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Inhomogeneous GPBE

In the remainder of this section, we introduce the principal modeling issues related to spatial transport using moment methods. First, we discuss the realizability of the NDF and of moment sets (which are related to the numerical errors discussed above). Second, we introduce the phenomenon of particle trajectory crossing (PTC) that occurs with the inhomogeneous KE (and is exactly captured by the NDF), and describe how it leads to a closure problem in the moment-transport equations. Next, we look at issues related to coupling between spatial and phase-space transport in the GPBE (i.e. due to correlations between velocity and internal coordinates such as particle volume). Finally, we introduce KBFVM for solving the moment-transport equations in connection with QBMM, and briefly discuss how they can be used to ensure realizability as well as to capture PTC and to treat coupled moments. [Pg.330]

The quadrature method of moments (QMOM) and the direct quadrature method of moments (DQMOM) were introduced in Chapter 3 as equivalent methods for solving a homogeneous GPBE. In fact, the DQMOM was derived by Marchisio Fox (2005) primarily for the purpose of solving spatially inhomogeneous multivariate moment-transport equations. Unlike for the univariate case, where the moment-inversion algorithm is uniquely defined for a given set of moments, the QMOM in the multivariate case is much... [Pg.337]


See other pages where Inhomogeneous GPBE is mentioned: [Pg.29]    [Pg.373]    [Pg.373]    [Pg.375]    [Pg.377]    [Pg.379]    [Pg.381]    [Pg.383]    [Pg.385]    [Pg.387]    [Pg.389]    [Pg.391]    [Pg.393]    [Pg.397]    [Pg.399]    [Pg.525]    [Pg.29]    [Pg.373]    [Pg.373]    [Pg.375]    [Pg.377]    [Pg.379]    [Pg.381]    [Pg.383]    [Pg.385]    [Pg.387]    [Pg.389]    [Pg.391]    [Pg.393]    [Pg.397]    [Pg.399]    [Pg.525]    [Pg.29]    [Pg.188]    [Pg.266]    [Pg.329]   


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