Campus Units

Chemical and Biological Engineering, Ames Laboratory

Document Type


Research Focus Area

Computational Fluid Dynamics

Publication Version

Submitted Manuscript

Publication Date


Journal or Book Title



QBMMlib is an open source Mathematica package of quadrature-based moment methods and their algorithms. Such methods are commonly used to solve fully-coupled disperse flow and combustion problems, though formulating and closing the corresponding governing equations can be complex. QBMMlib aims to make analyzing these techniques simple and more accessible. Its routines use symbolic manipulation to formulate the moment transport equations for a population balance equation and a prescribed dynamical system. However, the resulting moment transport equations are unclosed. QBMMlib trades the moments for a set of quadrature points and weights via an inversion algorithm, of which several are available. Quadratures then closes the moment transport equations. Embedded code snippets show how to use QBMMlib, with the algorithm initialization and solution spanning just 13 total lines of code. Examples are shown and analyzed for linear harmonic oscillator and bubble dynamics problems.


This is a pre-print of the article Bryngelson, Spencer H., Tim Colonius, and Rodney O. Fox. "QBMMlib: A library of quadrature-based moment methods." arXiv preprint arXiv:2008.05063 (2020). Posted with permission.

Copyright Owner

The Author(s)



File Format


Published Version