Efficient numerical schemes for population balance models. (June 2022)

• Record Type: Journal Article
• Authors: Inguva, Pavan K.; Schickel, Kaylee C.; Braatz, Richard D.
• Is Part Of: Computers & chemical engineering. Volume 162(2022)
• Publication Date: 2022-06
• Subjects: Population balance models -- Numerical methods -- Species balances -- Numerical simulation -- Numerical analysis; Chemical engineering -- Data processing -- Periodicals; 660.0285
• DOI: 10.1016/j.compchemeng.2022.107808
• Languages: English
• ISSNs: 0098-1354

Abstract

Highlights: A finite difference scheme is proposed that has zero numerical discretization error. The scheme is demonstrated for classes of population balance models. The scheme employs specially constructed meshes and/or variable transformations. The scheme has very low computational cost, sometimes as low as memory reallocation. The scheme operates at the limit of numerical stability. Abstract: Population balance models (PBM) describe a wide array of physical, chemical, and biological processes having a distribution over some intrinsic property, and are used to model cells, viruses, aggregates, bubbles, and crystals. The ubiquity of PBMs motivates generalizable and accurate approaches for their numerical solution. Typically, high-order finite difference or finite volume methods are used. We propose a finite difference scheme at the limit of numerical stability that results in discretization error that is zero for certain classes of PBMs and low enough to be acceptable in other applications. The scheme employs specially constructed meshes and, in some cases, variable transformations. The scheme has very low computational cost – sometimes as low as memory reallocation with no floating point operations. Case studies are presented throughout that demonstrate the scheme's performance in relation to other commonly employed schemes.