Simulation of two-fluid flows using a finite element/level set method. Application to bubbles and vesicle dynamics

Journal of Computational and Applied Mathematics

Volumn 246, Issue , 2013, Pages 251-259

  Doyeux, V ^a   Guyot, Y ^a   Chabannes, V ^a   Prud'Homme, C ^a,b   Ismail, M ^a  

^a UNIV GRENOBLE ALPES   (France)

^b UNIVERSITÉ DE STRASBOURG   (France)

Author keywords

Finite elements; High order level set; Navier Stokes; Two fluid; Vesicle membrane

Indexed keywords

FLOW OF FLUIDS; LAGRANGE MULTIPLIERS; NAVIER STOKES EQUATIONS; POLYNOMIAL APPROXIMATION;

LEVEL SET; MECHANICAL BEHAVIOR; NAVIER STOKES; RED BLOOD CELL; TUMBLING MOTION; TWO-FLUID; VESICLE DYNAMICS; VESICLE MEMBRANES;

FINITE ELEMENT METHOD;

EID: 84899814519     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2012.05.004     Document Type: Article

References (24)

1. B. Kaoui, J. Harting, and C. Misbah Two-dimensional vesicle dynamics under shear flow: effect of confinement Physical Review E 83 6 2011 066319 10.1103/PhysRevE.83.066319 arXiv:1011.6061
2. J. Beaucourt, F. Rioual, T. Seacuteon, T. Biben, and C. Misbah Steady to unsteady dynamics of a vesicle in a flow Physical Review E 69 1 2004 011906
3. E. Maitre, C. Misbah, P. Peyla, A. Raoult, Comparison between advected-field and level-set methods in the study of vesicle dynamics, ArXiv e-prints arXiv:1005.4120.
4. D. Salac, and M. Miksis A level set projection model of lipid vesicles in general flows Journal of Computational Physics 230 22 2011 8192 8215
5. A. Laadhari, P. Saramito, C. Misbah, Computing the dynamics of biomembranes by combining conservative level set and adaptive finite element methods, cNRS, June 2011. URL: http://hal.archives-ouvertes.fr/hal-00604145/en/.
6. M. Ismail, A. Lefebvre, A "necklace" model for vesicles simulation in 2d, Journal of Computational Physics (2012) (submitted for publication) arXiv:1202.3034v1.
7. C. Winkelmann, Interior penalty finite element approximation of Navier-Stokes equations and application to free surface flows, Ph.D. Thesis, 2007.
8. S. Osher, and J.A. Sethian Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations Journal of Computational Physics 79 1 1988 12 49
9. J. Sethian Level Set Methods and Fast Marching Methods 1996 Cambridge University Press
10. Stanley Osher, and Ronald Fedkiw S.S. Antman, J.E. Marsden, L. Sirovich, Level Set Methods and Dynamic Implicit Surfaces 2003 Springer-Verlag New York
11. G.-H. Cottet, and E. Maitre A level set method for fluid-structure interactions with immersed surfaces Mathematical Models and Methods in Applied Sciences 16 3 2006 415 438
12. C. Prud'Homme, V. Chabannes, V. Doyeux, M. Ismail, A. Samake, G. Pena, Feel++: a computational framework for galerkin methods and advanced numerical methods, ESAIM Proc. (Jan.) (2012) (in press) URL: http://hal.archives-ouvertes.fr/hal-00662868.
13. C. Prud'homme, V. Chabannes, G. Pena, Feel++: finite element embedded language in C++, Free Software available at http://www.feelpp.org, contributions from A. Samake, V. Doyeux, M. Ismail and S. Veys.
14. C. Prud'homme, A domain specific embedded language in C++ for automatic differentiation, projection, integration and variational formulations, Scientific Programming 14.
15. L.P. Franca, S.L. Frey, and T.J. Hughes Stabilized finite element methods: I. Application to the advective-diffusive model Computer Methods in Applied Mechanics and Engineering 95 2 1992 253 276
16. E. Burman, and P. Hansbo Edge stabilization for the generalized stokes problem: a continuous interior penalty method Computer Methods in Applied Mechanics and Engineering 195 19-22 2006 2393 2410
17. V. Chabannes, G. Pena, C. Prud'homme, High order fluid structure interaction in 2d and 3d. application to blood flow in arteries, in: Fifth International Conference on Advanced COmputational Methods in ENgineering, ACOMEN 2011, 2011.
18. S. Hysing, S. Turek, D. Kuzmin, N. Parolini, E. Burman, S. Ganesan, and L. Tobiska Quantitative benchmark computations of two-dimensional bubble dynamics International Journal for Numerical Methods in Fluids 60 11 2009 1259 1288 10.1002/fld.1934
19. P. Canham The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell Journal of Theoretical Biology 26 1 1970 61 81 10.1016/S0022-5193(70)80032-7
20. W. Helfrich Elastic properties of lipid bilayers: theory and possible experiments Zeitschrift für Naturforschung 28c 1973 693 703
21. D. Jamet, and C. Misbah Towards a thermodynamically consistent picture of the phase-field model of vesicles: local membrane incompressibility Physical Review E 76 5 2007 051907 10.1103/PhysRevE.76.051907
22. S.K. Veerapaneni, D. Gueyffier, D. Zorin, and G. Biros A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2d Journal of Computational Physics 228 7 2009 2334 2353 10.1016/j.jcp.2008.11.036
23. V. Doyeux, C. Prud'homme, M. Ismail, A framework toward high order level set method (in preparation).
24. G. Ghigliotti, T. Biben, and C. Misbah Rheology of a dilute two-dimensional suspension of vesicles Journal of Fluid Mechanics 653 2010 489 518 10.1017/S0022112010000431