Stability Analysis of the Immersed Boundary Method for a Two-Dimensional Membrane with Bending Rigidity
Year: 2008
Communications in Computational Physics, Vol. 3 (2008), Iss. 3 : pp. 704–723
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-CiCP-7871
Communications in Computational Physics, Vol. 3 (2008), Iss. 3 : pp. 704–723
Published online: 2008-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20