Benchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems

TL;DR

This paper introduces a fully variational immersed finite element method for fluid-structure interaction that handles elastic solids with different densities and responses, validated through various benchmarks.

Contribution

It presents a novel fully variational immersed finite element formulation that does not rely on approximate delta functions and can model diverse elastic solids.

Findings

Validated against multiple benchmarks for fluid-structure interaction.

First to model elastic compressible solids with incompressible fluids using an immersed method.

Demonstrates the method's accuracy and flexibility in complex FSI scenarios.

Abstract

We present an implementation of a fully variational formulation of an immersed method 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.