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

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A Python toolbox for the numerical solution of the Maxey-Riley equation. / Urizarna-Carasa, Julio; Ruprecht, Daniel; von Kameke, Alexandra et al.
In: Proceedings in applied mathematics and mechanics, Vol. 22, No. 1, e202200242, 01.03.2023.

Research output: Journal contributionsConference article in journalResearchpeer-review

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Urizarna-Carasa J, Ruprecht D, von Kameke A, Padberg-Gehle K. A Python toolbox for the numerical solution of the Maxey-Riley equation. Proceedings in applied mathematics and mechanics. 2023 Mar 1;22(1):e202200242. doi: 10.1002/pamm.202200242

Bibtex

@article{b51aa27e24874ad4bee00dae34bb15d2,
title = "A Python toolbox for the numerical solution of the Maxey-Riley equation",
abstract = "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.",
keywords = "Mathematics",
author = "Julio Urizarna-Carasa and Daniel Ruprecht and {von Kameke}, Alexandra and Kathrin Padberg-Gehle",
note = "{\textcopyright} 2023 The Authors. Proceedings in Applied Mathematics & Mechanicspublished by Wiley-VCH GmbH; 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics - GAMM 2022, GAMM 2022 ; Conference date: 15-08-2022 Through 19-08-2022",
year = "2023",
month = mar,
day = "1",
doi = "10.1002/pamm.202200242",
language = "English",
volume = "22",
journal = "Proceedings in applied mathematics and mechanics",
issn = "1617-7061",
publisher = "Wiley-VCH Verlag",
number = "1",
url = "https://jahrestagung.gamm-ev.de/annual-meeting-2022/annual-meeting/",

}

RIS

TY - JOUR

T1 - A Python toolbox for the numerical solution of the Maxey-Riley equation

AU - Urizarna-Carasa, Julio

AU - Ruprecht, Daniel

AU - von Kameke, Alexandra

AU - Padberg-Gehle, Kathrin

N1 - Conference code: 92

PY - 2023/3/1

Y1 - 2023/3/1

N2 - 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.

AB - 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.

KW - Mathematics

UR - https://onlinelibrary.wiley.com/doi/10.1002/pamm.202200242

UR - https://www.mendeley.com/catalogue/3e170a4b-e6b2-38c5-8edf-c2faeb4cfe79/

U2 - 10.1002/pamm.202200242

DO - 10.1002/pamm.202200242

M3 - Conference article in journal

VL - 22

JO - Proceedings in applied mathematics and mechanics

JF - Proceedings in applied mathematics and mechanics

SN - 1617-7061

IS - 1

M1 - e202200242

T2 - 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics - GAMM 2022

Y2 - 15 August 2022 through 19 August 2022

ER -

DOI