The immersed boundary method for advection-electrodiffusion with implicit timestepping and local mesh refinement.
We describe an immersed boundary method for problems of fluid-solute-structure interaction. The numerical scheme employs linearly implicit timestepping, allowing for the stable use of timesteps that are substantially larger than those permitted by an explicit method, and local mesh refinement, making it feasible to resolve the steep gradients associated with the space charge layers as well as the chemical potential, which is used in our formulation to control the permeability of the membrane to the (possibly charged) solute. Low Reynolds number fluid dynamics are described by the time-dependent incompressible Stokes equations, which are solved by a cell-centered approximate projection method. The dynamics of the chemical species are governed by the advection-electrodiffusion equations, and our semi-implicit treatment of these equations results in a linear system which we solve by GMRES preconditioned via a fast adaptive composite-grid (FAC) solver. Numerical examples demonstrate the capabilities of this methodology, as well as its convergence properties.
Lee
Pilhwa
P
Department of Cell Biology, University of Connecticut Health Center, 263 Farmington Avenue, Farmington, CT 06030-3505.
Griffith
Boyce E
BE
Peskin
Charles S
CS
Neuron. 2008 Sep 25;59(6):861-72
18817727
Cell Mol Biol (Noisy-le-grand). 2001 Jul;47(5):901-23
11728102
Proc Natl Acad Sci U S A. 2000 Oct 24;97(22):11744-50
11050204
J Cell Sci. 2002 Jan 15;115(Pt 2):367-84
11839788
Biophys J. 2004 Jul;87(1):81-91
15240447
J Gen Physiol. 1960 Sep;44:169-94
13777653
Curr Opin Neurobiol. 2005 Feb;15(1):67-72
15721746
Nature. 2002 Jan 10;415(6868):198-205
11805843
Neuron. 1998 Jul;21(1):13-26
9697848