A Stabilized Arbitrary Lagrangian-eulerian Sliding Interface Method for Fluid-structure Interaction with a Rotating Rigid Structure

We introduce a novel sliding interface formulation for fluid-structure interaction (FSI) between a rotating rigid structure and incompressible fluid, improving existing methodologies with a skew-symmetric Nitsche’s stabilization term applied on an artificial sliding interface alongside a rotational arbitrary Lagrangian-Eulerian framework. This innovative approach not only preserves the energy-dissipating property at the continuous level but also provides a robust foundation for further advancements in FSI modeling. Our methodology includes a first-order full discretization that maintains these critical energy-dissipating properties at the discrete level, ensuring numerical stability and accuracy. While prior contributions such as the original sliding interface method introduced by Bazilevs and Hughes (Comput. Mech., 43(1):143-150, 2008) have been significant, theoretical analyses such as the inf-sup condition on nonmatching meshes have gone largely unaddressed. We fill this gap by proving the inf-sup condition within the context of the isoparametric finite element method (FEM), where meshes are not only nonmatching but also overlapping, thus extending the applicability and robustness of our approach. Leveraging this inf-sup condition along with the inherent energy-dissipating properties, we establish the unique solvability of the fully discrete scheme. Through extensive numerical experiments, we illustrate the convergence, efficiency, and energy-dissipating property of the proposed method.