Volume 3, Issue 3
Stability Analysis of the Immersed Boundary Method for a Two-dimensional Membrane with Bending Rigidity

Zhaoxin Gong, Huaxiong Huang & Chuanjing Lu

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Commun. Comput. Phys., 3 (2008), pp. 704-723.

Published online: 2008-03

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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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@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 = {

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. 

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7871.html} }
TY - JOUR T1 - Stability Analysis of the Immersed Boundary Method for a Two-dimensional Membrane with Bending Rigidity AU - Zhaoxin Gong, Huaxiong Huang & Chuanjing Lu JO - Communications in Computational Physics VL - 3 SP - 704 EP - 723 PY - 2008 DA - 2008/03 SN - 3 DO - http://dor.org/ UR - https://global-sci.org/intro/cicp/7871.html KW - AB -

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. 

Zhaoxin Gong, Huaxiong Huang & Chuanjing Lu. (1970). Stability Analysis of the Immersed Boundary Method for a Two-dimensional Membrane with Bending Rigidity. Communications in Computational Physics. 3 (3). 704-723. doi:
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