An Unfitted Finite Element Method for Two-Phase Stokes Problems with Slip Between Phases
An Unfitted Finite Element Method for Two-Phase Stokes Problems with Slip Between Phases
复制标题
DOI：
10.1007/s10915-021-01658-x
复制
发表时间：
2021-01
影响因子：
2.5
通讯作者：
M. Olshanskii;A. Quaini;Qi Sun
中科院分区：
文献类型：
--
作者：
M. Olshanskii;A. Quaini;Qi Sun
本文提出了一种等参数非拟合有限元方法，用于模拟两相间滑移的Stokes问题。对于未拟合的广义泰勒-胡德有限元对，我们展示了一种稳定特性，其稳定常数与粘度比、滑移系数、界面相对于背景网格的位置以及网格尺寸无关。此外，我们证明了稳定性和最优误差估计遵循这一特性。我们提供了二维和三维的数值结果来证实理论发现，并证明了我们的方法在粘度、滑移系数值和相对于固定计算网格的界面位置方面的鲁棒性。
We present an isoparametric unfitted finite element approach of the CutFEM or Nitsche-XFEM family for the simulation of two-phase Stokes problems with slip between phases. For the unfitted generalized Taylor–Hood finite element pair,, we show an inf-sup stability property with a stability constant that is independent of the viscosity ratio, slip coefficient, position of the interface with respect to the background mesh and, of course, mesh size. In addition, we prove stability and optimal error estimates that follow from this inf-sup property. We provide numerical results in two and three dimensions to corroborate the theoretical findings and demonstrate the robustness of our approach with respect to the contrast in viscosity, slip coefficient value, and position of the interface relative to the fixed computational mesh.