Numerical simulation of Stokes flow down an inclined plane

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 452, Issue 1946, 1996, Pages 543-565

  Gwynllyw, D R H ^a   Peregrine, D H ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b ABERYSTWYTH UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

SIMULATION-NUMERICAL; STOKES FLOW;

EID: 0029656531     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1996.0028     Document Type: Article

References (23)

1. Baker, G. R., Meiron, D. I. & Orszag, S. A. 1982 Generalized vortex methods for free-surface flow problems. J. Fluid Mech. 123, 477-501.
2. Benncy, D. J. I960 Long waves on liquid films. J. Math. Phys. 45, 150-155.
3. Cokelet, E. D. 1978 Mechanics of wave induced forces on cylinders (ed. T. L. Shaw), pp. 287-301. London: Pitman.
4. Cooker, M. J., Peregrine, D. H., Vidai, C. & Dold, J. W. 1990 The interaction between a solitary wave and a submerged circular cylinder. J. Fluid Mech. 215, 1-22.
5. Cooker, M. J. & Peregrine, D. H. 1990 Computations of violent motion due to waves breaking against a wall. In Proc. 22nd Int. Conf. Coastal Engng. Delft. A.S.C.E., vol. 1, pp. 164-176.
6. Dold, J. W. 1992 An efficient surface-integral algorithm applied to unsteady gravity waves. J. Comp. Phys. 103, 90-115.
7. Dold, J. \V. & Peregrine, D. H. 1986 An efficient boundary-integral method for steep unsteady water waves. In Numerical methods for fluid dynamics (ed. K. W. Morton & M. J. Baines), vol. II, pp. 671-679. Oxford: Clarendon.
8. Gjevik, B. 1970 Occurrence of finite-amplitude surface waves on falling liquid films. Physics Fluids 13, 1918-1925.
9. Hopper, R. W. 1990 Plane Stokes flow driven by capillarity on a free surface J. Fluid Mech. 213, 349-375
10. Ingham, D. B. & Kelmanson, M. A. 1984 Boundary integral equation analyses of singular, potential and biharmonic problems, Springer Lecture Notes in Engineering 7 (ed. C. A. Brebbia & S. A. Orszag). Berlin: Springer.
11. Jaswon, M. A. & Symm, G. T. 1977 Integral equation methods in potential theory and electrostatics. New York: Academic.
12. Jeong, J.-T. & Moffatt, H. K. 1992 Free-surface cusps associated with flow at low Reynolds number. J. Fluid Mech. 241, 1-22.
13. Kuiken, H. K. 1990 Viscous sintering: the surface-tension-driven flow of a liquid form under the influence of curvature gradients at its surface. J. Fluid Mech. 214, 503-515.
14. Langlois, W. E. 1964 Slow viscous flow. New York: Macmillan.
15. Longuet-Higgins, M. S. & Gokelet, E. D. 1976 The deformation of steep surface waves on water. I. A numerical method of computation. Proc. R. Soc. Land. A 350, 1-26.
16. Nakaya, C. 1975 Long Waves on thin fluid layer flowing down an inclined plane. Physics Fluids 18, 1407-1412.
17. Ohring, S. & Lugt, H. J. 1991 Interaction of a viscous vortex pair with a free surface. J. Fluid Mech. 227, 47-70.
18. Orchard, S. E. 1962 On surface levelling in viscous liquids and gels. Appl. Sci. Res. All, 451-464.
19. Pozrikidis, C. 1988 Flow of a liquid film along a periodic wall. J. Fluid Mech. 188, 275-300.
20. Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T. 1986 Numerical recipes. Cambridge University Press.
21. Stone, H. A. & Leal, L. G. 1989 Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. J. Fluid Mech. 198, 399-427.
22. Tanaka, M., Dold, J. W., Lewy, M. & Peregrine, D. H. 1987 Instability and breaking of a solitary wave. J. Fluid Mech. 185, 235-248.
23. Zeng, Y. & Weinbaum, S. 1994 Stokes flow through periodic orifices in a channel. J. Fluid Mech. 263, 207-226.