A Python toolbox for the numerical solution of the Maxey-Riley equation

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The Maxey-Riley equation (MRE) models the motion of a finite-sized, spherical particle in a fluid. It is a second-order integro-differential equation with a kernel with a singularity at initial time. Because solving the integral term is numerically challenging, it is often neglected despite its often non-negligible impact. Recently, Prasath et al. showed that the MRE can be rewritten as a time-dependent heat equation on a semi-infinite domain with a nonlinear, Robin-type boundary condition. This approach avoids the need to deal with the integral term. They also describe a numerical approach for solving the transformed MRE based on Fokas method. We provide a Python toolbox implementing their approach, verify it against some of their numerical examples and demonstrate its flexibility by computing the trajectory of a particle in a velocity field given by experimental data.
Original languageEnglish
Article numbere202200242
JournalProceedings in applied mathematics and mechanics
Issue number1
Number of pages6
Publication statusPublished - 01.03.2023
Event92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics - GAMM 2022 - RWTH Aachen Universität, Aachen, Germany
Duration: 15.08.202219.08.2022
Conference number: 92

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© 2023 The Authors. Proceedings in Applied Mathematics & Mechanicspublished by Wiley-VCH GmbH