An Adaptive Version of the Immersed Boundary Method

Alexandre M. Roma, Charles S. Peskin, Marsha J. Berger

Research output: Contribution to journalArticlepeer-review


A computational setting for the Immersed Boundary Method employing an adaptive mesh refinement is presented. Enhanced accuracy for the method is attained locally by covering an immersed boundary vicinity with a sequence of nested, progressively finer rectangular grid patches which dynamically follow the immersed boundary motion. The set of equations describing the interaction between a non-stationary, viscous incompressible fluid and an immersed elastic boundary is solved by coupling a projection method, specially designed for locally refined meshes, to an implicit formulation of the Immersed Boundary Method. The main contributions of this work concern the formulation and the implementation of a multilevel self-adaptive version of the Immersed Boundary Method on locally refined meshes. This approach is tested for a particular two-dimensional model problem, for which no significant difference is found between the solutions obtained on a mesh refined locally around the immersed boundary, and on the associated uniform mesh, built with the resolution of the finest level.

Original languageEnglish (US)
Pages (from-to)509-534
Number of pages26
JournalJournal of Computational Physics
Issue number2
StatePublished - Aug 10 1999


  • Immersed boundary method
  • Incompressible flows
  • Interface problems
  • Mesh refinement
  • Projection methods

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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