一种用于粘性流中固态颗粒的快速积分方程方法：利用扩展求积法
A fast integral equation method for solid particles in viscous flow using quadrature by expansion
AI总结：
本文提出了一种快速准确的框架，用于模拟周期性斯托克斯流中的椭球体，采用完成的双层边界积分公式，并结合扩展求积法和谱埃瓦尔德方法，实现高精度计算。
摘要：
边界积分方法在模拟刚性颗粒周围的粘性流时具有优势，因为其减少了未知数的数量并简化了几何处理。本文提出了一种快速准确的框架，用于模拟周期性斯托克斯流中的椭球体，该框架基于完成的双层边界积分公式。该框架实现了一种称为扩展求积法（QBX）的新方法，利用层势的代理局部展开来在颗粒表面内外实现极高的精度。该求积方法通过新开发的预计算方案加速。远距离相互作用通过谱埃瓦尔德（SE）快速求和方法计算，整合QBX后，所得到的系统可以在M log M时间内求解，其中M是颗粒的数量。该框架适用于大规模颗粒系统的模拟，可用于研究如多孔介质模型等。
英文摘要：
Boundary integral methods are advantageous when simulating viscous flow around rigid particles, due to the reduction in number of unknowns and straightforward handling of the geometry. In this work we present a fast and accurate framework for simulating spheroids in periodic Stokes flow, which is based on the completed double layer boundary integral formulation. The framework implements a new method known as quadrature by expansion (QBX), which uses surrogate local expansions of the layer potential to evaluate it to very high accuracy both on and off the particle surfaces. This quadrature method is accelerated through a newly developed precomputation scheme. The long range interactions are computed using the spectral Ewald (SE) fast summation method, which after integration with QBX allows the resulting system to be solved in M log M time, where M is the number of particles. This framework is suitable for simulations of large particle systems, and can be used for studying e.g. porous media models.
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