Study of stabilized mixed formulations for fluid-structure interaction problems within a variational multiscale framework

This work applies and compares mixed formulations for both fluid and solid domains in Fluid-Structure Interaction (FSI) problems to the standard irreducible formulations. The study focuses on a nonlinear setting involving laminar incompressible Newtonian fluids and hyperelastic solids, with the fluid described using an arbitrary Lagrangian-Eulerian framework and the solid modeled within a total Lagrangian framework. Stabilization is achieved through the use of the variational multiscale method, which allows for arbitrary interpolations of the unknowns. The results demonstrate that mixed formulations not only enhance stability and accuracy but also address key numerical challenges in FSI problems. These formulations effectively mitigate volumetric locking in nearly or fully incompressible materials and shear locking in bending-dominated scenarios, ensuring robust performance across a wide range of conditions. Additionally, they provide significantly improved precision in stress computations, which is particularly valuable in FSI problems where traction conditions at the interface must be accurately satisfied. While mixed formulations introduce additional degrees of freedom per node, they achieve comparable accuracy to standard irreducible formulations even with coarser meshes, making them a highly competitive and efficient alternative for complex coupled simulations. The mixed formulations are tested through FSI numerical results for semi-stationary and fully transient cases, highlighting their potential for robust and efficient FSI simulations.