A fast numerical method for computing doubly-periodic regularized Stokes flow in 3D

Ricardo Cortez; Franz Hoffmann

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A fast numerical method for computing doubly-periodic regularized Stokes flow in 3D

机译：计算3D双周期正则Stokes流的快速数值方法

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A new numerical method for computing three-dimensional Stokes flow driven by a doubly-periodic array of regularized forces is presented. The method is based on deriving an analytical representation of a regularized Green's function in Fourier space. Then only an inverse fast Fourier transform (inverse FFT) has to be computed to determine the fluid velocity on a grid in the physical domain. The velocity at other points can be interpolated from this grid. Accuracy is verified by comparing numerical results to a solution that is independent of the method. Although the regularized forces lead to a smooth velocity field, the Green's function may contain rapid transitions that are not captured properly on a coarse grid. In that case, an Ewald splitting technique is used to compute the grid-resolved part of the flow using an inverse FFT and a sum in physical space for the localized part of the velocity. The splitting parameter can be chosen as small as a few grid cells, which makes the sum in physical space converge extremely fast. We present numerical examples that demonstrate that fact. In some cases, when the grid size is sufficiently small compared to the regularization parameter, the Ewald splitting is not needed.

机译：提出了一种新的数值方法，用于计算由正周期力的双周期阵列驱动的三维斯托克斯流。该方法基于推导傅立叶空间中正则化格林函数的解析表示。然后，仅需计算快速傅立叶逆变换（FFT）即可确定物理域中网格上的流体速度。可以从该网格内插其他点的速度。通过将数值结果与独立于该方法的解决方案进行比较，可以验证准确性。尽管规则力导致平滑的速度场，但格林函数可能包含快速跳变，而在粗糙的网格上无法正确捕获。在那种情况下，使用Ewald分裂技术使用逆FFT和速度局部化的物理空间总和来计算流的网格解析部分。分裂参数可以选择为只有几个网格单元，从而使物理空间中的总和收敛极快。我们提供了数值示例来证明这一事实。在某些情况下，当栅格大小与正则化参数相比足够小时，不需要进行Ewald分裂。

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来源
《Journal of Computational Physics》 |2014年第null期|共14页
作者
Ricardo Cortez; Franz Hoffmann;
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正文语种 eng
中图分类数学物理方法;
关键词
Stokes flow; Ewald summation; FFT;

机译：斯托克斯流量;埃瓦尔德求和;FFT;

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1. A fast numerical method for computing doubly-periodic regularized Stokes flow in 3D [J] . Ricardo Cortez, Franz Hoffmann Journal of Computational Physics . 2014,第Null期

机译：计算3D双周期正则Stokes流的快速数值方法
2. Computation of the singular and regularized image systems for doubly-periodic Stokes flow in the presence of a wall [J] . Hoang-Ngan Nguyen, Leiderman Karin Journal of Computational Physics . 2015,第Null期

机译：存在壁时双周期斯托克斯流的奇异和正则化图像系统的计算
3. Integral equation methods for Stokes flow in doubly-periodic domains [J] . LESLIE GREENGARD, MARY CATHERINE KROPINSKI Journal of engineering mathematics . 2004,第2期

机译：双周期域中Stokes流的积分方程方法
4. Regularization fast multipole boundary element method for potential flow problems in 3D vortex method [C] . Jie Zhai, Baoshan Zhu, Shuliang Cao International Conference on Boundary Elements and Other Mesh Reduction Methods . 2014

机译：3D Vortex方法中潜在流动问题的正则化快速多极边界元方法
5. A numerical method for doubly-periodic stokes flow in 3D with and without a bounding plane. [D] . Hoffmann, Franz. 2015

机译：具有和不具有边界平面的3D双周期斯托克斯流的数值方法。
6. A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries [O] . Liang Ge, Fotis Sotiropoulos -1

机译：具有复杂浸入边界的曲线域中求解3D非稳态不可压缩Navier-Stokes方程的数值方法
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A fast numerical method for computing doubly-periodic regularized Stokes flow in 3D

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