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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:268

Article

Liu, Hailiang¹  Wang, Zhongming² 

[1] Iowa State Univ, Dept Math, Ames, IA 50011 USA

[2] Florida Int Univ, Dept Math & Stat, Miami, FL 33199 USA

关键词: Poisson equation;    Nernst-Planck equation;    Free energy;    Positivity;   

DOI  :  10.1016/j.jcp.2014.02.036

来源: Elsevier

【 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.

【 授权许可】

Free