A fast numerical method for ideal fluid flow in domains with multiple stirrers

TL;DR

This paper introduces a fast, accurate numerical method for computing ideal fluid flow around multiple arbitrarily-shaped stirrers in two dimensions, using boundary integral equations and efficiently handling complex multiply connected domains.

Contribution

The paper presents a novel boundary integral equation approach with a generalized Neumann kernel for rapid simulation of fluid flow in systems with many stirrers, improving computational efficiency.

Findings

Method effectively handles many stirrers with minimal computational cost

Numerical scheme achieves high accuracy in complex multiply connected domains

Applicable to various shapes and configurations of fluid stirrers

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 problem. We show that this Riemann-Hilbert 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.