An immersed boundary method for simulating vesicle dynamics in three dimensions

Yunchang Seol, Wei Fan Hu, Yongsam Kim, Ming-Chih Lai*

*Corresponding author for this work

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

We extend our previous immersed boundary (IB) method for 3D axisymmetric inextensible vesicle in Navier-Stokes flows (Hu et al., 2014 [17]) to general three dimensions. Despite a similar spirit in numerical algorithms to the axisymmetric case, the fully 3D numerical implementation is much more complicated and is far from straightforward. A vesicle membrane surface is known to be incompressible and exhibits bending resistance. As in 3D axisymmetric case, instead of keeping the vesicle locally incompressible, we adopt a modified elastic tension energy to make the vesicle surface patch nearly incompressible so that solving the unknown tension (Lagrange multiplier for the incompressible constraint) can be avoided. Nevertheless, the new elastic force derived from the modified tension energy has exactly the same mathematical form as the original one except the different definitions of tension. The vesicle surface is discretized on a triangular mesh where the elastic tension and bending force are calculated on each vertex (Lagrangian marker in the IB method) of the triangulation. A series of numerical tests on the present scheme are conducted to illustrate the robustness and applicability of the method. We perform the convergence study for the immersed boundary forces and the fluid velocity field. We then study the vesicle dynamics in various flows such as quiescent, simple shear, and gravitational flows. Our numerical results show good agreements with those obtained in previous theoretical, experimental and numerical studies.

Original languageEnglish
Pages (from-to)125-141
Number of pages17
JournalJournal of Computational Physics
Volume322
DOIs
StatePublished - 1 Oct 2016

Keywords

  • Immersed boundary method
  • Incompressible membrane
  • Navier-Stokes equations
  • Three-dimensional vesicle

Fingerprint Dive into the research topics of 'An immersed boundary method for simulating vesicle dynamics in three dimensions'. Together they form a unique fingerprint.

  • Cite this