论文标题
对粘性流中纤维的细长配方中积分的准确评估
Accurate evaluation of integrals in slender-body formulations for fibers in viscous flow
论文作者
论文摘要
可以得出一个细长的柔性纤维流动中的非本地细长体近似，可以得出沿纤维的中心线的积分方程，涉及细长的参数。该公式包含所谓的有限部分单数积分，在几种纤维或流场评估的情况下，需要评估几乎奇异的积分。 我们引入了一种数值技术，以准确有效地评估有限部分的积分。该技术可以与任何基于面板的正交规则相结合，除了修改正交重量的小预约外，不会增加额外的成本。我们还展示了如何将最近引入的相关技术应用于近乎奇异积分的评估。
A non-local slender body approximation for slender flexible fibers in Stokes flow can be derived, yielding an integral equation along the center lines of the fibers that involves a slenderness parameter. The formulation contains a so-called finite part singular integral, and can in the case of several fibers or evaluation of the flow field require the evaluation of nearly singular integrals. We introduce a numerical technique to accurately and efficiently evaluate the finite part integral. This technique can be applied combined with any panel based quadrature rule and will add no additional cost except for a small precomputation of modified quadrature weights. We also show how a related technique that was recently introduced can be applied for the evaluation of the nearly singular integrals.
