QBMMlib: A library of quadrature-based moment methods

TL;DR

QBMMlib is an open source Mathematica package that simplifies the formulation and solution of quadrature-based moment methods for disperse flow and combustion problems, making advanced techniques more accessible.

Contribution

It provides a user-friendly, symbolic manipulation toolkit with multiple inversion algorithms for closing moment transport equations in population balance models.

Findings

Successfully applied to linear harmonic oscillator problems

Effectively analyzed bubble dynamics scenarios

Demonstrated simplicity and efficiency of the package

Abstract

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.