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 -