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arXiv · 2610.36189

QMOMKit: A C++ library for quadrature-based moment methods

Fabian Denner·Bruna Campos·Bruno Blais
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Abstract

QMOMKit is an open-source C++ library for the phase-space evolution of population balance equations with quadrature-based moment methods. The present version implements the quadrature method of moments (QMOM) and the conditional quadrature method of moments (CQMOM). QMOMKit is designed to be independent of any particular application and can be used either as a standalone solver for spatially homogeneous population models or as a local phase-space solver coupled to a host application. It handles the numerical aspects of the evolution of a population in phase space, including quadrature reconstruction, advection of the quadrature abscissas, and changes to the population through moment sources and phase-space boundary contributions. The number of quadrature nodes is adapted to what the supplied moments support, subject to prescribed bounds of the phase-space coordinates, and the CQMOM implementation supports an arbitrary number of phase-space dimensions as well as any conditioning order. The principal numerical algorithms of QMOMKit are verified against analytical and manufactured solutions. Standalone spatially homogeneous applications, ranging from aerosol evaporation to particle dynamics and fragmentation, are compared with Monte Carlo solutions of the same population models, while coupling examples with OpenFOAM and deal.II demonstrate how QMOMKit can be embedded in finite-volume and discontinuous-Galerkin simulation frameworks. Together, these capabilities provide a tested and reusable foundation for a wide range of population-balance problems, and a basis for extending QMOMKit to other quadrature-based moment methods.

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Fabian Denner, Bruna Campos, Bruno Blais. 2026-10-26. QMOMKit: A C++ library for quadrature-based moment methods. https://arxiv.org/abs/2610.36189

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