We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called Phi-FEM, that uses the description of the solid with a level-set function. One of the advantages of our method is the use of standard finite element spaces and classical integration tools, while maintaining the optimal convergence (theoretically in the H1 norm for the velocity and L2 for pressure; numerically also in the L2 norm for the velocity).

翻译：摘要：我们提出了一种浸入边界法，用于模拟由斯托克斯方程描述的流体中刚性颗粒的蠕动运动。该方法采用基于非拟合网格的有限元策略进行离散化，称为Phi-FEM，通过水平集函数描述固体。本方法的优势之一在于能够使用标准有限元空间和经典积分工具，同时保持最优收敛性（理论上速度场在H1范数、压力场在L2范数下收敛；数值实验中速度场在L2范数下同样收敛）。