Three-Field Fluid-Structure Interaction by Means of the Variational Multiscale Method

TL;DR

This paper introduces a three-field variational multiscale formulation for fluid-structure interaction that enhances stability and accuracy, allowing coarser meshes and demonstrating competitive performance against standard methods in 2D and 3D benchmarks.

Contribution

It develops a novel three-field VMS-based FSI formulation with improved stability and efficiency, applicable to nonlinear fluid and solid interactions.

Findings

The three-field formulation is more stable than traditional two-field models.

It achieves comparable accuracy with coarser meshes.

Numerical benchmarks confirm its effectiveness in 2D and 3D scenarios.

Abstract

Three-field Fluid-Structure Interaction (FSI) formulations for fluid and solid are applied and compared to the standard two field-one field formulation for fluid and solid, respectively. Both formulations are applied in a non linear setting for a Newtonian fluid and a neo-Hookean solid in an updated Lagrangian form, both approximated using finite elements and stabilized by means of the Variational Multiscale (VMS) Method to permit the use of arbitrary interpolations. It is shown that this type of coupling leads to a more stable solution. Even though the new formulation poses the necessity of additional degrees of freedom, it is possible to achieve the same degree of accuracy as standard FSI by means of coarser meshes, thus making the method competitive. We enhance the stability of the formulation by assuming that the sub-grid scales of the model evolve through time. Benchmarking of the formulation is carried out. Numerical results are presented for semi-stationary and a fully transient cases for well known benchmarks for 2D and 3D scenarios.