Talk by Jitendra Kumar
Posted on: 13 May 2026
Title: Moment-Preserving Numerical Methods for Population Balances in Particulate Systems
Speaker: Jitendra Kumar, Dept. of Mathematics, IIT Ropar
Date: 19 May 2026
Time: 4 PM IST
Venue: LH-111
Abstract
Particulate processes such as crystallization, granulation, aerosol dynamics, and polymerization, among others are governed by particle populations whose size distributions evolve through nucleation, growth, aggregation, and breakage mechanisms. Tracking individual particles is infeasible at industrially relevant scales, so these systems are modelled in the continuum framework using population balance equations (PBEs), a class of integro-differential equations that describe the evolution of the particle size distribution.
While PBEs offer a tractable and mechanistically grounded description, solving them numerically is far from straightforward. The nonlocal integral terms associated with aggregation and breakage introduce strong coupling across the particle size domain, making the design of accurate and stable numerical methods difficult. Moreover, standard discretization techniques, including widely used finite volume schemes, often fail to preserve important moments of the distribution. This limitation is significant because such moments are directly related to physically meaningful and industrially relevant quantities.
This talk will focus on the development of weighted finite volume schemes for PBEs that are specifically designed to preserve mass together with selected higher-order moments, while maintaining computational efficiency and numerical stability. The underlying mathematical formulation and construction of these moment-preserving schemes will be discussed in detail, with emphasis on consistency, conservation properties, and implementation aspects. Numerical results will be presented for benchmark problems possessing analytical solutions, as well as for application- oriented test cases arising in particulate process engineering, demonstrating the accuracy, robustness and effectiveness of the proposed methods.