Solution of Stokes flow in complex nonsmooth 2D geometries via a linear-scaling high-order adaptive integral equation scheme

被引：9
作者：
Wu B. [1 ]
Zhu H. [1 ]
Barnett A. [2 ]
Veerapaneni S. [1 ]
机构：
[1] Department of Mathematics, University of Michigan, Ann Arbor, 48109, MI
[2] Flatiron Institute, Simons Foundation, New York, 10022, NY
来源：
Journal of Computational Physics | 2020年 / 410卷
基金：
美国国家科学基金会;
关键词：
Boundary integral methods; Corner singularities; Fast algorithms; Stokes flow;
D O I：
10.1016/j.jcp.2020.109361
中图分类号：
学科分类号：
摘要：
We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex—possibly nonsmooth—geometries in two dimensions. We apply the panel-based quadratures of Helsing and coworkers to evaluate to high accuracy the weakly-singular, hyper-singular, and super-singular integrals arising in the Nyström discretization, and also the near-singular integrals needed for flow and traction evaluation close to boundaries. The resulting linear system is solved iteratively via calls to a Stokes fast multipole method. We include an automatic algorithm to “panelize” a given geometry, and choose a panel order, which will efficiently approximate the density (and hence solution) to a user-prescribed tolerance. We show that this adaptive panel refinement procedure works well in practice even in the case of complex geometries with large number of corners, or close-to-touching smooth curves. In one example, for instance, a model 2D vascular network with 378 corners required less than 200K discretization points to obtain a 9-digit solution accuracy. © 2020 Elsevier Inc.
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