Application of Proper Orthogonal Decomposition to Population Balance Equations of Particulate Processes

Abstract

This work deals with population balance equations, investigating on a particle size distribution model developed by the Research Center Pharmaceutical Engineering in Graz to simulate crystallization processes. The model outlined in detail in this work consists of coupled population balance equations with non-local integro terms and takes crystal growth and aggregation processes into account. Solving the full order model takes a high computational effort, yet various solution snapshot sets from different parameters are required for investigating on the unknown parameters appearing in the model. Therefore, a reduced order model is set up from a full order solution snapshot set by applying the Galerkin projection with a basis computed through the proper orthogonal decomposition method. Numerical results of the model reduction are presented and further numerical approaches, for example greedy methods, are discussed.