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An inverse averaging finite element method for solving three-dimensional Poisson-Nernst-Planck equations in nanopore system simulations
Zhang, Qianru1,2; Wang, Qin1,2; Zhang, Linbo1,2; Lu, Benzhuo1,2
2021-11-21
Source PublicationJOURNAL OF CHEMICAL PHYSICS
ISSN0021-9606
Volume155Issue:19Pages:13
AbstractThe 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.
DOI10.1063/5.0066194
Indexed BySCI
Language英语
Funding ProjectNational 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 Research AreaChemistry ; Physics
WOS SubjectChemistry, Physical ; Physics, Atomic, Molecular & Chemical
WOS IDWOS:000719748700001
PublisherAIP Publishing
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/59575
Collection中国科学院数学与系统科学研究院
Corresponding AuthorLu, Benzhuo
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, CEMS,LSEC, Beijing, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
Recommended Citation
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.
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