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Fully implicit methodology for the dynamics of biomembranes and capillary interfaces by combining the level set and Newton methods

Aymen Laadhari, Pierre Saramito, Chaouqi Misbah, and Gábor Székely
Journal of Computational Physics
April 2017, in press

Abstract

This framework is concerned with the numerical modeling of the dynamics of isolated vesicles and interfacial flows with surface tension in a surrounding Newtonian fluid. A level set method helps to follow the interface motion. Our method features the use of a high order fully implicit time integration scheme that enables to overcome stability issues related to the explicit discretisation of the highly non-linear bending elastic force or surface tension force. At each time step, the resulting nonlinear problem is solved by a Newton method, showing superlinear convergence properties. Several quasi-Newton approximations of the Jacobian system are also explored for both capillary and vesicle problems. We address in detail the main features of the proposed method, and we report several experiments with the aim of illustrating its accuracy and efficiency.


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@Article{eth_biwi_01358,
  author = {Aymen Laadhari and Pierre Saramito and Chaouqi Misbah and and Gábor Székely},
  title = { Fully implicit methodology for the dynamics of biomembranes and capillary interfaces by combining the level set and Newton methods},
  journal = { Journal of Computational Physics},
  year = {2017},
  month = {April},
  pages = {},
  volume = {},
  number = {},
  keywords = {Red Blood Cells; Newtonian flow; Newton method; Finite element method; Inexact Jacobian;},
  note = {in press}
}