On collocation schemes for integral equations arising in slender-body approximations of flow past particles with circular cross-section
On collocation schemes for integral equations arising in slender-body approximations of flow past particles with circular cross-section
复制标题
圆形截面流过粒子细长体近似中积分方程的配置方案
DOI：
10.1023/a:1015200931176
复制
发表时间：
2002
影响因子：
1.3
通讯作者：
T. Götz
中科院分区：
文献类型：
--
作者：
T. Götz
提出了求解细长体粘性流细长体近似中第二类奇异积分方程的配置方法。当积分算子的谱表示明确已知时，可以使用配置方法来恢复连续算子的谱。估计了积分算子的两个离散化的近似误差，并证明了收敛性。该搭配方案针对多个测试用例进行了验证，并扩展到频谱未知的情况。
A collocation method is presented for solving a singular integral equation of the second kind arsing in the slender-body approximation of viscous flow past slender bodies. When the spectral representation of the integral operator is explicitly known, the collocation method is shown to recover the spectrum of the continuous operator. The approximation error is estimated for two discretizations of the integral operator, and convergence is proved. The collocation scheme is validated for several test cases and extended to situations where the spectrum is not explicitly known.