Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment

作     者：Da Meng Bin Zheng Guang Lin Maria L.Sushko 

作者机构：Pacific Northwest National LaboratoryRichlandWA 99352USA. Department of MathematicsSchool of Mechanical EngineeringPurdue UniversityWest LafayetteIN 47907USA. 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2014年第16卷第10期

页      面：1298-1322页

核心收录：

学科分类：07[理学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：the Materials Synthesis and Simulation across Scales(MS3)Initiative(Laboratory Directed Research and Development(LDRD)Program)at Pacific Northwest National Laboratory(PNNL).Work by GL was supported by the U.S.Department of Energy(DOE)Office of Science’s Advanced Scientific Computing Research Applied Mathematics program and work by BZ by Early Career Award Initiative(LDRD Program)at PNNL.PNNL is operated by Battelle for the DOE under Contract DE-AC05-76RL01830 

主　　题：Poisson-Nernst-Planck equations classical density functional theory algebraic multigrid method fast Fourier transform Li-ion battery 

摘      要：We have developed efficient numerical algorithms for solving 3D steadystate Poisson-Nernst-Planck(PNP)equations with excess chemical potentials described by the classical density functional theory(cDFT).The coupled PNP equations are discretized by a finite difference scheme and solved iteratively using the Gummel method with *** Nernst-Planck equations are transformed into Laplace equations through the Slotboom ***,the algebraic multigrid method is applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations.A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed,which reduces computational complexity from O(N2)to O(NlogN),where N is the number of grid *** involving the Dirac delta function are evaluated directly by coordinate transformation,which yields more accurate results compared to applying numerical quadrature to an approximated delta *** results for ion and electron transport in solid electrolyte for lithiumion(Li-ion)batteries are shown to be in good agreement with the experimental data and the results from previous studies.