Boundary integral numerical methods are among the most accurate methods for interfacial Stokes flow, and are widely applied. They have the advantage that only the boundary of the domain must be discretized, which reduces the number of discretization points and allows the treatment of complicated interfaces. Despite their popularity, there is no analysis of the convergence of these methods for interfacial Stokes flow. In practice, the stability of discretizations of the boundary integral formulation can depend sensitively on details of the discretization and on the application of numerical filters. We present a convergence analysis of the boundary integral method for Stokes flow, focusing on a rather general method for computing the evolution of an elastic capsule, viscous drop, or inviscid bubble in 2D strain and shear flows. The analysis clarifies the role of numerical filters in practical computations.
翻译:边界整体数字方法是最精确的干涉斯托克斯流的方法,而且广泛应用,其优点是,只有域的边界必须分离,这样可以减少离散点的数量,并能够处理复杂的界面。尽管这些方法很受欢迎,但没有分析这些方法的汇合作用。实际上,边界整体配方的离散稳定性可以敏感地取决于离散的细节和数字过滤器的应用。我们对斯托克斯流的边界整体方法进行了趋同分析,重点是一种比较一般的方法,用以计算弹性胶囊的演变、粘度下降或2D菌株和剪切流的隐形泡。分析澄清了数字过滤器在实际计算中的作用。