标题： 一种用于多搅拌器区域中理想流体流动的快速数值方法 显示英文标题

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

摘要： 由任意形状的固体物体组成的一组物体，每个物体以恒定速度移动，可以用来混合或搅拌理想流体，并能产生有趣的流动模式。 假设这些流体搅拌系统是二维的，那么在给定任何有限数量的指定形状和速度的搅拌器的特定分布的情况下，解析流动场的数学问题可以被表述为黎曼-希尔伯特问题。 我们表明，这个黎曼-希尔伯特问题可以使用一种快速且精确的算法进行数值求解，该算法基于带有广义诺伊曼核的边界积分方程，适用于任何有限数量的搅拌器。 考虑了各种流体搅拌系统，我们的数值方案被证明能够以最小的计算成本处理高度多连通区域（即许多流体搅拌器的系统）。 显示英文摘要

摘要： 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.