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Solution of Stokes flow in complex nonsmooth 2D geometries via a linear-scaling high-order adaptive integral equation scheme
Journal of Computational Physics ( IF 4.1 ) Pub Date : 2020-03-09 , DOI: 10.1016/j.jcp.2020.109361
Bowei Wu , Hai Zhu , Alex Barnett , Shravan Veerapaneni

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.



中文翻译:

线性尺度高阶自适应积分方程方案求解复杂非光滑二维几何中的斯托克斯流

我们提出了一种快速,高阶的精确自适应边界积分方案,用于求解二维的复杂(可能是非光滑)几何中的Stokes方程。我们应用Helsing和同事的基于面板的正交函数,以高精度评估Nyström离散化中产生的弱奇异积分,超奇异积分和超奇异积分,以及流和牵引力评估所需的近奇异积分。到边界。通过调用Stokes快速多极点方法迭代地求解所得的线性系统。我们提供了一种自动算法,可以“面板化”给定的几何形状,并选择面板顺序,该顺序将有效地将密度(从而求解)近似为用户指定的公差。我们表明,即使在具有大量拐角或接近触摸的平滑曲线的复杂几何形状的情况下,这种自适应面板细化过程在实践中也能很好地工作。例如,在一个示例中,具有378个角的模型2D血管网络需要少于200K离散点才能获得9位数的求解精度。

更新日期:2020-03-09
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