(165h) Be Careful How You Discretize: Convergence Issues with Quadrature Method of Moments (QMOM)

The Quadrature Method of Moments (QMOM) is a fast and efficient strategy for discretizing population balance equations (PBE), especially in applications involving coupled PBE and complex fluid dynamics (CFD) calculations. In this talk, we will highlight some of the lesser-known limitations of QMOM, including a “false convergence” issue that arises for log-normal particle size distributions. We provide benchmark calculations using a symmetric binary breakage kernel and discuss (1) scenarios where QMOM works well, (2) scenarios where it seems to work but actually fails, and (3) scenarios where it seems to fail but technically still works. We will also introduce an alternative low-mode discretization strategy based on solving for the “inverse cumulative distribution function” of a particle size distribution (miCDF). This method uses simple finite differences to solve for the median particle size in specified percentile ranges of the cumulative particle mass distribution function. Overall, we show that miCDF is a viable alternative to QMOM under scenarios (2) and (3), which potentially covers a broad range of applications.