A least-squares method with direct minimization for the solution of the breakage-coalescence population balance equation

Authors:
Zhengjie Zhu;C. A. Dorao;H. A. Jakobsen
Affiliations:
Department of Chemical Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway;SINTEF Material and Chemistry, N-7465 Trondheim, Norway;Department of Chemical Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
Venue:
Mathematics and Computers in Simulation
Year:
2008

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Abstract

A least-squares method with a direct minimization algorithm is introduced to solve the non-linear population balance equation that consists of both breakage and coalescence terms. The least-squares solver, direct minimization solver together with a finite difference solver are implemented for comparisons. It is shown that the coalescence term introduces a strong non-linear behavior which can affect the robustness of the numerical solvers. In the comparison with the least-squares method, the direct minimization method is proved to be capable of producing equally accurate results, while its formulation is better conditioned. In the case of a non-linear population balance equation system, the direct minimization method converges faster than the standard least-squares method.