Quadrature-based moment methods QBMM

The reconstruction of the NDF using quadrature-based moment methods (QBMM) is described in detail in Chapter 3. In comparison with the moment closures introduced above, QBMM have the following similarities and advantages. 

Quadrature-based moment methods (QBMM) constitute a particular class of very successful moment methods that overcome the closure problem by using quadrature approximations. A general (multivariate) quadrature of N nodes for M internal coordinates requires knowledge of N weights, w , and N nodes (or abscissas), y M,a),... 

Chapter 3 provides an introduction to Gaussian quadrature and the moment-inversion algorithms used in quadrature-based moment methods (QBMM). In this chapter, the product-difference (PD) and Wheeler algorithms employed for the classical univariate quadrature method of moments (QMOM) are discussed, together with the brute-force, tensor-product, and conditional QMOM developed for multivariate problems. The chapter concludes with a discussion of the extended quadrature method of moments (EQMOM) and the direct quadrature method of moments (DQMOM). 

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