A free energy satisfying finite difference method for Poisson-Nernst-Planck equations

被引：62
作者：
Liu, Hailiang [1 ]
Wang, Zhongming [2 ]
机构：
[1] Iowa State Univ, Dept Math, Ames, IA 50011 USA
[2] Florida Int Univ, Dept Math & Stat, Miami, FL 33199 USA
来源：
JOURNAL OF COMPUTATIONAL PHYSICS | 2014年 / 268卷
基金：
美国国家科学基金会;
关键词：
Poisson equation; Nernst-Planck equation; Free energy; Positivity; ELECTROSTATIC FREE-ENERGY; BOLTZMANN EQUATION; LIQUID-JUNCTION; TIME BEHAVIOR; DIFFUSION; MODELS; GRAMICIDIN; ELECTRODIFFUSION; CHANNEL; LONG;
D O I：
10.1016/j.jcp.2014.02.036
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this work we design and analyze a free energy satisfying finite difference method for solving Poisson-Nernst-Planck equations in a bounded domain. The algorithm is of second order in space, with numerical solutions satisfying all three desired properties: i) mass conservation, ii) positivity preserving, and iii) free energy satisfying in the sense that these schemes satisfy a discrete free energy dissipation inequality. These ensure that the computed solution is a probability density, and the schemes are energy stable and preserve the equilibrium solutions. Both one- and two-dimensional numerical results are provided to demonstrate the good qualities of the algorithm, as well as effects of relative size of the data given. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：363 / 376
页数：14
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