Computing the dynamics of biomembranes by combining conservative level set and adaptive finite element methods

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Laadhari , Aymen; Saramito , Pierre; Misbah , Chaouqi;
(2014)
  • Publisher: Elsevier
  • Related identifiers: doi: 10.1016/j.jcp.2013.12.032
  • Subject: [ PHYS.PHYS.PHYS-COMP-PH ] Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph] | [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP] | [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA] | Helfrich energy | [ PHYS.PHYS.PHYS-FLU-DYN ] Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn] | [ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph] | [PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph] | adaptive finite element method | [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] | mass conservation | [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] | [PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn] | vesicle dynamics | [PHYS.PHYS.PHYS-BIO-PH]Physics [physics]/Physics [physics]/Biological Physics [physics.bio-ph] | [ PHYS.PHYS.PHYS-BIO-PH ] Physics [physics]/Physics [physics]/Biological Physics [physics.bio-ph] | level set method | fluid mechanics | [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] | fluid mechanics.
    arxiv: Quantitative Biology::Subcellular Processes | Physics::Fluid Dynamics

International audience; The numerical simulation of the deformation of vesicle membranes under simple shear external fluid flow is considered in this paper. A new saddle-point approach is proposed for the imposition of the fluid incompressibility and the membrane inexte... View more
  • References (14)
    14 references, page 1 of 2

    1 [1] R. A. Adams and J. J. F. Fournier. Sobolev spaces. Elsevier, second edition, 2003.

    [5] J. Beaucourt, F. Rioual, T. Seon, T. Biben, and C. Misbah. Steady to unsteady dynamics of a vesicle in a flow. Phys. Rev. E, 69:011906, 2004.

    [6] T. Biben, K. Kassner, and C. Misbah. Phase-field approach to threedimensional vesicle dynamics. Phys. Rev. E, 72:041921, 2005.

    [7] T. Biben and C. Misbah. Tumbling of vesicles under shear flow within an advected-field approach. Phys. Rev. E, 67:031908, 2003.

    [8] G. Boedec, M. Leonetti, and M. Jaeger. 3d vesicle dynamics simulations with a linearly triangulated surface. J. Comput. Phys., 230(4):1020-1034, 2011.

    [9] A. Bonito, R. H. Nochetto, and M. S. Pauletti. Parametric FEM for geometric biomembranes. J. Comput. Phys., 229(9):3171-3188, 2010.

    [10] S. C. Brenner and L. R. Scott. The mathematical theory of finite element methods. Springer, third edition, 2008.

    [17] Q. Du, C. Liu, R. Ryham, and X. Wang. Energetic variational approaches in modeling vesicle and fluid interactions. Physica D, 238:923-930, 2009.

    [18] Q. Du, C. Liu, and X. Wang. A phase field approach in the numerical study of the elastic bending energy for vesicle membranes. J. Comput. Phys., 198:450-468, 2004.

    [19] Q. Du and J. Zhang. Adaptive finite element method for a phase field bending elasticity model of vesicle membrane deformation. SIAM J. Ssci. Comput., 30(3):1634-1657, 2008.

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