Variational coupling of non-matching discretizations across finitely deforming fluid-structure interfaces

Area of Science:

• Computational Mechanics
• Fluid-Structure Interaction (FSI)
• Numerical Methods

Background:

• Accurate simulation of fluid-structure interaction is crucial in many engineering applications.
• Coupling incompressible viscous fluids with finitely deforming elastic solids presents significant numerical challenges, especially across non-matching interfacial meshes.
• Existing methods often struggle with stability and accuracy at the fluid-solid interface.

Purpose of the Study:

• To present a stabilized monolithic method for coupling incompressible viscous fluids with finitely deforming elastic solids.
• To develop a robust numerical framework that handles non-matching interfacial meshes effectively.
• To introduce a systematic procedure for deriving interface stabilization terms.

Main Methods:

• The proposed Variational Multiscale Discontinuous Galerkin (VMDG) method combines Discontinuous Galerkin (DG) ideas within the Variational Multiscale (VMS) framework.
• Governing equations are formulated in appropriate frames (Lagrangian for solid, Arbitrary Lagrangian-Eulerian for fluid) to manage large interface motions.
• Interface coupling terms are derived by locally resolving fine-scale variational equations and analytically determining the traction Lagrange multiplier.

Main Results:

• A novel interface stabilization tensor is systematically derived, emerging naturally from the VMDG formulation.
• The stabilization tensor exhibits area-averaging and stress-averaging properties and evolves with the interface's nonlinear fields.
• Numerical verification using benchmark problems confirms the method's accuracy and stability for finitely deforming fluid-structure interfaces.

Conclusions:

• The VMDG method provides a stable and accurate approach for monolithic fluid-structure interaction simulations.
• The derived interface stabilization tensor effectively addresses challenges associated with non-matching meshes and large deformations.
• The method demonstrates robust performance for complex fluid-structure interaction scenarios.