Quadrature-based moment methods example

The other two collision source vectors, and can be evaluated using the definitions in Eqs. (6.104) and (6.106). As mentioned earlier, will be closed in terms of the moments of order two and lower, and their gradients. In contrast, C will not be closed in terms of any finite set of moments. Nevertheless, it can be approximated using quadrature-based moment methods as described in Section 6.5. In the fluid-particle limit d d2), neither CI2 i or C will contribute terms involving spatial gradients of the fluid properties (i.e. buoyancy, lift, etc.) to the fluid-phase momentum equation. As mentioned earlier, such terms result from the model for gapi i-n) and would appear, for example, on using the expression in Eq. (6.81). With the latter, Eq. (6.161) becomes... 

The conditional quadrature method of moments (CQMOM) is based on the concept of a conditional density function (Yuan Fox, 2011). Conditional density functions represent, in turn, the probability of having one internal coordinate within an infinitesimal limit when one or more of the other internal coordinates are fixed and equal to specific values. For example, in the case of a generic NDF the expression... 

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