Mathematics

We present an implementation of a fully variational formulation of an
immersed methods for fluid-structure interaction problems based on the finite
element method. While typical implementation of immersed methods are
characterized by the use of approximate Dirac delta distributions, fully
variational formulations of the method do not require the use of said
distributions. In our implementation the immersed solid is general in the sense
that it is not required to have the same mass density and the same viscous
response as the surrounding fluid. We assume that the immersed solid can be
either viscoelastic of differential type or hyperelastic. Here we focus on the
validation of the method via various benchmarks for fluid-structure interaction
numerical schemes. This is the first time that the interaction of purely
elastic compressible solids and an incompressible fluid is approached via an
immersed method allowing a direct comparison with established benchmarks.