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Computational Models for Polydisperse Particulate and Multiphase Systems by Daniele L. Marchisio, Rodney O. Fox

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3

Quadrature-based moment methods

In this chapter we discuss the basic theory of Gaussian quadrature, which is at the heart of quadrature-based moment methods (QBMM). Proofs for most of the results are not included and, for readers requiring more extensive analytical treatments, references to the literature are made. In addition to a summary of the relevant theory, different algorithms to calculate the abscissas (or nodes) and the weights of the quadrature approximation from a known set of moments are presented, and their advantages and disadvantages are critically discussed. It is important to remind readers that most of the theory for quadrature formulas was developed for mono-dimensional integrals, namely integrals of a single independent ...

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