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

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Appendix C

Moment methods with hyperbolic equations

In the literature (Mazzei, 2011) it has been argued that quadrature-based moment methods (QBMM) cannot be used to represent solutions to hyperbolic kinetic equations without adding “diffusion” terms. The argument goes that diffusion terms are necessary to represent “micromixing” between two NDFs originating from spatially distinct regions of the system. The purpose of this appendix is to present an analytical counterexample that clearly shows that the exact solution to the hyperbolic kinetic equation (i.e. without diffusion terms) can result in a “completely mixed” (or, more precisely, a homogeneous) NDF at large times. As we shall see, this solution arises entirely due to the size dependence ...

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