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Summary: Efficient solutions to robust, semi-implicit
discretizations of the Immersed Boundary Method
Hector D. Ceniceros
Department of Mathematics, University of California Santa Barbara , CA 93106
Jordan E. Fisher
Department of Mathematics, University of California Santa Barbara , CA 93106
Alexandre M. Roma
Departamento de Matem´atica Aplicada, Universidade de S~ao Paulo, Caixa Postal 66281,
CEP 05311-970, S~ao Paulo-SP, Brasil.
Abstract
The Immersed Boundary Method is a versatile tool for the investigation of
flow-structure interaction. In a large number of applications, the immersed
boundaries or structures are very stiff and strong tangential forces on these
interfaces induce a well-known, severe time-step restriction for explicit dis-
cretizations. This excessive stability constraint can be removed with fully
implicit or suitable semi-implicit schemes but at a seemingly prohibitive com-
putational cost. While economical alternatives have been proposed recently
for some special cases, there is a practical need for a computationally effi-
cient approach that can be applied more broadly. In this context, we revisit
a robust semi-implicit discretization introduced by Peskin in the late 70's
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