Analysis of finite difference discretization schemes for diffusion in spheres with variable diffusivity
Name
Braatz_Analysis of finite difference.pdf
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1.43 MB
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Author(s)
Ford-Versypt, Ashlee Nicole
Braatz, Richard D
Date Issued
August 2014
Journal
Computers & Chemical Engineering
Publisher
Elsevier
Citation
Ford Versypt, Ashlee N., and Richard D. Braatz. “Analysis of Finite Difference Discretization Schemes for Diffusion in Spheres with Variable Diffusivity.” Computers & Chemical Engineering 71 (2014): 241–252.
Version
Author's final manuscript
Abstract
Two finite difference discretization schemes for approximating the spatial derivatives in the diffusion equation in spherical coordinates with variable diffusivity are presented and analyzed. The numerical solutions obtained by the discretization schemes are compared for five cases of the functional form for the variable diffusivity: (I) constant diffusivity, (II) temporally dependent diffusivity, (III) spatially dependent diffusivity, (IV) concentration-dependent diffusivity, and (V) implicitly defined, temporally and spatially dependent diffusivity. Although the schemes have similar agreement to known analytical or semi-analytical solutions in the first four cases, in the fifth case for the variable diffusivity, one scheme produces a stable, physically reasonable solution, while the other diverges. We recommend the adoption of the more accurate and stable of these finite difference discretization schemes to numerically approximate the spatial derivatives of the diffusion equation in spherical coordinates for any functional form of variable diffusivity, especially cases where the diffusivity is a function of position.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/j.compchemeng.2014.05.022
