# A numerical comparison of the method of moments for the population balance equation

## TL;DR

This paper compares various moment closure methods for solving the population balance equation, analyzing their accuracy, realizability, and computational efficiency through diverse numerical examples.

## Contribution

It provides a comprehensive numerical comparison of polynomial, maximum entropy, and quadrature moment methods for population balance equations, including implementation insights.

## Key findings

- Quadrature method of moments (QMOM) shows favorable accuracy and efficiency.
- Maximum entropy closures offer good realizability properties.
- Method of moments accuracy depends on the closure type and problem complexity.

## Abstract

We investigate the application of the method of moments approach for the one-dimensional population balance equation. We consider different types of moment closures, namely polynomial (P_N) closures, maximum entropy (M_N) closures and the quadrature method of moments QMOM_N. Realizability issues and implementation details are discussed. The numerical examples range from spatially homogeneous cases to a population balance equation coupled with fluid dynamic equations for a lid-driven cavity test case. A detailed numerical discussion of accuracy, order of the moment method and computational time is given.