Implicit second-order immersed boundary methods with boundary mass

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A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions (2008, background): “Recently, stable semi- and fully-implicit temporal discretizations to couple the velocity field and the boundary force for elastic boundaries have been proposed by [24,22].”
Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method (2010, methodology): “There are methods to increase stability using either implicit or semi-implicit methods [37, 41].”
Numerical Methods for Fluid-Structure Interaction — A Review (2012, methodology): “A variation of this scheme was studied by Mori and Peskin (2008), who proposed a fully implicit method in which the system that requires iterative solves has the same structure as the linearized https://doi.org/10.4208/cicp.291210.290411s Published online by Cambridge University Press semi-implicit…”
An immersed boundary method for fluid–flexible structure interaction (2009, background): “We also note a recent effort in Mori and Peskin [20] where the mass of the elastic structure immersed in a fluid is incorporated as a d’Alembert force.”