On the stability of the finite element immersed boundary method

TitleOn the stability of the finite element immersed boundary method
Publication TypeJournal Article
Year of Publication2008
AuthorsHeltai L
JournalComputers & Structures
Volume86
Pagination598–617
KeywordsCFL condition, Finite element method, Immersed boundary method, Numerical stability
Abstract

The immersed boundary (IB) method is a mathematical formulation for fluid-structure interaction problems, where immersed incompressible visco-elastic bodies or boundaries interact with an incompressible fluid. The original numerical scheme associated to the IB method requires a smoothed approximation of the Dirac delta distribution to link the moving Lagrangian domain with the fixed Eulerian one. We present a stability analysis of the finite element immersed boundary method, where the Dirac delta distribution is treated variationally, in a generalized visco-elastic framework and for two different time-stepping schemes.

URLhttp://www.sciencedirect.com/science/article/B6V28-4PYMWK8-2/2/9eac499cefb93e5d1a6fb60640ef5573