Multi-resolution technique integrated with smoothed particle element method (SPEM) for modeling fluid-structure interaction problems with free surfaces

Free-surface flows, especially those associated with fluid-structure interactions (FSIs), pose challenging problems in numerical simulations. The authors of this work recently developed a smoothed particle element method (SPEM) to simulate FSIs. In this method, both the fluid and solid regions are initially modeled using a smoothed finite element method (S-FEM) in a Lagrangian frame, whereas the fluid regions undergoing large deformations are adaptively converted into particles and modeled with an improved smoothed particle hydrodynamics (SPH) method. This approach greatly improves computational accuracy and efficiency because of the advantages of the S-FEM in efficiently treating solid/fluid regions showing small deformations and the SPH method in effectively modeling moving interfaces. In this work, we further enhance the efficiency of the SPEM while effectively capturing local fluid information by introducing a multi-resolution technique to the SPEM and developing an effective approach to treat multi-resolution element-particle interfaces. Various numerical examples demonstrate that the multiresolution SPEM can significantly reduce the computational cost relative to the original version with a constant resolution. Moreover, the novel approach is effective in modeling various incompressible flow problems involving FSIs.