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

Research output: Journal contributionsConference article in journalResearchpeer-review

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 languageEnglish
Article numbere202200242
JournalProceedings in applied mathematics and mechanics
Volume22
Issue number1
Number of pages6
ISSN1617-7061
DOIs
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
https://jahrestagung.gamm-ev.de/annual-meeting-2022/annual-meeting/

Bibliographical note

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

DOI

Recently viewed

Publications

  1. A Wavelet Packet Tree Denoising Algorithm for Images of Atomic-Force Microscopy
  2. Automatic enumeration of all connected subgraphs.
  3. Methodologies for Noise and Gross Error Detection using Univariate Signal-Based Approaches in Industrial Application
  4. Binary Random Nets I
  5. Using Natural Language Processing Techniques to Tackle the Construct Identity Problem in Information Systems Research
  6. Modeling Effective and Ineffective Knowledge Communication and Learning Discourses in CSCL with Hidden Markov Models
  7. Methodologies for noise and gross error detection using univariate signal-based approaches in industrial applications
  8. Modelling tasks—The relation between linguistic skills, intra-mathematical skills, and context-related prior knowledge
  9. Authenticity and authentication in language learning
  10. Development of a Didactic Graphical Simulation Interface on MATLAB for Systems Control
  11. Knowledge Graph Question Answering Using Graph-Pattern Isomorphism
  12. Graph Conditional Variational Models: Too Complex for Multiagent Trajectories?
  13. Using learning protocols for knowledge acquisition and problem solving with individual and group incentives
  14. Analysis of Complexity Reduction in Kalman Filters Through Decoupling Control With Chattered Inputs in PMSM
  15. Towards a Dynamic Interpretation of Subjective and Objective Values
  16. Analysis of priority rule-based scheduling in dual-resource-constrained shop-floor scenarios
  17. Substructure, subgraph, and walk counts as measures of the complexity of graphs and molecules.
  18. Essentializing the binary self
  19. Using Decision Trees and Reinforcement Learning for the Dynamic Adjustment of Composite Sequencing Rules in a Flexible Manufacturing System
  20. Using mixture distribution models to test the construct validity of the Physical Self-Description Questionnaire
  21. Adaptive and Dynamic Feedback Loops between Production System and Production Network based on the Asset Administration Shell
  22. A sufficient asymptotic stability condition in generalised model predictive control to avoid input saturation
  23. Predicting the Difficulty of Exercise Items for Dynamic Difficulty Adaptation in Adaptive Language Tutoring
  24. Evaluation of Time/Phase Parameters in Frequency Measurements for Inertial Navigation Systems
  25. The Scalable Question Answering Over Linked Data (SQA) Challenge 2018
  26. A Lightweight Simulation Model for Soft Robot's Locomotion and its Application to Trajectory Optimization
  27. Optimal regulation for dynamic hybrid systems based on dynamic programming in the case of an intelligent vehicle drive assistant
  28. Expertise in research integration and implementation for tackling complex problems
  29. Application of non-convex rate dependent gradient plasticity to the modeling and simulation of inelastic microstructure development and inhomogeneous material behavior
  30. Isocodal and isospectral points, edges, and pairs in graphs and how to cope with them in computerized symmetry recognition
  31. Set-oriented numerical computation of rotation sets
  32. On the Power and Performance of a Doubly Latent Residual Approach to Explain Latent Specific Factors in Multilevel-Bifactor-(S-1) Models
  33. Machine Learning and Knowledge Discovery in Databases
  34. Building a process layer for business applications using the blackboard pattern
  35. A discrete approximate solution for the asymptotic tracking problem in affine nonlinear systems
  36. Closed-loop control of product geometry by using an artificial neural network in incremental sheet forming with active medium
  37. Global text processing in CSCL with learning protocols
  38. Neural network-based adaptive fault-tolerant control for strict-feedback nonlinear systems with input dead zone and saturation
  39. Unity and diversity in the law of state responsibility