A fast numerical method for ideal fluid flow in domains with multiple stirrers
Abstract
A collection of arbitrarilyshaped 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 twodimensional, 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 RiemannHilbert problem. We show that this RiemannHilbert 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2016
 DOI:
 10.48550/arXiv.1701.00115
 arXiv:
 arXiv:1701.00115
 Bibcode:
 2017arXiv170100115N
 Keywords:

 Mathematics  Complex Variables