. Meth. Eng. 13 1 2006 91-128
15. M. Somasi B. Khomami N.J. Woo J.S. Hur E.S.G. Shaqfeh Brownian dynamics simulations of bead-rod and bead-spring chains: Numerical algorithms and coarse-graining issues J. Non-Newtonian Fluid Mech. 108 1-3 2002 227-255
16. G. Venkiteswaran M. Junk A QMC approach for high dimensional Fokker-Planck equations modelling polymeric liquids Math. Comput. Simulat. 68 2005 43-56