A Positivity Preserving and Free Energy Dissipative Difference Scheme for the Poisson-Nernst-Planck System
A Positivity Preserving and Free Energy Dissipative Difference Scheme for the Poisson-Nernst-Planck System
复制标题
泊松-能斯特-普朗克系统的保正和自由能耗散差分格式
DOI：
10.1007/s10915-019-01025-x
复制
发表时间：
2019-10-01
影响因子：
2.5
通讯作者：
Yue, Xiaoqiang
中科院分区：
文献类型：
--
作者：
He, Dongdong;Pan, Kejia;Yue, Xiaoqiang
本文基于对Nernst-Planck方程的重新表述，构造了时变Poisson-Nernst-Planck系统的一个无条件稳定的半隐式线性化差分格式。该方法在完全离散的水平上保留了几个重要的物理定律，而不受时间步长的限制，包括：质量守恒、离子浓度正性、自由能耗散。该方法是一种线性化的方法，可以有效地实现。此外，该方法可以毫无困难地推广到多离子的情况。最后给出了与理论结果相吻合的数值结果。
In this paper, based on the reformulation of the Nernst-Planck equations, we construct an unconditionally stable semi-implicit linearized difference scheme for the time dependent Poisson-Nernst-Planck system. The method preserves several important physical laws at full discrete level without any constraints on the time step size, including: mass conservation, ion concentration positivity, free energy dissipation. The proposed method is a linearized method, which can be implemented efficiently. Furthermore, the method can be extended to the case of multi-ions without any difficulty. The paper ends with supporting numerical results which confirm well with theoretical findings.