An analysis of the numerical stability of the immersed boundary method

Mengjian Hua, Charles S. Peskin

Research output: Contribution to journalArticlepeer-review


We present a numerical stability analysis of the immersed boundary (IB) method for a special case which is constructed so that Fourier analysis is applicable. We examine the stability of the immersed boundary method with the discrete Fourier transforms defined differently on the fluid grid and the boundary grid. This approach gives accurate theoretical results about the stability boundary since it takes the effects of the spreading kernel of the immersed boundary method on the numerical stability into account. In this paper, the spreading kernel is the standard 4-point IB delta function. A three-dimensional incompressible viscous flow and a no-slip planar boundary are considered. The case of a planar elastic membrane is also analyzed using the same analysis framework and it serves as an example of many possible generalizations of our theory. We present some numerical results and show that the observed stability behaviors are consistent with what are predicted by the theory.

Original languageEnglish (US)
Article number111435
JournalJournal of Computational Physics
StatePublished - Oct 15 2022


  • Band-limited functions
  • Fourier analysis
  • Immersed boundary method
  • Regularized delta function
  • Stability analysis
  • Target point method

ASJC Scopus subject areas

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


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