TY - JOUR
T1 - The immersed boundary method for advection-electrodiffusion with implicit timestepping and local mesh refinement
AU - Lee, Pilhwa
AU - Griffith, Boyce E.
AU - Peskin, Charles S.
N1 - Funding Information:
P.L. was supported in part by a Go Abroad Scholarship from the Korea Science and Engineering Foundation (Grant No. M06-2003-000-10337-0 ). B.E.G. was supported in part by an American Heart Association Postdoctoral Fellowship (Grant No. 0626001T). C.S.P. was supported in part by the Systems Biology Center in New York through Grant No. P50GM071558 from the National Institute of General Medical Sciences.
PY - 2010/7
Y1 - 2010/7
N2 - 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.
AB - 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.
KW - Advection-electrodiffusion
KW - FAC
KW - Fast adaptive composite
KW - Immersed boundary method
KW - Implicit
KW - Local mesh refinement
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U2 - 10.1016/j.jcp.2010.03.036
DO - 10.1016/j.jcp.2010.03.036
M3 - Article
AN - SCOPUS:77952420857
SN - 0021-9991
VL - 229
SP - 5208
EP - 5227
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 13
ER -