On the lubrication paradox and the use of regularisation methods for lubrication flows

Journal of Non-Newtonian Fluid Mechanics

Volumn 163, Issue 1-3, 2009, Pages 62-77

  Putz, A ^a   Frigaard, I A ^a   Martinez, D M ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Asymptotic methods; Bingham fluids; Lubrication theory; Numerical methods

Indexed keywords

ANALYTICAL ESTIMATES; ASYMPTOTIC METHODS; ASYMPTOTIC SOLUTIONS; AUGMENTED LAGRANGIAN METHODS; BINGHAM FLUID; BINGHAM FLUIDS; CRITICAL STRAINS; EXTENSIONAL STRESS; LONG WAVELENGTH; LUBRICATION FLOWS; LUBRICATION THEORY; LUBRICATION-TYPE FLOWS; NUMERICAL COMPUTATIONS; PLANE CHANNELS; PLASTIC FLUIDS; REGULARISATION; SMALL AMPLITUDE; VISCOSITY REGULARISATION METHODS; WAVY-WALLED CHANNELS; YIELD SURFACE;

ASYMPTOTIC ANALYSIS; ERRORS; FLUIDS; LAGRANGE MULTIPLIERS; LUBRICATION; NUMBER THEORY; PLASTIC FLOW; STRAIN RATE;

NUMERICAL METHODS;

EID: 70350224105     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2009.06.006     Document Type: Article

References (21)

1. Frigaard I., and Ryan D. Flow of a visco-plastic fluid in a channel of slowly varying width. J. Non-Newt. Fluid Mech. 123 (2004) 67-83
2. Lipscomb G., and Denn M. Flow of Bingham fluids in complex geometries. J. Non-Newt. Fluid Mech. 14 (1984) 337-346
3. Walton I., and Bittleston S. The axial flow of a Bingham plastic in a narrow eccentric annulus. J. Fluid Mech. 222 (1991) 30-60
4. Szabo P., and Hassager O. Flow of viscoplastic fluids in eccentric annular geometries. J. Non-Newt. Fluid Mech. 45 (1992) 149-169
5. Fortin M., and Glowinski R. Augmented Lagrangian Methods (1983), North-Holland
6. Glowinski R. Numerical Methods For Nonlinear Variational Problems (1983), Springer-Verlag
7. Glowinski R., and le Tallec P. Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics (1989), SIAM
8. Roquet N., and Saramito P. An adaptive finite element method for Bingham fluid flows around a cylinder. Comp. Meth. Appl. Mech. Eng. 192 (2003) 3317-3341
9. Wilson S. A note on thin-layer theory for Bingham plastics. J. Non-Newt. Fluid Mech. 85 (1999) 29-33
10. Allouche M., Frigaard I., and Sona G. Static wall layers in the displacement of two visco-plastic fluids in a plane channel. J. Fluid Mech. 424 (2000) 243-277
11. Papanastasiou T. Flows of materials with yield. J. Rheol. 31 (1987) 385-404
12. Prager W. On Slow Visco-Plastic Flow (1954), Academic Press pp. 208-216
13. Duvaut G., and Lions J.-L. Inequalities in Mechanics And Physics (1976), Springer-Verlag
14. Ekeland I., and Temam R. Convex Analysis And Variational Problems (1999), SIAM
15. Borouchaki H., George P.-L., Hecht F., Laug P., and Saltel E. Delaunay mesh generation governed by metric specifications. I. Algorithms. Finite Elem. Anal. Des. 25 (1997) 61-83
16. Borouchaki H., Hecht F., and Frey P. Mesh gradation control. Int. J. Num. Meth. Eng. 43 (1998) 1143-1165
17. Balmforth N., and Craster R. A consistent thin-layer theory for Bingham plastics. J. Non-Newt. Fluid Mech. 84 (1999) 65-81
18. Hinch E. Perturbation Methods (1991), Cambridge University Press
19. Frigaard I., and Nouar C. On the usage of viscosity regularisation methods for visco-plastic fluid flow computation. J. Non-Newt. Fluid Mech. 127 (2005) 1-26
20. Bercovier M., and Engleman M. A finite-element method for incompressible non-Newtonian flows. J. Comp. Phys. 36 (1980) 313-326
21. Smyrnaios D.N., and Tsamopoulos J.A. Squeeze flow of Bingham plastics. J. Non-Newt. Fluid Mech. 100 1-3 (2001) 165-189