Low Reynolds number fluid flows are governed by the Stokes equations. In two dimensions, Stokes flows can be described by two analytic functions, known as Goursat functions. Brubeck and Trefethen (2022) recently introduced a lightning Stokes solver that uses rational functions to approximate the Goursat functions in polygonal domains. In this paper, we present a solver for computing 2D Stokes flows in domains with smooth boundaries and multiply-connected domains using lightning and AAA rational approximation (Nakatsukasa et al., 2018). This leads to a new rational approximation algorithm "LARS" that is suitable for computing many bounded 2D Stokes flow problems. After validating our solver against known analytical solutions, we solve a variety of 2D Stokes flow problems with physical and engineering applications. The computations take less than a second and give solutions with at least 6-digit accuracy.

翻译：低雷诺数流体流动由Stokes方程控制。在二维情况下，Stokes流可由两个解析函数描述，称为Goursat函数。Brubeck和Trefethen（2022）近期引入了一种Lightning Stokes求解器，该求解器在多边形区域内使用有理函数逼近Goursat函数。本文提出一种求解器，通过Lightning和AAA有理逼近（Nakatsukasa等，2018）计算光滑边界区域及多连通区域中的二维Stokes流。由此衍生出一种适用于计算众多有界二维Stokes流问题的新型有理逼近算法"LARS"。在利用已知解析解验证求解器性能后，本文求解了一系列具有物理与工程应用背景的二维Stokes流问题。计算耗时不足一秒，且解精度至少达到6位有效数字。