A highly accurate method for simulating surfactant-covered droplets in two-dimensional Stokes flow with solid boundaries is presented. The method handles both periodic channel flows of arbitrary shape and stationary solid constrictions. A boundary integral method together with a special quadrature scheme is applied to solve the Stokes equations to high accuracy, also for closely interacting droplets. The problem is considered in a periodic setting and Ewald decompositions for the Stokeslet and stresslet are derived. Computations are accelerated using the spectral Ewald method. The time evolution is handled with a fourth order, adaptive, implicit-explicit time-stepping scheme. The numerical method is tested through several convergence studies and other challenging examples and is shown to handle drops in close proximity both to other drops and solid objects to high accuracy.

中文翻译：

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壁限斯托克斯流中紧密相互作用的表面活性剂覆盖液滴的积分方程方法

提出了一种在具有固体边界的二维斯托克斯流中模拟表面活性剂覆盖液滴的高精度方法。该方法处理任意形状的周期性通道流和固定固体收缩。应用边界积分方法和特殊的正交方案来高精度求解斯托克斯方程，也适用于密切相互作用的液滴。在周期性设置中考虑该问题，并推导出 Stokeslet 和应力波的 Ewald 分解。使用频谱 Ewald 方法可以加速计算。时间演化采用四阶、自适应、隐式-显式时间步进方案处理。