Convergence proof of the velocity field for a stokes flow immersed boundary method

Yoichiro Mori

Research output: Contribution to journalArticle

31 Scopus citations

Abstract

The immersed boundary (IB) method is a computational framework for problems involving the interaction of a fluid and immersed elastic structures. It is characterized by the use of a uniform Cartesian mesh for the fluid, a Lagrangian curvilinear mesh on the elastic material, and discrete delta functions for communication between the two grids. We consider a simple IB problem in a two-dimensional periodic fluid domain with a one-dimensional force generator. We obtain error estimates for the velocity field of the IB solution for the stationary Stokes problem. We use this result to prove convergence of a simple small-amplitude dynamic problem. We test our error estimates against computational experiments.

Original languageEnglish (US)
Pages (from-to)1213-1263
Number of pages51
JournalCommunications on Pure and Applied Mathematics
Volume61
Issue number9
DOIs
StatePublished - Sep 1 2008

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