An unconditionally energy stable immersed boundary method with application to vesicle dynamics

Wei Fan Hu, Ming Chih Lai

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We develop an unconditionally energy stable immersed boundary method, and apply it to simulate 2D vesicle dynamics. We adopt a semi-implicit boundary forcing approach, where the stretching factor used in the forcing term can be computed from the derived evolutional equation. By using the projection method to solve the fluid equations, the pressure is decoupled and we have a symmetric positive definite system that can be solved efficiently. The method can be shown to be unconditionally stable, in the sense that the total energy is decreasing. A resulting modification benefits from this improved numerical stability, as the time step size can be significantly increased (the severe time step restriction in an explicit boundary forcing scheme is avoided). As an application, we use our scheme to simulate vesicle dynamics in Navier-Stokes flow.

Original languageEnglish
Pages (from-to)247-262
Number of pages16
JournalEast Asian Journal on Applied Mathematics
Volume3
Issue number3
DOIs
StatePublished - Aug 2013

Keywords

  • Immersed boundary method
  • Inextensible vesicle
  • Navier-Stokes flow
  • Unconditionally energy stable

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