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A smoothed particle element method (SPEM) for modeling fluid-structure interaction problems with large fluid deformations. (English) Zbl 1441.76097
Summary: Fluid-structure interaction (FSI) problems with large fluid deformations can be a great challenge for numerical simulations using conventional methods. In this paper, we propose a novel hybrid approach of an improved Smoothed Particle hydrodynamics and smoothed finite Element Method (SPEM) for modeling FSI problems. In SPEM, the edge-based smoothed finite element method (S-FEM) is developed in Lagrangian frame and is used for the first time to model both elastic structures and incompressible flows. For fluid regions with large deformations, the associated finite elements are adaptively converted into particles and the corresponding regions are subsequently modeled using the decoupled finite particle method (DFPM), which is an improved smoothed particle hydrodynamics (SPH) method suitable for modeling incompressible flows with free surfaces. A ghost particle-based interface algorithm to couple existing S-FEM elements and DFPM particles is developed in SPEM to implement the modeling of FSI problems. As the smoothed FEM and decoupled FPM are enhanced FEM and SPH respectively and DFPM is only used for local fluid regions with large deformations, it is expected that SPEM is more accurate and more efficient than the existing coupling approaches of conventional FEM and SPH. Five numerical examples are tested using the proposed SPEM and the comparative studies with results from other sources reveal that SPEM is an effective approach for modeling FSI problems with large fluid deformations.

##### MSC:
 76M28 Particle methods and lattice-gas methods 65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 76Bxx Incompressible inviscid fluids 76Dxx Incompressible viscous fluids
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