Remarks on Regularized Stokeslets in Slender Body Theory
Remarks on Regularized Stokeslets in Slender Body Theory
复制标题
细长体理论中正则化斯托克斯列的评述
作者：
Laurel Ohm
我们评论了正则化stokeslet在关于半径为λ >的细纤维的Stokes流的细长体理论（SBT）近似中的使用。用δ表示正则化参数，我们考虑基于最常见的正则化Stokeslet加上正则化双元校正的正则化SBT。给定沿细丝的足够光滑的力数据，我们推导出正则化SBT与经典对应的δ、λ和力数据之间差异的L∞界。我们表明，灯丝本身速度的正则化表达式和经典表达式的差异与log（δ/ λ）成正比；特别地，δ= λ是必要的，以避免理论之间的O(1)差异。然而，纤维表面的流动与log（1+δ2/ϵ2）成正比，任何δ∝λ的选择都会导致O(1)的差异，因为λ→0。因此，由于正则SBT的作用，细长光纤周围的流动并不收敛于经典SBT近似的定常细长体偏微分方程的解。数值验证了这种0(1)差异，但也表明这种差异在实践中可能影响不大。
We remark on the use of regularized Stokeslets in the slender body theory (SBT) approximation of Stokes flow about a thin fiber of radius ϵ>0. Denoting the regularization parameter by δ, we consider regularized SBT based on the most common regularized Stokeslet plus a regularized doublet correction. Given sufficiently smooth force data along the filament, we derive L∞ bounds for the difference between regularized SBT and its classical counterpart in terms of δ, ϵ, and the force data. We show that the regularized and classical expressions for the velocity of the filament itself differ by a term proportional to log(δ/ϵ); in particular, δ=ϵ is necessary to avoid an O(1) discrepancy between the theories. However, the flow at the surface of the fiber differs by an expression proportional to log(1+δ2/ϵ2), and any choice of δ∝ϵ will result in an O(1) discrepancy as ϵ→0. Consequently, the flow around a slender fiber due to regularized SBT does not converge to the solution of the well-posed slender body PDE which classical SBT is known to approximate. Numerics verify this O(1) discrepancy but also indicate that the difference may have little impact in practice.
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DOI：
10.48550/arxiv.2001.06468
发表时间：
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