A non-conforming finite element formulation for modeling compressible viscous fluid and flexible solid interaction

In modeling fluid–solid interaction (FSI), considering the impact of fluid compressibility is necessary to describe sound propagation. Furthermore, in micro-scale, fluid viscosity is important. We present a finite element formulation for modeling a flexible solid coupled to a compressible viscous fluid. We use the linearized Navier–Stokes equations for a Newtonian fluid and describe the linear elastic solid using the linearized balance of momentum. For coupling between fluid and solid, we develop a non-conforming finite element formulation, and propose an estimation for the necessary penalty factor by applying a scaling approach. The formulation is validated based on several test cases for various material combinations and shows good agreement with analytical solutions. Further, Nitsche-based and symmetrization-free formulations are compared, and spatial convergence is studied. Finally, we present an application example of a miniature Helmholtz resonator, which depicts a notable impact of the solid interaction on the viscous flow. In sum, our study indicates the potential for widespread use of the presented numerical approach in modeling FSI in miniature systems.