An adaptive remeshing strategy for free-surface fluid flow problems. Part I: The axisymmetric case

Journal of Polymer Engineering

Volumn 26, Issue 1, 2006, Pages 21-57

  Fortin, A ^a   Benmoussa, K ^a  

^a UNIVERSITÉ LAVAL   (Canada)

Author keywords

Amsotropie adaptive remeshing; Deformation and breaking of drops; Free surfaces; Hierarchical error estimator; Shear thinning fluids; Surface tension

Indexed keywords

ANISOTROPY; COMPUTER SIMULATION; DEFORMATION; SURFACE TENSION; VISCOSITY;

AMSOTROPIE ADAPTIVE REMESHING; DEFORMATION AND BREAKING OF DROPS; FREE SURFACES; HIERARCHICAL ERROR ESTIMATOR;

FLOW OF FLUIDS;

EID: 33644935655     PISSN: 03346447     EISSN: None     Source Type: Journal    
DOI: 10.1515/POLYENG.2006.26.1.21     Document Type: Article

References (26)

1. Sussman M, Almgren AS, Bell JB, Colella P, Howell LH, Welcome ML (1999) An adaptive level set approach for incompressible two-phase flows. J Comp Phys, 148:81-124.
2. Belhamadia Y, Fortin A, Chamberland É (2004) Anisotropie mesh adaptation for the solution of the Stefan problem. J Comp Phys, 194(1):233-255.
3. Belhamadia Y, Fortin A, Chamberland É (2004) Three-dimensional anisotropic mesh adaptation for phase change problems. J Comp Phys 201(2):723-752.
4. Fortin A, Fortin M, Boulanger-Nadeau PE (2004) An anisotropic adaptive remeshing strategy for two-dimensional laminar Navier-Stokes equations. Int J Numer Meth Fluids, to appear.
5. Brezzi F, Fortin M (1991) Mixed and Hybrid Finite Element Methods. Springer-Verlag.
6. Tornberg A-K, Engquist B (2000) A finite element based level set method for multiphase flow applications. Comp. and Visualization in Science, 3:93-101.
7. Osher S, Sethian JA (1988) A. Front propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comp Phys, 79:12-49.
8. Sethian JA (1996) Level Sets Methods and Fast Marching Methods. Number 3 in Cambridge Monograph on applied and computational mathematics. Cambridge University Press.
9. Hughes TJ, Brooks A (1982) A theoretical framework for PetrovGalerkin methods with discontinuous weighting functions. Applications to the streamline upwind procedure. In: Gallagher RH (Ed), Finite Element in Fluids, Volume IV. Wiley, 1982.
10. Hirt CW, Nichols B (1981) Volume of fluid VOF for the dynamics of free boundaries. J Comp Phys, 39.
11. Sussman M, Fatemi E (1999) An efficient interface preserving level set re-distancing algorithm and its application to interfacial incompressible fluid flow. SI AM J Sci Comp, 20(4): 1165-1191.
12. Sussman M, Fatemi M, Smereka P, Osher S (1998) An improved level set method for incompressible two-phase flows. J Comp Phys, 27:663-680.
13. Brackbill JU, Kothe DB, Zemach C (1992) A continuum method for modeling surface tension. J Comp Phys, 100:335-383.
14. Béliveau A, Fortin A, Demay Y (1998) A two-dimensional numerical method for the deformation of drops with surface tension. Int J Comp Fluid Dyn, 10:225-240.
15. Renardy Y, Renardy M (2002) PROST: A parabolic reconstruction of surface tension for the volume-of-fluid method. J Comp Phys, 183:400-421.
16. Bank RE (1998) A simple analysis of a posteriori error estimates. Applied Numerical Mathematics, 26:153-164.
17. Bank FE, Smith RK (1993) A posteriori error estimates based on hierarchical bases. SIAM Journal on Numerical Analysis, 30:921-935, 1993.
18. Zhang Z (2001) A posteriori error estimates on irregular grids based on gradient recovery. Advances in Computational Mathematics, 15(1-4):363-374.
19. Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimate, Part I: The recovery technique. Int J Numer Meth Engrg, 33:1331-1364.
20. Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimate, Part II: Error estimates and adaptivity. Int J Numer Meth Engrg, 33:1365-1382.
21. Pichelin É, Fortin M, Boivin S (2000) É tude numérique d'estimations d'erreurs a posteriori. REÉR, 9(4):467-486.
22. Kim SJ, Kim SD, Kwon Y (2003) Deformation of multiple non-Newtonian drops in the entrance region. Korea-Australian Rheology Journal, 15(2):75-82.
23. Kim SJ, Han CD (2001). FEM analysis of axisymmetric creeping motion of a deformable non-newtonian drop in the entrance region of a cylindrical tube. Journal of Rheology, 45(6):1279-1303.
24. Bentley BJ, Leal LG (1986) An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows. J Fluid Mech, 167:241-283.
25. Stegeman Y (2002) Time dependent behavior of droplets in elongational flows. PhD thesis, University of Eindhoven, The Netherlands.
26. Ha JW, Leal LG (2001) An experimental study of drops deformation and breakup in extensional flow at high capillary numbers. Physics of Fluids 13(6): 1568-1576.