A fictitious domain/distributed Lagrange multiplier method for the particulate flow of Oldroyd-B fluids: A positive definiteness preserving approach

Journal of Non-Newtonian Fluid Mechanics

Volumn 156, Issue 1-2, 2009, Pages 95-111

  Hao, Jian ^a   Pan, Tsorng Whay ^a   Glowinski, Roland ^a   Joseph, Daniel D ^b  

^a University of Houston   (United States)

^b University of Minnesota   (United States)

Author keywords

Fictitious domain; Finite element; Oldroyd B fluid; Operator splitting; Particulate flow; Positive definiteness

Indexed keywords

COERCIVE FORCE; ELASTICITY; FLUID DYNAMICS; FLUIDS; FREQUENCY MULTIPLYING CIRCUITS; LAGRANGE MULTIPLIERS; LIQUIDS; MACH NUMBER; MAGNETIC PROPERTIES; NEWTONIAN LIQUIDS; SEDIMENTATION; TURBULENT FLOW;

FICTITIOUS DOMAIN; FINITE ELEMENT; OLDROYD-B FLUID; OPERATOR SPLITTING; PARTICULATE FLOW; POSITIVE DEFINITENESS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 57449088020     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2008.07.006     Document Type: Article

References (34)

1. Adams J., Swarztrauber P., and Sweet R. FISHPAK: A package of Fortran subprograms for the solution of separable elliptic partial differential equations (1980), The National Center for Atmospheric Research, Boulder, CO
2. Baaijens F.P.T. Mixed finite element methods for viscoelastic flow analysis: a review. J. Non-Newtonian Fluid Mech. 79 (1998) 361-385
3. Binous H., and Phillips R.J. Dynamic simulation of one and two particles sedimenting in viscoelastic suspensions of FENE dumbbells. J. Non-Newtonian Fluid Mech. 83 (1999) 93-130
4. Chhabra R.P. Bubbles, Drops, and Particles in Non-Newtonian Fluids (1993), CRC Press, Boca Raton, FL
5. Chorin A.J., Hughes T.J.R., McCracken M.F., and Marsden J.E. Product formulas and numerical algorithms. Comm. Pure Appl. Math. 31 (1978) 205-256
6. Ciarlet P.G. The Finite Element Method for Elliptic Problems (1978), North-Holland, Amsterdam
7. P.G. Ciarlet, Basic error estimates for elliptic problems, in: P.G. Ciarlet, J.L. Lions (Eds.), Handbook of Numerical Analysis, vol. II, North-Holland, Amsterdam, 1991, pp. 17-351.
8. Dean E.J., and Glowinski R. A wave equation approach to the numerical solution of the Navier-Stokes equations for incompressible viscous flow. C.R. Acad. Sci. Paris, Ser. 1 325 (1997) 783-791
9. E.J. Dean, R. Glowinski, T.W. Pan, A wave equation approach to the numerical solution, in: J.A. De Santo (Ed.), Mathematical and Numerical Aspects of Wave Propagation, SIAM, Philadelphia, 1998, pp. 65-74.
10. Fattal R., and Kupferman R. Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation. J. Non-Newtonian Fluid Mech. 126 (2005) 23-37
11. Feng J., Huang P.Y., and Joseph D.D. Dynamic simulation of sedimentation of solid particles in an Oldroyd-B fluid. J. Non-Newtonian Fluid Mech. 63 (1996) 63-88
12. R. Glowinski, Finite element methods for incompressible viscous flows, in: P.G. Ciarlet, J.L. Lions (Eds.), Handbook of Numerical Analysis, vol. IX, North-Holland, Amsterdam, 2003, pp. 3-1176.
13. Glowinski R., Pan T.-W., and Periaux J. Distributed Lagrange multiplier methods for incompressible flow around moving rigid bodies. Comput. Methods Appl. Mech. Eng. 151 (1998) 181-194
14. Glowinski R., Pan T.-W., Hesla T., and Joseph D.D. A distributed Lagrange multiplier/fictitious domain method for particulate flows. Int. J. Multiphase Flow 25 (1999) 755-794
