An adaptive meshfree method for phase-field models of biomembranes. Part II: A Lagrangian approach for membranes in viscous fluids

Christian Peco Regales, A. Rosolen, M. Arroyo

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We present a Lagrangian phase-field method to study the low Reynolds number dynamics of vesicles embedded in a viscous fluid. In contrast to previous approaches, where the field variables are the phase-field and the fluid velocity, here we exploit the fact that the phase-field tracks a material interface to reformulate the problem in terms of the Lagrangian motion of a background medium, containing both the biomembrane and the fluid. We discretize the equations in space with maximum-entropy approximants, carefully shown to perform well in phase-field models of biomembranes in a companion paper. The proposed formulation is variational, lending itself to implicit time-stepping algorithms based on minimization of a time-incremental energy, which are automatically nonlinearly stable. The proposed method deals with two of the major challenges in the numerical treatment of coupled fluid/phase-field models of biomembranes, namely the adaptivity of the grid to resolve the sharp features of the phase-field, and the stiffness of the equations, leading to very small time-steps. In our method, local refinement follows the features of the phase-field as both are advected by the Lagrangian motion, and large time-steps can be robustly chosen in the variational time-stepping algorithm, which also lends itself to time adaptivity. The method is presented in the axisymmetric setting, but it can be directly extended to 3D.

Original languageEnglish (US)
Pages (from-to)320-336
Number of pages17
JournalJournal of Computational Physics
Volume249
DOIs
StatePublished - Sep 5 2013

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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