LEoPart: a particle library for FEniCS

TL;DR

LEoPart is a new add-on for FEniCS that enables efficient, accurate, and scalable Lagrangian particle advection and projection within finite element methods, supporting high-order accuracy and conservation.

Contribution

It introduces a variational framework-based particle-mesh projection operator for diffusion-free advection with optimal convergence in FEniCS.

Findings

Demonstrates high-order accurate particle advection

Achieves conservation of particle quantities

Shows scalable parallel performance

Abstract

This paper introduces LEoPart, an add-on for the open source finite element software library FEniCS to seamlessly integrate Lagrangian particle functionality with (Eulerian) mesh-based finite element (FE) approaches. LEoPart - which is so much as to say: `Lagrangian-Eulerian on Particles' - contains tools for efficient, accurate and scalable advection of Lagrangian particles on arbitrary polyhedral meshes. In addition, LEoPart comes with several projection operators for exchanging information between the scattered particles and the mesh and \textit{vice versa}. These projection operators are based on a variational framework, which allows extension to high-order accuracy. In particular, by implementing a dedicated PDE-constrained particle-mesh projection operator, LEoPart provides all the tools for diffusion-free advection, while simultaneously achieving optimal convergence and ensuring conservation of the projected particle quantities on the underlying mesh. A range of numerical examples that are prototypical to passive and active tracer methods highlight the properties and the parallel performance of the different tools in LEoPart. Finally, future developments are identified. The source code for LEoPart is actively maintained and available under an open source license at https://bitbucket.org/jakob_maljaars/leopart.