An Adaptive Mesh Algorithm for Evolving Surfaces: Simulations of Drop Breakup and Coalescence

Journal of Computational Physics

Volumn 168, Issue 2, 2001, Pages 445-463

  Cristini, Vittorio ^a   Blawzdziewicz, Jerzy ^a   Loewenberg, Michael ^a  

^a Yale University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIOMEDICAL ENGINEERING; COMPUTATIONAL FLUID DYNAMICS; DROP BREAKUP; IMAGE PROCESSING;

ADAPTIVE MESHES; BREAKUP AND COALESCENCES; DEFORMATION HISTORY; DISCRETIZATION ALGORITHMS; DISCRETIZATIONS; ENERGY FUNCTIONS; LENGTH SCALE; MESH ALGORITHMS; MINIMISATION; SURFACE SIMULATIONS;

MESH GENERATION;

EID: 0001039633     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2001.6713     Document Type: Article

References (34)

1. A. J. Stoddart, A. Hilton, and J. Illingworth, SLIME: A new deformable surface, in Proceedings British Machine Vision Conference 1994, pp. 285-294.
2. Bulpitt A. J., Efford N. D. An efficient 3d deformable model with a self-optimizing mesh. Image Vision Comput. 14:1996;573.
3. Wilson R. C., Hancock E. R. Bias-variance analysis for controlling adaptive surface meshes. Comput. Vision Image Understanding. 77:2000;25.
4. Mavriplis D. J. Unstructured grid techniques. Ann. Rev. Fluid. Mech. 29:1997;473.
5. Unverdi O. S., Tryggvason G. A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100:1992;25.
6. Kwak S., Pozrikidis C. Adaptive triangulation of evolving, closed, or open surfaces by the advancing-front method. J. Comput. Phys. 145:1998;61.
7. C. L. Lawson, Software for C1 surface interpolation, in Mathematical Software III, edited by J. R. RiceAcademic Press, New York, 1977, pp. 161-194.
8. Lee D. T., Schacter B. J. Two algorithms for constructing a Delaunay triangulation. Int. J. Computer Information Sci. 9:1980;219.
9. De Floriani L. Surface representation based on triangular grids. The Visual Computer. 3:1987;27.
10. Rallison J. M. A numerical study of the deformation and burst of a viscous drop in general linear shear flows. J. Fluid Mech. 109:1981;465.
11. Schmitt F. J. M., Barsky B. A., Du W. H. An adaptive subdivision method for surface fitting from sampled data. SIGGRAPH. 20:1986;176.
12. Bartels R. H., Beatty J. C., Barsky B. A. An Introduction to the Use of Splines in Computer Graphics. 1987.
13. Zinchenko A. Z., Davis R. H. An efficient algorithm for hydrodynamical interaction of many deformable drops. J. Comput. Phys. 157:2000;1.
14. Zinchenko A. Z., Rother M. A., Davis R. H. A novel boundary-integral algorithm for viscous interaction of deformable drops. Phys. Fluids A. 9:1997;1493.
15. Loewenberg M., Hinch E. J. Numerical simulation of a concentrated emulsion in shear flows. J. Fluid Mech. 321:1996;395.
16. Rallison J. M., Acrivos A. A numerical study of the deformation and burst of a drop in an extensional flow. J. Fluid Mech. 89:1978;191.
17. Pozrikidis C. Boundary Integral and Singularity Methods for Linearized Viscous Flow. 1992.
18. Saad Y., Schultz M. H. GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7:1986;856.
19. Loewenberg M., Hinch E. J. Collision of deformable drops in shear-flow. J. Fluid Mech. 338:1997;299.
20. Cristini V., Blawzdziewicz J., Loewenberg M. Drop breakup in three-dimensional viscous flows. Phys. Fluids. 10:1998;1781.
21. Tjahjadi M., Stone H. A., Ottino J. M. Satellite and subsatellite formation in capillary breakup. J. Fluid Mech. 243:1992;297.
22. Janssen J. M. H., Meijer H. E. H. Droplet breakup mechanisms: Stepwise equilibrium versus transient dispersion. J. Rheol. 37:1993;597.
23. Blawzdziewicz J., Cristini V., Loewenberg M. Analysis of drop breakup in creeping flows. Bull. Am. Phys. Soc. 42:1997;2125.
24. Lister J. R., Stone H. A. Capillary breakup of a viscous thread surrounded by another viscous fluid. Phys. Fluids. 10:1998;2758.
25. D. Papadopoulos, M. Nemer, X. Chen, J. Blawzdziewicz, and, M. Loewenberg, unpublished.
26. Guido S., Simeone M. Binary collision of drops in simple shear flow by computer-assisted video optical microscopy. J. Fluid Mech. 357:1998;1.
27. T. W. Secomb, Mechanics of blood flow in the microcirculation, in, Biological Fluid Dynamics, edited by, C. P. Ellinton and T. J. Pedley, Company of Biologists, Cambridge, UK, 1995.
28. Skalak R., Özkaya N. Biofluid mechanics. Ann. Rev. Fluid Mech. 21:1989;167.
29. Evans E. A., Skalak R. Mechanics and Thermodynamics of Biomembranes. 1980.
30. Secomb T. W., Skalak R., Özkaya N., Gross J. F. Flow of axisymmetric red blood cells in narrow capillaries. J. Fluid Mech. 163:1986;405.
31. Hughes T. J. R. The Finite-Element Method: Linear Static and Dynamic Finite Element Analysis. 1987.
32. McInerney D., Terzopoulos D. A dynamic finite-element surface model for segmentation and tracking in multidimensional medical images with application to cardiac 4D image-analysis. Comput. Medical Imaging Graphics. 19:1995;69.
33. Kalvin A. D., Cutting C. B., Haddad B., Noz M. E. Constructing topologically connected surfaces for the comprehensive analysis of 3D medical structures. SPIE Image Process. 1445:1991;247.
34. Scarlatos L., Pavlidis T. Hierarchical triangulation using cartographic coherence. CVGIP: Graphical Models Image Process. 54:1992;147.