A free energy satisfying finite difference method for Poisson--Nernst--Planck equations
Numerical Analysis
2015-06-17 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1308.6632,
title = {A free energy satisfying finite difference method for Poisson--Nernst--Planck equations},
author = {Hailiang Liu and Zhongming Wang},
journal= {arXiv preprint arXiv:1308.6632},
year = {2015}
}