Solution of Stokes flow in complex nonsmooth 2D geometries via a linear-scaling high-order adaptive integral equation scheme
Solution of Stokes flow in complex nonsmooth 2D geometries via a linear-scaling high-order adaptive integral equation scheme
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DOI：
10.1016/j.jcp.2020.109361
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发表时间：
2019-08
期刊：
影响因子：
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通讯作者：
Bowei Wu;Hai-Ping Zhu;A. Barnett;S. Veerapaneni
中科院分区：
文献类型：
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作者：
Bowei Wu;Hai-Ping Zhu;A. Barnett;S. Veerapaneni
提出了一种快速、高阶、精确、自适应的边界积分格式，用于求解二维复杂非光滑几何中的Stokes方程。我们应用Helsing和同事基于面板的正交来高精度地评估Nyström离散化中产生的弱奇异、超奇异和超奇异积分，以及边界附近流动和牵引力评估所需的近奇异积分。通过调用Stokes快速多极方法迭代求解得到的线性系统。我们包含了一个自动算法来“面板化”给定的几何形状，并选择面板顺序，这将有效地将密度（因此解决方案）近似于用户规定的公差。我们表明，即使在具有大量角的复杂几何形状或接近接触的光滑曲线的情况下，这种自适应面板改进程序在实践中也能很好地工作。例如，在一个例子中，一个有378个角的2D血管网络模型需要不到200K的离散点来获得9位数的解精度。
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.