Numerical simulation of fluid membranes in two-dimensional space

Peng Song, Dan Hu, Pingwen Zhang

Research output: Contribution to journalArticlepeer-review


The membrane's dynamics is very important for cells. A membrane in 2-dimensional space can be seen as an incompressible closed curve in a plane or a cylindrical surface in 3-dimensional space. In this paper, we design a second-order accurate numerical algorithm to simulate the shape transformation of the membrane. In the algorithm, we use the tangent angles to present the curve and avoid the difficulties, from the constraint of curve's incompressible condition. A lot of interesting phenomena are obtained. Some of them are very like the life processes of cells, such as exocytosis and endocytosis. Furthermore, we can see the relation between two dynamic models clearly. At last, considering the influence of the inner incompressible fluids partially, we add a constraint: the area circled by the membrane maintain invariable. The numerical results show the dynamic motions of a curve remaining its local arc length and inner area constant.

Original languageEnglish (US)
Pages (from-to)794-821
Number of pages28
JournalCommunications in Computational Physics
Issue number4
StatePublished - Apr 2008


  • Constraint of the area
  • Curvature
  • Director model of the membrane
  • Osmotic pressure
  • Reduced model
  • Spontaneous

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


Dive into the research topics of 'Numerical simulation of fluid membranes in two-dimensional space'. Together they form a unique fingerprint.

Cite this