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Automatic differentiation‐based quadrature method of moments for solving population balance equations
Author(s) -
Kariwala Vinay,
Cao Yi,
K. Nagy Zoltan
Publication year - 2012
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.12613
Subject(s) - nyström method , robustness (evolution) , population balance equation , mathematics , quadrature (astronomy) , ordinary differential equation , nonlinear system , algebraic equation , taylor series , differential algebraic equation , uncertainty quantification , population , mathematical optimization , differential equation , mathematical analysis , integral equation , engineering , statistics , biochemistry , chemistry , physics , demography , quantum mechanics , sociology , electrical engineering , gene
The quadrature method of moments (QMOM) is a promising tool for the solution of population balance equations. QMOM requires solving differential algebraic equations (DAEs) consisting of ordinary differential equations related to the evolution of moments and nonlinear algebraic equations resulting from the quadrature approximation of moments. The available techniques for QMOM are computationally expensive and are able to solve for only a few moments due to numerical robustness deficiencies. In this article, the use of automatic differentiation (AD) is proposed for solution of DAEs arising in QMOM. In the proposed method, the variables of interest are approximated using high‐order Taylor series. The use of AD and Taylor series gives rise to algebraic equations, which can be solved sequentially to obtain high‐fidelity solution of the DAEs. Benchmark examples involving different mechanisms are used to demonstrate the superior accuracy, computational advantage, and robustness of AD‐QMOM over the existing state‐of‐the‐art technique, that is, DAE‐QMOM. © 2011 American Institute of Chemical Engineers AIChE J, 2012