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

Published online by Cambridge University Press:  03 June 2015

Da Meng ,
Bin Zheng ,
Guang Lin  and
Maria L. Sushko
Da Meng*
Affiliation:
Pacific Northwest National Laboratory, Richland, WA 99352, USA
Bin Zheng*
Affiliation:
Pacific Northwest National Laboratory, Richland, WA 99352, USA
Guang Lin*
Affiliation:
Pacific Northwest National Laboratory, Richland, WA 99352, USA Department of Mathematics, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
Maria L. Sushko*
Affiliation:
Pacific Northwest National Laboratory, Richland, WA 99352, USA
*
Email:da.meng@pnnl.gov
Email:bin.zheng@pnnl.gov
Corresponding author.Email:Guanglin@purdue.edu
Email:Maria.Sushko@pnnl.gov
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Abstract

We have developed efficient numerical algorithms for solving 3D steady-state 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 relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Then, 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 points. Integrals 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 function. Numerical 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.

Keywords

92C3535J4735J6035R0965M0665N5565T50Poisson-Nernst-Planck equationsclassical density functional theoryalgebraic multigrid methodfast Fourier transformLi-ion battery
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 5 , November 2014 , pp. 1298 - 1322
Copyright
Copyright © Global Science Press Limited 2014

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