A Python toolbox for the numerical solution of the Maxey-Riley equation
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Authors
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 language | English |
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Article number | e202200242 |
Journal | Proceedings in applied mathematics and mechanics |
Volume | 22 |
Issue number | 1 |
Number of pages | 6 |
ISSN | 1617-7061 |
DOIs | |
Publication status | Published - 01.03.2023 |
Event | 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics - GAMM 2022 - RWTH Aachen Universität, Aachen, Germany Duration: 15.08.2022 → 19.08.2022 Conference number: 92 https://jahrestagung.gamm-ev.de/annual-meeting-2022/annual-meeting/ |
Bibliographical note
© 2023 The Authors. Proceedings in Applied Mathematics & Mechanicspublished by Wiley-VCH GmbH
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