Efficient numerical schemes for multidimensional population balance models. (February 2023)

• Record Type: Journal Article
• Authors: Inguva, Pavan K.; Braatz, Richard D.
• Is Part Of: Computers & chemical engineering. Volume 170(2023)
• Publication Date: 2023-02
• Subjects: Population balance models -- Numerical methods -- Species balances -- Numerical simulation -- Numerical analysis -- Finite difference methods; Chemical engineering -- Data processing -- Periodicals; 660.0285
• DOI: 10.1016/j.compchemeng.2022.108095
• Languages: English
• ISSNs: 0098-1354

Abstract

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. Highlights: A finite difference scheme is proposed for multidimensional population balance models. The scheme employs operator splitting and specially constructed transformations and meshes. The scheme operates at the limit of numerical stability. The scheme has zero numerical error for some classes of population balance models. The scheme has very low computational cost, sometimes as low as memory reallocation.