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 the "LARS" algorithm (Lightning-AAA Rational Stokes) for computing 2D Stokes flows in domains with smooth boundaries and multiply-connected domains using lightning and AAA rational approximation (Nakatsukasa et al., 2018). After validating our solver against known analytical solutions, we solve a variety of 2D Stokes flow problems with physical and engineering applications. Using these examples, we show rational approximation can now be used to compute 2D Stokes flows in general domains. 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斯托克斯方程控制。在二维条件下，斯托克斯流可用两个解析函数（即古尔萨函数）描述。Brubeck与Trefethen（2022）近期提出一种闪电斯托克斯求解器，通过有理函数逼近多边形域中的古尔萨函数。本文提出"LARS"算法（Lightning-AAA Rational Stokes），采用闪电和AAA有理逼近（Nakatsukasa等，2018）计算光滑边界域及多连通域中的二维斯托克斯流。在验证求解器与已知解析解的一致性后，我们求解了多个具有物理与工程应用的二维斯托克斯流问题。通过这些实例，我们证明有理逼近方法现可用于计算一般域中的二维斯托克斯流。计算耗时不足一秒，且解的精度至少达到六位有效数字。