کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6595534 | 458533 | 2014 | 29 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Analysis of finite difference discretization schemes for diffusion in spheres with variable diffusivity
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی شیمی
مهندسی شیمی (عمومی)
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computers & Chemical Engineering - Volume 71, 4 December 2014, Pages 241-252
Journal: Computers & Chemical Engineering - Volume 71, 4 December 2014, Pages 241-252
نویسندگان
Ashlee N. Ford Versypt, Richard D. Braatz,