Modeling of coupled dynamics for fluid-structure interactions

In this paper, we introduce a numerical technique that fully couples the dynamics between a fluid and its immersed structure in a fluid-structure interaction system. This technique is developed based on the original mathematical formulation of the immersed finite element method (IFEM). These IFEM methods are considered as non-boundary-fitted numerical scheme that meshes fluid and its embedded structures independently. This paper details the concepts and assumptions made in the original formulation and its improvement made through a semi-implicit algorithm to allow solving a wider range of fluid-structure interaction problems with large property disparities, and finally to the modified immersed finite element method (mIFEM) that entirely reverses the logic of the original formulation and re-formulates the interaction process between the solid and the fluid so that the dynamics solutions are more accurately captured without unrealistic solid element distortion.