Stability Analysis of the Immersed Boundary Method for a Two-Dimensional Membrane with Bending Rigidity

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

Keywords: