Moment-transport equation EQMOM

As a final case, we will again consider the joint velocity-scalar NDF governed by Eq. (8.122), but without specifying a functional form for the scalar-conditioned velocity. The moment-transport equation is again given by Eq. (8.122). However, we will now use a scalar-conditioned multivariate EQMOM to reconstruct the joint NDE ... 

The application of QBMM to Eq. (C.l) will require a closure when m(7 depends on 7 Nevertheless, the resulting moment equations (used for the QMOM or the EQMOM) and transport equations for the weights and abscissas (used for the DQMOM) will still be hyperbolic. In terms of hyperbolic conservation laws, the moments are conserved variables (which result from a linear operation on /), while the weights and abscissas are primitive variables. Because conservation of moments is important to the stability of the moment-inversion algorithms, it is imperative that the numerical algorithm guarantee conservation. For hyperbolic systems, this is most easily accomplished using finite-volume methods (FVM) (or, more specifically, realizable FVM). The other important consideration is the accuracy of the moment closure used to close the function, as will be described below. 

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