Nearly Singular Integrals in 3D Stokes Flow
Nearly Singular Integrals in 3D Stokes Flow
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3D 斯托克斯流中的近奇异积分
DOI：
10.4208/cicp.020812.080213a
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发表时间：
2013
影响因子：
3.7
通讯作者：
J. Beale
中科院分区：
文献类型：
--
作者：
Svetlana Tlupova;J. Beale
本文给出了一种计算三维Stokes流的直接方法，这种方法在靠近表面的点上有很高的精度。使用自由空间格林函数将流量写成边界积分。为了计算边界附近的积分，对奇异核进行了正则化，并在坐标图中应用了一个简单的求积。通过增加对正则化和离散化误差的特殊修正，获得了高阶精度，该修正是利用局部渐近分析得出的。数值试验证明了该方法的一致收敛速度。
A straightforward method is presented for computing three-dimensional Stokes flow, due to forces on a surface, with high accuracy at points near the surface. The flow quantities are written as boundary integrals using the free-space Green’s function. To evaluate the integrals near the boundary, the singular kernels are regularized and a simple quadrature is applied in coordinate charts. High order accuracy is obtained by adding special corrections for the regularization and discretization errors, derived here using local asymptotic analysis. Numerical tests demonstrate the uniform convergence rates of the method.