Solution of the population balance equation by the direct dual quadrature method of generalized moments

The Direct Dual Quadrature Method of Generalized Moments (D2uQMoGeM) was formulated for the solution of the population balance equation. It mixes the properties of the Direct Quadrature Method of Moments (DQMoM) and the Dual Quadrature Method of Generalized Moments (DuQMoGeM). The weights and weighted abscissas are tracking directly as in DQMoM and the quadrature errors are controlled by an adaptive quadrature as in DuQMoGeM. The D2uQMoGeM was implemented and tested for several different problems with analytical solutions. It was shown to be more accurate than DQMoM with a reasonable increase in computational time.