An inverse averaging finite element method for solving three-dimensional Poisson-Nernst-Planck equations in nanopore system simulations

doi:10.1063/5.0066194

	An inverse averaging finite element method for solving three-dimensional Poisson-Nernst-Planck equations in nanopore system simulations
	Zhang, Qianru 1,2; Wang, Qin 1,2; Zhang, Linbo 1,2; Lu, Benzhuo 1,2
刊名	JOURNAL OF CHEMICAL PHYSICS
	2021-11-21
卷号	155 期号:19 页码:13
ISSN号	0021-9606
DOI	10.1063/5.0066194
英文摘要	The Poisson-Nernst-Planck (PNP) model plays an important role in simulating nanopore systems. In nanopore simulations, the large-size nanopore system and convection-domination Nernst-Planck (NP) equations will bring convergence difficulties and numerical instability problems. Therefore, we propose an improved finite element method (FEM) with an inverse averaging technique to solve the three-dimensional PNP model, named inverse averaging FEM (IAFEM). At first, the Slotboom variables are introduced aiming at transforming non-symmetric NP equations into self-adjoint second-order elliptic equations with exponentially behaved coefficients. Then, these exponential coefficients are approximated with their harmonic averages, which are calculated with an inverse averaging technique on every edge of each tetrahedral element in the grid. Our scheme shows good convergence when simulating single or porous nanopore systems. In addition, it is still stable when the NP equations are convection domination. Our method can also guarantee the conservation of computed currents well, which is the advantage that many stabilization schemes do not possess. Our numerical experiments on benchmark problems verify the accuracy and robustness of our scheme. The numerical results also show that the method performs better than the standard FEM when dealing with convection-domination problems. A successful simulation combined with realistic chemical experiments is also presented to illustrate that the IAFEM is still effective for three-dimensional interconnected nanopore systems.
资助项目	National Key R&D Program of China[2019YFA0709600] ; National Key R&D Program of China[2019YFA0709601] ; National Natural Science Foundation of China[11771435] ; National Natural Science Foundation of China[22073110]
WOS研究方向	Chemistry ; Physics
语种	英语
出版者	AIP Publishing
WOS记录号	WOS:000719748700001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59574]
专题	中国科学院数学与系统科学研究院
通讯作者	Lu, Benzhuo
作者单位	1.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, CEMS,LSEC, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Qianru,Wang, Qin,Zhang, Linbo,et al. An inverse averaging finite element method for solving three-dimensional Poisson-Nernst-Planck equations in nanopore system simulations[J]. JOURNAL OF CHEMICAL PHYSICS,2021,155(19):13.
APA	Zhang, Qianru,Wang, Qin,Zhang, Linbo,&Lu, Benzhuo.(2021).An inverse averaging finite element method for solving three-dimensional Poisson-Nernst-Planck equations in nanopore system simulations.JOURNAL OF CHEMICAL PHYSICS,155(19),13.
MLA	Zhang, Qianru,et al."An inverse averaging finite element method for solving three-dimensional Poisson-Nernst-Planck equations in nanopore system simulations".JOURNAL OF CHEMICAL PHYSICS 155.19(2021):13.