Stability Analysis of the Immersed Boundary Method for a Two-Dimensional Membrane with Bending Rigidity (Communications in Computational Physics, 2008)
In this paper, we analyze the stability of the Immersed Boundary Methodapplied 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 isstable for a membrane with bending rigidity. The smoothed version, using a standardregularization technique for the singular force, is also shown to be stable. Furthermore, we show that the coupled fluid-membrane system is stiff and smoothing helpsto 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 decayrates. Therefore numerical instability could occur more easily for an explicit methodwhen the time step size is not sufficiently small, even though the continuous problemis stable.