A moving overset grid method for interface dynamics applied to non-Newtonian Hele-Shaw flow

Journal of Computational Physics

Volumn 195, Issue 1, 2004, Pages 117-142

  Fast, Petri ^a   Shelley, Michael J ^b  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AIR; FLOW MEASUREMENT; NON NEWTONIAN FLOW; RHEOLOGY; SHEAR FLOW; SHEAR THINNING; VISCOUS FLOW;

AIR BUBBLES; FLUID DOMAIN; HELE-SHAW FLOW; INTERFACE DYNAMIC; NON-NEWTONIAN; NON-NEWTONIAN FLUIDS; OVERSET GRID; OVERSET GRID METHODS; SHEAR-THINNING; TIME SIMULATIONS;

NON NEWTONIAN LIQUIDS;

EID: 1542426445     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2003.08.034     Document Type: Article

References (40)

1. R.F. Almgren, W.-S. Dai, V. Hakim, Scaling behavior in anisotropic Hele-Shaw flow, Phys. Rev. Lett. 71 (1993) 3461-3464.
2. Satish Balay, William D. Gropp, Lois Curfman McInnes, Barry F. Smith. PETSc 2.0 users manual, Technical Report ANL-95/11 - Revision 2.0.24, Argonne National Laboratory, 1999.
3. M. Ben Amar, Exact self-similar shapes in viscous fingering, Phys. Rev. A 43 (1991) 5724.
4. R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids, Wiley, New York, 1987.
5. J.O'M. Bockris, A.K.N. Reddy, Modern Electrochemistry, Plenum Press, New York, 1970.
6. D.L. Brown, W.D. Henshaw, and D.J. Quinlan, Overture: An object oriented framework for solving partial differential equations, in: Scientific Computing in Object-Oriented Parallel Environments, Springer Lecture Notes in Computer Science, vol. 1343, 1997.
7. A. Buka, J. Kertesz, T. Viscek, Nature 323 (1986) 424.
8. A. Buka, P. Palffy-Muhoray, Z. Racz, Viscous fingering in liquid crystals, Phys. Rev. A 36 (1987) 3984.
9. W.M. Chan, Hyperbolic methods for surface and field grid generation, in: J.F. Thompson, B.K. Soni, N.P. Weatherill (Eds.), Handbook of Grid Generation, CRC Press, Boca Raton, 1999 (Chapter 5).
10. G. Chesshire, W.D. Henshaw, Composite overlapping meshes for the solution of partial differential equations, J. Comput. Phys. 90 (1990) 1.
11. M. Constantin, M. Widom, J.A. Miranda, Mode-coupling approach to non-Newtonian Hele-Shaw flows, Phys. Rev. E 67 (2003) 026313.
12. H. Van Damme, E. Lemaire, Non-Newtonian fingering and visco-elastic fracturing, in: J.C. Charmet, S. Roux, E. Guyon (Eds.), Disorder and Fracture, Plenum Press, New York, 1990, p. 83.
13. P. Fast, Interfacial conditions for shear-thinning Hele-Shaw flow, J. Non-Newtonian Fluid Mech., submitted, available as LLNL Tech. Rep. UCRL-JC-149 667, 2002.
14. P. Fast, W.D. Henshaw, Time accurate simulation of viscous flow around deforming bodies using overset grids, AIAA paper 2001-2604, 2001.
15. P. Fast and W.D. Henshaw, Oges user guide, version 2: A solver for steady state boundary value problems on overlapping grids. Research Report UCRL-MA-132234, Lawrence Livermore National Laboratory, 2002.
16. P. Fast, L. Kondic, M.J. Shelley, P. Palffy-Muhoray, Pattern formation in non-Newtonian Hele-Shaw flow, Phys. Fluids 13 (2001) 1191-1212.
17. B. Fornberg, A Practical Guide to Pseudospectral Methods, Cambridge University Press, Cambridge, UK, 1996.
18. W.D. Henshaw, A fourth-order accurate method for the incompressible Navier-Stokes equations on overlapping grids, J. Comput. Phys. (1994) 13-25.
19. W.D. Henshaw, Ogen: The Overture overlapping grid generator, Technical Report UCRL-MA-132237, Lawrence Livermore National Laboratory, 2002.
20. G.M. Homsy, Viscous fingering in porous media, Ann. Rev. Fluid Mech. 19 (1987) 271.
21. T. Hou, J. Lowengrub, M.J. Shelley, Removing the stiffness from interfacial flow with surface-tension, J. Comput. Phys. 114 (1994) 312.
22. T. Hou, J. Lowengrub, M.J. Shelley, Boundary integral methods for multicomponent fluids and multiphase materials, J. Comput. Phys. 169 (2001) 302.
23. T.Y. Hou, Z. Li, S. Osher, H. Zhao, A hybrid method for moving interface problems with application to the Hele-Shaw flow, J. Comput. Phys. 134 (2) (1997) 236-252.
24. L. Kondic, P. Palffy-Muhoray, M.J. Shelley, Models of non-Newtonian Hele-Shaw flow, Phys. Rev. E 54 (1996) 4536.
25. L. Kondic, M.J. Shelley, P. Palffy-Muhoray, Non-Newtonian Hele-Shaw flow and the Saffman-Taylor instability, Phys. Rev. Lett. 80 (1998) 1433.
26. J.S. Langer, in: H.E. Stanley (Ed.), Statistical Physics, North-Holland, Amsterdam, 1986.
27. A. Lindner, D. Bonn, E.-C. Poire, M. Ben Amar, J. Meunier, Viscous fingering in non-newtonian fluids, J. Fluid Mech. 469 (2002) 237.
28. R.L. Meakin, Composite overset structured grids, in: J.F. Thompson, B.K. Soni, N.P. Weatherill (Eds.), Handbook of Grid Generation, CRC Press, Boca Raton, 1999 (Chapter 11).
29. S.S. Park, D.J. Durian, Viscous and elastic fingering instabilities in foam, Phys. Rev. Lett. 72 (1994) 3347.
30. L. Paterson, Radial fingering in a Hele-Shaw cell, J. Fluid Mech. 113 (1981) 513.
31. E.C. Poiré, M. Ben Amar, Finger behavior of a shear thinning fluid in a Hele-Shaw cell, Phys. Rev. Lett. 81 (1998) 2048-2051.
32. J.S. Ro, G.M. Homsy, Viscoelastic free surface flows: Thin film hydrodynamics of Hele-Shaw and dip coating flows, J. Non-Newtonian Fluid Mech. 57 (1995) 203-225.
33. Y. Saad, Iterative methods for Sparse Linear Systems, PWS Publishing, New York, 1996.
34. P.G. Saffman, G.I. Taylor, The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid, Proc. Roy. Soc. London., Ser. A 245 (1958) 312.
35. J. Sethian, Level Set Methods, Cambridge University Press, New York, 1996.
36. J. Strain, A boundary integral approach to unstable solidification, J. Comput. Phys. 85 (1989) 342.
37. Y. Tu, Saffman-Taylor problem in sector geometry: Solution and selection, Phys. Rev. A 44 (1991) 1203.
38. J. Zhang, S. Childress, A. Libchaber, M.J. Shelley, Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind, Nature 408 (2000) 835-839.
39. H. Zhao, J.V. Maher, Viscoelastic effects in patterns between miscible liquids, Phys. Rev. A 45 (1992) 8328.
40. H. Zhao, J.V. Maher, Associating-polymer effects in a Hele-Shaw experiment, Phys. Rev. E 47 (1993) 4278.