Volume preserving immersed boundary methods for two-phase fluid flows

Yibao Li, Eunok Jung, Wanho Lee, Hyun Geun Lee, Junseok Kim

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


In this article, we propose a simple area-preserving correction scheme for two-phase immiscible incompressible flows with an immersed boundary method (IBM). The IBM was originally developed to model blood flow in the heart and has been widely applied to biofluid dynamics problems with complex geometries and immersed elastic membranes. The main idea of the IBM is to use a regular Eulerian computational grid for the fluid mechanics along with a Lagrangian representation of the immersed boundary. Using the discrete Dirac delta function and the indicator function, we can include the surface tension force, variable viscosity and mass density, and gravitational force effects. The principal advantage of the IBM for two-phase fluid flows is its inherent accuracy due in part to its ability to use a large number of interfacial marker points on the interface. However, because the interface between two fluids is moved in a discrete manner, this can result in a lack of volume conservation. The idea of an area preserving correction scheme is to correct the interface location normally to the interface so that the area remains constant. Various numerical experiments are presented to illustrate the efficiency and accuracy of the proposed conservative IBM for two-phase fluid flows.

Original languageEnglish
Pages (from-to)842-858
Number of pages17
JournalInternational Journal for Numerical Methods in Fluids
Issue number4
Publication statusPublished - 2012 Jun 10
Externally publishedYes


  • Area preserving
  • Finite difference
  • Immersed boundary method
  • Indicator function
  • Multigrid method
  • Two-phase fluid flow

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics


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