Decoupled second-order transient schemes for the flow of viscoelastic fluids without a viscous solvent contribution

Journal of Non-Newtonian Fluid Mechanics

Volumn 165, Issue 23-24, 2010, Pages 1602-1612

  D'Avino, G ^a   Hulsen, M A ^b  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Decoupled transient schemes; Finite element method; Numerical simulations; Viscoelastic fluid flow

Indexed keywords

BENCH-MARK PROBLEMS; COMPUTATIONAL COSTS; CONTINUITY EQUATIONS; CRANK-NICOLSON; CRANK-NICOLSON SCHEME; DECOUPLED TRANSIENT SCHEMES; DISCRETIZATIONS; EULER SCHEME; FINITE ELEMENT; FIRST-ORDER; GLOBAL SYSTEMS; GOVERNING EQUATIONS; LINEAR SYSTEM OF EQUATIONS; MOMENTUM BALANCES; MOMENTUM EQUATION; NEWTONIAN SOLVENTS; NON-LINEAR; NUMERICAL SCHEME; NUMERICAL SIMULATION; SECOND ORDER CONVERGENCE; SECOND ORDERS; SOLVENT VISCOSITY; SPECIFIC PROBLEMS; STRESS TENSORS; TIME MARCHING; TIME-INTEGRATION SCHEME; TRANSIENT FLOW; VELOCITY FIELD; VISCO-ELASTIC FLUID; VISCOELASTIC FLUID FLOWS; VISCOUS SOLVENTS;

COMPUTER SIMULATION; CONSTITUTIVE EQUATIONS; CONVERGENCE OF NUMERICAL METHODS; FLUIDS; LINEAR SYSTEMS; MOMENTUM; POLYMER MELTS; SOLVENTS; STEADY FLOW;

FINITE ELEMENT METHOD;

EID: 78149467264     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2010.08.007     Document Type: Article

References (33)

