Non-conforming interface formulations for coupling viscous compressible fluids and elastic solids

Abstract

Many studies have focused on the interaction between fluids and solids, ranging from non-compressible to compressible, inviscid to viscous fluids, with conforming and non-conforming interfaces. In many applications, such as microelectromechanical systems (MEMS), considering the interaction between fluid and solid is essential to simulate their behavior accurately. We model the fluid, e.g., usually air, as viscous and compressible flow by considering small acoustic perturbations in the linearized conservation equations for both mass and momentum. Similarly, the balance of momentum for the solid is linear when assuming small strains and linear elastic material behavior. This paper describes two non-conforming finite elements (FE) formulations for modeling the interaction between viscous acoustic and solid domains; a Nitsche-based and a Mortar FE formulations. In the Nitsche-based FE formulation, the continuity of velocity is enforced by a penalty factor selected by a scaling approach which makes the formulation dimensionally consistent. Alternatively, the Mortar formulation introduces a Lagrange multiplier (LM) to enforce the interface conditions. We present a performance comparison between these two formulations for a 2D wave propagation case study.