Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jcp.2009.08.018
Title: An implicit immersed boundary method for three-dimensional fluid-membrane interactions
Authors: Le, D.V. 
White, J.
Peraire, J.
Lim, K.M. 
Khoo, B.C. 
Keywords: Immersed boundary method
Membrane capsules
Navier-Stokes equations
Newton-Krylov method
Red blood cells
Issue Date: 1-Dec-2009
Source: Le, D.V., White, J., Peraire, J., Lim, K.M., Khoo, B.C. (2009-12-01). An implicit immersed boundary method for three-dimensional fluid-membrane interactions. Journal of Computational Physics 228 (22) : 8427-8445. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jcp.2009.08.018
Abstract: We present an implicit immersed boundary method for the incompressible Navier-Stokes equations capable of handling three-dimensional membrane-fluid flow interactions. The goal of our approach is to greatly improve the time step by using the Jacobian-free Newton-Krylov method (JFNK) to advance the location of the elastic membrane implicitly. The most attractive feature of this Jacobian-free approach is Newton-like nonlinear convergence without the cost of forming and storing the true Jacobian. The Generalized Minimal Residual method (GMRES), which is a widely used Krylov-subspace iterative method, is used to update the search direction required for each Newton iteration. Each GMRES iteration only requires the action of the Jacobian in the form of matrix-vector products and therefore avoids the need of forming and storing the Jacobian matrix explicitly. Once the location of the boundary is obtained, the elastic forces acting at the discrete nodes of the membrane are computed using a finite element model. We then use the immersed boundary method to calculate the hydrodynamic effects and fluid-structure interaction effects such as membrane deformation. The present scheme has been validated by several examples including an oscillatory membrane initially placed in a still fluid, capsule membranes in shear flows and large deformation of red blood cells subjected to stretching force. © 2009 Elsevier Inc.
Source Title: Journal of Computational Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/51328
ISSN: 00219991
DOI: 10.1016/j.jcp.2009.08.018
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