期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 230, 期 5, 页码 2125-2140出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2010.12.008
关键词
Nonlinear Poisson-Boltzmann equation; Non-graded adaptive grid; Octree data structure; Second-order discretization; Arbitrary geometries; Supercapacitors
资金
- Office of Naval Research [N00014-11-1-0027]
- Department of Energy [DE-FG02-08ER15991]
- National Science Foundation [DMS 0713858]
- Institute for Collaborative Biotechnologies [W911NF-09-D-0001]
- US Army Research Office
In this paper we present a finite difference scheme for the discretization of the nonlinear Poisson-Boltzmann (PB) equation over irregular domains that is second-order accurate. The interface is represented by a zero level set of a signed distance function using Octree data structure, allowing a natural and systematic approach to generate non-graded adaptive grids. Such a method guaranties computational efficiency by ensuring that the finest level of grid is located near the interface. The nonlinear PB equation is discretized using finite difference method and several numerical experiments are carried which indicate the second-order accuracy of method. Finally the method is used to study the supercapacitor behaviour of porous electrodes. (C) 2010 Elsevier Inc. All rights reserved.
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