Efficient Conservative Numerical Schemes for 1D Nonlinear Spherical Diffusion Equations with Applications in Battery Modeling
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Author(s)
Zeng, Yi
Albertus, Paul
Klein, Reinhardt
Chaturvedi, Nalin
Kojic, Aleksandar
Bazant, Martin Z.
Christensen, Jake
Date Issued
July 2013
Journal
Journal of the Electrochemical Society
Citation
Zeng, Y., P. Albertus, R. Klein, N. Chaturvedi, A. Kojic, M. Z. Bazant, and J. Christensen. “Efficient Conservative Numerical Schemes for 1D Nonlinear Spherical Diffusion Equations with Applications in Battery Modeling.” Journal of the Electrochemical Society 160, no. 9 (January 1, 2013): A1565–A1571. © 2013 The Electrochemical Society.
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Final published version
Abstract
Mathematical models of batteries which make use of the intercalation of a species into a solid phase need to solve the corresponding mass transfer problem. Because solving this equation can significantly add to the computational cost of a model, various methods have been devised to reduce the computational time. In this paper we focus on a comparison of the formulation, accuracy, and order of the accuracy for two numerical methods of solving the spherical diffusion problem with a constant or non-constant diffusion coefficient: the finite volume method and the control volume method. Both methods provide perfect mass conservation and second order accuracy in mesh spacing, but the control volume method provides the surface concentration directly, has a higher accuracy for a given numbers of mesh points and can also be easily extended to variable mesh spacing. Variable mesh spacing can significantly reduce the number of points that are required to achieve a given degree of accuracy in the surface concentration (which is typically coupled to the other battery equations) by locating more points where the concentration gradients are highest.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1149/2.102309jes
