@Article{CiCP-3-704,
author = {Zhaoxin Gong, Huaxiong Huang and Chuanjing Lu},
title = {Stability Analysis of the Immersed Boundary Method for a Two-Dimensional Membrane with Bending Rigidity},
journal = {Communications in Computational Physics},
year = {2008},
volume = {3},
number = {3},
pages = {704--723},
abstract = {<p style="text-align: justify;">In this paper, we analyze the stability of the Immersed Boundary Method
applied to a membrane-fluid system with a plasma membrane immersed in an incompressible viscous fluid. We show that for small deformations, the planar rest state is
stable for a membrane with bending rigidity. The smoothed version, using a standard
regularization technique for the singular force, is also shown to be stable. Furthermore, we show that the coupled fluid-membrane system is stiff and smoothing helps
to reduce the stiffness. Compared to the system of elastic fibers immersed in an incompressible fluid, membrane with bending rigidity consist of a wider range of decay
rates. Therefore numerical instability could occur more easily for an explicit method
when the time step size is not sufficiently small, even though the continuous problem
is stable.</p>},
issn = {1991-7120},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cicp/7871.html}
}