### Abstract

A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix or stir ideal fluid, and can give rise to interesting flow patterns. Assuming these systems of fluid stirrers are two-dimensional, the mathematical problem of resolving the flow field - given a particular distribution of any finite number of stirrers of specified shape and speed - can be formulated as a Riemann-Hilbert (R-H) problem. We show that this R-H problem can be solved numerically using a fast and accurate algorithm for any finite number of stirrers based around a boundary integral equation with the generalized Neumann kernel. Various systems of fluid stirrers are considered, and our numerical scheme is shown to handle highly multiply connected domains (i.e. systems of many fluid stirrers) with minimal computational expense.

Original language | English |
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Pages (from-to) | 815-837 |

Number of pages | 23 |

Journal | Nonlinearity |

Volume | 31 |

Issue number | 3 |

DOIs | |

Publication status | Published - 7 Feb 2018 |

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### Keywords

- fluid stirrers
- generalized Neumann kernel
- ideal fluid
- multiply connected domains
- Riemann-Hilbert problem

### Cite this

*Nonlinearity*,

*31*(3), 815-837. https://doi.org/10.1088/1361-6544/aa99a5