Open AccessApplication of Gaussian cubature to model two-dimensional population balances
Author(s) -
J. Bałdyga,
Grzegorz Tyl,
Mounir Bouaifi
Publication year - 2017
Publication title -
inżynieria chemiczna i procesowa/chemical and process engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.188
H-Index - 20
eISSN - 2300-1925
pISSN - 0208-6425
DOI - 10.1515/cpe-2017-0030
Subject(s) - gaussian quadrature , gaussian , nyström method , population , multivariate statistics , mathematics , population balance equation , multivariate normal distribution , quadrature (astronomy) , mathematical optimization , statistical physics , mathematical analysis , physics , chemistry , statistics , integral equation , computational chemistry , demography , sociology , optics
In many systems of engineering interest the moment transformation of population balance is applied. One of the methods to solve the transformed population balance equations is the quadrature method of moments. It is based on the approximation of the density function in the source term by the Gaussian quadrature so that it preserves the moments of the original distribution. In this work we propose another method to be applied to the multivariate population problem in chemical engineering, namely a Gaussian cubature (GC) technique that applies linear programming for the approximation of the multivariate distribution. Examples of the application of the Gaussian cubature (GC) are presented for four processes typical for chemical engineering applications. The first and second ones are devoted to crystallization modeling with direction-dependent two-dimensional and three-dimensional growth rates, the third one represents drop dispersion accompanied by mass transfer in liquid-liquid dispersions and finally the fourth case regards the aggregation and sintering of particle populations