WIAS Preprint No. 1621, (2011)

A numerical method for the simulation of an aggregation-driven population balance system


  • Hackbusch, Wolfgang
  • John, Volker
    ORCID: 0000-0002-2711-4409
  • Khachatryan, Aram
  • Suciu, Carina

2010 Mathematics Subject Classification

  • 45K05 44A35


  • Population balance systems, aggregation, integro partial differential equation, stabilised methods, convolution, calibration of parameters


A population balance system which models the synthesis of urea is studied in this paper. The equations for the flow field, the mass and the energy balances are given in a three-dimensional domain and the equation for the particle size distribution (PSD) in a four-dimensional domain. This problem is convection-dominated and aggregation-driven. Both features require the application of appropriate numerical methods. This paper presents a numerical approach for simulating the population balance system which is based on finite element schemes, a finite difference method and a modern method to evaluate convolution integrals that appear in the aggregation term. Two experiments are considered and the numerical results are compared with experimental data. Unknown parameters in the aggregation kernel have to be calibrated. For appropriately chosen parameters, good agreements are achieved of the experimental data and the numerical results computed with the proposed method. A detailed study of the computational results reveals the influence of different parts of the aggregation kernel.

Appeared in

  • Internat. J. Numer. Methods Fluids, 69 (2012) pp. 1646--1660.

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