Coupling of the meshless finite volume particle method and the finite element method for fluid–structure interaction with thin elastic structures

Abstract

A novel fluid–structure interaction (FSI) scheme is developed in this article, with the meshless finite volume particle method (FVPM) for fluid dynamics and the finite element (FE) solver FEBio for solid mechanics. Like smoothed particle hydrodynamics (SPH), FVPM is based on compactly supported particle kernels, but kernels are interpreted as a partitioning of volume, leading to a scheme with properties of both SPH and classical finite volume methods. Particle methods are advantageous for fluid modelling in FSI of highly deformable structures, as the particles can conform to the dynamic geometry of the fluid–structure interface. In FVPM, in particular, particles are rigorously truncated by boundaries, and the novel FSI scheme incorporates a sharp interface between the fluid and solid. A new method is described which avoids the possibility of unphysical communication between fluid particles separated by a thin structure. The method proposed here ensures that particles interact with the correct neighbour particles and boundaries, regardless of the particle overlap with the thin structure, allowing for particle size that can be chosen independently of structure thickness. The new method is validated for a hydrostatic water column on an elastic plate, a dam-break with elastic gate, a dam-break with a downstream elastic wall, and a 2-D model of a heart valve leaflet. In the latter two cases, the structure thickness is less than the particle diameter by a factor of up to 16. The results agree well with experimental data from the literature for fluid velocity field and solid deformation. Where quantitative data is available, the numerical results converge with decreasing particle size.