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  4. 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

Citation Link: https://doi.org/10.15480/882.5043
Publikationstyp
Conference Paper
Date Issued
2023-03-24
Sprache
English
Author(s)
Urizarna Carasa, Julio  
Ruprecht, Daniel  orcid-logo
Kameke, Alexandra von  
Padberg-Gehle, Kathrin  
Institut
Mathematik E-10  
TORE-DOI
10.15480/882.5043
TORE-URI
http://hdl.handle.net/11420/15119
Journal
Proceedings in applied mathematics and mechanics  
Volume
22
Issue
1
Article Number
e202200242
Citation
Proceedings in applied mathematics and mechanics 22 (1): e202200242 (2023-03-24)
Contribution to Conference
92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics, GAMM 2022  
Publisher DOI
10.1002/pamm.202200242
Publisher
Wiley-VCH
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.
DDC Class
600: Technik
620: Ingenieurwissenschaften
Funding(s)
Projekt DEAL  
Publication version
publishedVersion
Lizenz
https://creativecommons.org/licenses/by-nc/4.0/
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