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On the impact of the scheme for solving the higher dimensional equation in coupled population balance systems
Author(s) -
John Volker,
Roland Michael
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2830
Subject(s) - flow (mathematics) , population balance equation , population , mathematics , volume fraction , domain (mathematical analysis) , finite volume method , mathematical optimization , mathematical analysis , mechanics , physics , geometry , thermodynamics , demography , sociology
Population balance systems are models for processes in nature and industry that lead to a coupled system of equations (Navier–Stokes equations, transport equations, etc.) where the equations are defined in domains with different dimensions. This paper will study the impact of using different schemes for solving the three‐dimensional (3D) equation of a precipitation process in a two‐dimensional flow domain. The numerical schemes for the 3D equation are assessed with respect to the median of the volume fraction of the particle size distribution and the computational costs. It turns out that in the case of a structured flow field with small variations in time all schemes give qualitatively the same results. For a highly time‐ dependent flow field, the evolution of the median of the volume fraction differs considerably between first order and higher order schemes. Copyright © 2010 John Wiley & Sons, Ltd.