Numerical aspects of direct quadrature-based moment methods for solving the population balance equation

Abstract

-Direct-quadrature generalized moment based methods were analysed in terms of accuracy, computational cost and robustness for the solution of the population balance problems in the [0, ) ∞ and [0,1] domains. The minimum condition number of the coefficient matrix of their linear system of equations was obtained by global optimization. An heuristic scaling rule from the literature was also evaluated. The results indicate that the methods based on Legendre generalized moments are the most robust for the finite domain problems, while the DQMoM formulation that solves for the abscissas and weights using the heuristic scaling rule is the best for the infinite domain problems.

The solution of continuous kinetic lumping models using the adaptive characterization method

“…They used only Laguerre polynomials in semi‐infinite domain problems, concluding that the methods were only marginally more robust than the corresponding methods using regular moments. On the other hand, Santos et al analyzed problems in semi‐infinite and finite domains, using Laguerre and Legendre polynomials, respectively. They concluding that, for finite domain problems, the usage of Legendre polynomial moments improves the method robustness.…”

“…They concluding that, for finite domain problems, the usage of Legendre polynomial moments improves the method robustness. The reformulated DQMoM was named as DQMoGeM by Santos et al…”

“…Therefore, this work developed an alternate methodology to solve kinetic models of continuous mixtures by using the adaptive QBMM method called DQMoGeM . Three test cases were solved to verify its accuracy.…”