1. Baaijens F.P.T. Mixed finite element methods for viscoelastic flow analysis: a review. J. Non-Newtonian Fluid Mech. 1998, 79:361-385.
2. Owens R.G., Phillips T.N. Computational Rheology 2002, World Scientific.
3. Rajagopalan D., Armstrong R.C., Brown R.A. Finite element methods for calculation of steady, viscoelastic flow using constitutive equations with a Newtonian viscosity. J. Non-Newtonian Fluid Mech. 1990, 36:159-192.
4. Guénette R., Fortin M. A new mixed finite element method for computing viscoelastic flows. J. Non-Newtonian Fluid Mech. 1995, 60:27-52.
5. Marchal J.M., Crochet M.J. A new mixed finite element method for calculating viscoelastic flow. J. Non-Newtonian Fluid Mech. 1987, 26:77-114.
6. Brooks A.N., Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Meth. Appl. Mech. Eng. 1982, 32:199-256.
7. Fattal R., Kupferman R. Constitutive laws for the matrix-logarithm of the conformation tensor. J. Non-Newtonian Fluid Mech. 2004, 123:281-285.
8. Tanner R.I., Xue S.-C. Computing transient flows with high elasticity. Korea-Aust. Rheol. J. 2002, 14:143-159.
9. Northey P.J., Armstrong R.C., Brown R.A. Finite-amplitude time-periodic states in viscoelastic Taylor-Couette flow described by the UCM model. J. Non-Newtonian Fluid Mech. 1992, 42:117-139.
10. Bodart C., Crochet M.J. Time-dependent numerical simulation of viscoelastic flow and stability. Theor. Comput. Fluid Dyn. 1993, 5:57-75.
11. Bodart C., Crochet M.J. The time-dependent flow of a viscoelastic fluid around a sphere. J. Non-Newtonian Fluid Mech. 1994, 54:303-329.
12. Glowinksi R., Pironneau O. Finite element methods for Navier-Stokes equations. Ann. Rev. Fluid Mech. 1992, 24:167-204.
13. Singh P., Leal L.G. Finite element simulation of the start-up problem for a viscoelastic fluid in in eccentric rotating cylinder geometry using a third-order upwind scheme. Theor. Comput. Fluid Dyn. 1993, 5:107-137.
14. Saratimo P. A new Θ-scheme algorithm and incompressible FEM for viscoelastic fluid flows. Math. Model. Numer. Anal. 1994, 28:1-34.
15. Saratimo P. Efficient simulation of non-linear viscoelastic fluid flows. J. Non-Newtonian Fluid Mech. 1996, 60:199-223.
16. Sureshkumar R., Smith M.D., Armstrong R.C., Brown R.A. Linear stability and dynamics of viscoelastic flows using time-dependent numerical simulations. J. Non-Newtonian Fluid Mech. 1999, 82:57-104.
17. Hwang W.R., Hulsen M.A., Meijer H.E.H. Direct simulations of particle suspensions in a viscoelastic fluid in sliding bi-periodic frames. J. Non-Newtonian Fluid Mech. 2004, 121:15-33.
18. D'Avino G., Maffettone P.L., Hulsen M.A., Peters G.W.M. Numerical simulation of planar elongational flow of concentrated rigid particle suspensions in a viscoelastic fluid. J. Non-Newtonian Fluid Mech. 2008, 150:65-79.
19. Pan T.-W., Hao J., Glowinski R. On the simulation of a time-dependent cavity flow of an Oldroyd-B fluid. Int. J. Numer. Meth. Fluids 2007, 60:791-808.
20. D'Avino G., Tuccillo T., Maffettone P.L., Greco G., Hulsen M.A. Numerical simulations of particle migration in a viscoelastic fluid subjected to shear flow. Comp. Fluids 2010, 39:709-721.
21. D'Avino G., Maffettone P.L., Greco G., Hulsen M.A. Viscoelasticity-induced migration of a rigid sphere in confined shear flow. J. Non-Newtonian Fluid Mech. 2010, 165:466-474.
22. Sadanandan B., Sureshkumar R. Global linear stability analysis of viscoelastic flow through a periodic channel. J. Non-Newtonian Fluid Mech. 2004, 122:55-67.
23. Harlen O.G., Rallison J.M., Szabo P. A split Lagrangian-Eulerian method for simulating transient viscoelastic flows. J. Non-Newtonian Fluid Mech. 1995, 60:81-104.
24. Bogaerds A.C.B., Hulsen M.A., Peters G.W.M., Baaijens F.P.T. Time dependent finite element analysis of the linear stability of viscoelastic flows with interfaces. J. Non-Newtonian Fluid Mech. 2003, 116:33-54.
25. D'Avino G., Cicale G., Hulsen M.A., Greco F., Maffettone P.L. Effects of confinement on the motion of a single sphere in a sheared viscoelastic liquid. J. Non-Newtonian Fluid Mech. 2009, 157:101-107.
26. Bogaerds A.C.B., Grillet A.M., Peters G.W.M., Baaijens F.P.T. Stability analysis of polymer shear flows using the extended pom-pom constitutive equations. J. Non-Newtonian Fluid Mech. 2002, 108:187.
27. D'Avino G., Hulsen M.A., Snijkers F., Vermant J., Greco F., Maffettone P.L. Rotation of a sphere in a viscoelastic liquid subjected to shear flow. Part I. Simulation results. J. Rheol. 2008, 52:1331-1346.
28. HSL, A Collection of Fortran Codes for Large Scale Scientific Computation, 2002. Available from: http://www.cse.clrc.ac.uk/nag/hsl/.
29. Hulsen M.A., Fattal R., Kupferman R. Flow of viscoelastic fluids past a cylinder at high Weissenberg number: stabilized simulations using matrix logarithms. J. Non-Newtonian Fluid Mech. 2005, 127:27-39.
30. Waters N.D., King M.J. Unsteady flow of an elastico-viscous liquid. Rheol. Acta 1970, 9:345-355.
31. Brady J.F. The Einstein viscosity correction in n dimensions. Int. J. Multiphase Flow 1984, 10:113-114.
32. Kupferman R. On the linear stability of plane Couette flow for an Oldroyd-B fluid and its numerical approximation. J. Non-Newtonian Fluid Mech. 2005, 127:169-190.
33. Gorodtsov V.A., Leonov A.I. On a linear instability of a plane parallel Couette flow of a viscoelastic fluid. J. Appl. Math. Mech. 1967, 31:310-319.