15. Glowinski R., Pan T.-W., Hesla T., Joseph D.D., and Periaux J. A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow. J. Comput. Phys. 169 (2001) 363-426
16. Hu H.H. Direct simulation of flows of solid-liquid mixtures. Int. J. Multiphase Flow 22 (1996) 335
17. Hu H.H., Joseph D.D., and Crochet M.J. Direct simulation of fluid particle motions. Theor. Comp. Fluid Dyn. 3 (1992) 285-306
18. Hu H.H., Patankar N.A., and Zhu M.Y. Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique. J. Comput. Phys. 169 (2001) 427-462
19. Huang P.Y., Hu H.H., and Joseph D.D. Direct simulation of the sedimentation of elliptic particles in Oldroy-B fluids. J. Fluid Mech. 362 (1998) 297-325
20. Johnson C. Streamline diffusion methods for problems in fluid mechanics. In: Gallagher R. (Ed). Finite Element in Fluids IV (1985), Wiley-Interscience, Chichester, England and New York 251-261
21. Joseph D.D. Fluid Dynamics of Viscoelastic Liquids (1990), Springer, New York
22. Joseph D.D., Liu Y.J., Poletto M., and Feng J. Aggregation and dispersion of spheres falling in viscoelastic liquids. J. Non-Newtonian Fluid Mech. 54 (1994) 45-86
23. R. Keunings, A survey of computational rheology, in: D.M. Binding et al. (Eds.), 13th International Congress on Rheology, vol. 1, British Society of Rheology, Glasgow, 2000, 7 pp.
24. Lee Y.-J., and Xu J. New formulations, positivity preserving discretizations and stability analysis for non-Newtonian flow models. Comput. Methods Appl. Mech. Eng. 195 (2006) 1180-1206
25. Lozinski A., and Owens R.G. An energy estimate for the Oldroyd B model: theory and applications. J. Non-Newtonian Fluid Mech. 112 (2003) 161-176
26. McKinley G.H. Steady and transient motion of spherical particles in viscoelastic liquids. In: De Kee D., and Chhabra R.P. (Eds). Transport Processes in Bubbles, Drops & Particles. 2nd ed. (2002), Taylor & Francis, New York 338-375
27. Pan T.-W., and Glowinski R. Direct simulation of the motion of neutrally buoyant circular cylinders in plane Poiseuille flow. J. Comput. Phys. 181 (2002) 260-279
28. Pan T.-W., and Glowinski R. Direct simulation of the motion of neutrally buoyant balls in a three-dimensional Poiseuille flow. C.R. Mécanique, Acad. Sci. Paris 333 (2005) 884-895
29. Patankar N.A., and Hu H.H. A numerical investigation of the Detachment of the trailing particle from a chain sedimenting in Newtonian and viscoelastic fluids. J. Fluids Eng. 122 (2000) 517-521
30. Singh P., Joseph D.D., Helsa T.I., Glowinski R., and Pan T.-W. A distributed Lagrange multiplier/fictitious domain method for viscoelastic particulate flows. J. Non-Newtonian Fluid Mech. 91 (2000) 165-188
31. Singh P., and Joseph D.D. Sedimentation of a sphere near a vertical wall in an Oldroyd-B fluid. J. Non-Newtonian Fluid Mech. 94 (2000) 179-203
32. Singh P., and Leal L.G. Finite-Element simulation of the start-up problem for a viscoelastic fluid in an eccentric rotating cylinder geometry using a third-order upwind scheme. Theor. Comput. Fluid Dyn. 5 (1993) 107-137
33. Yu Z., Phan-Thien N., Fan Y., and Tanner R.I. Viscoelastic mobility problem of a system of particles. J. Non-Newtonian Fluid Mech. 104 (2002) 87-124
34. Yu Z., Waches A., and Peysson Y. Numerical simulation of particle sedimentation in shear-shinning fluids with a fictitious domain method. J. Non-Newtonian Fluid Mech. 136 (2006) 126-139