Efficient numerical schemes for multidimensional population balance models
Name
2206.12404v1.pdf
Description
Accepted version
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5.12 MB
Format
Adobe PDF
Checksum (MD5)
99ea5613f9f52e0f960b8f8915315c9b
Author(s)
Inguva, Pavan K
Braatz, Richard D
Date Issued
February 2023
Journal
Computers & Chemical Engineering
Publisher
Elsevier BV
Citation
Inguva, Pavan K and Braatz, Richard D. 2023. "Efficient numerical schemes for multidimensional population balance models." Computers & Chemical Engineering, 170.
Version
Author's final manuscript
Abstract
Multidimensional population balance models (PBMs) describe chemical and biological processes having a
distribution over two or more intrinsic properties (such as size and age, or two independent spatial variables).
The incorporation of additional intrinsic variables into a PBM improves its descriptive capability and can be
necessary to capture specific features of interest. As most PBMs of interest cannot be solved analytically,
computationally expensive high-order finite difference or finite volume methods are frequently used to obtain
an accurate numerical solution. We propose a finite difference scheme based on operator splitting and solving
each sub-problem at the limit of numerical stability that achieves a discretization error that is zero for
certain classes of PBMs and low enough to be acceptable for other classes. In conjunction to employing
specially constructed meshes and variable transformations, the scheme exploits the commutative property of
the differential operators present in many classes of PBMs. The scheme has very low computational cost –
potentially as low as just memory reallocation. Multiple case studies demonstrate the performance of the
proposed scheme.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
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Creative Commons Attribution-Noncommercial-ShareAlike
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DOI of Published Version
https://doi.org/10.1016/j.compchemeng.2022.108095
