A Moving Mesh Method for Fluid-Solid-Acoustic Interactions in MEMS Devices

In multi-physical investigations, modeling moving objects at the micro-scale often requires the inclusion of mesh movement and viscous losses due to boundary layers. State-of-the-art approaches use, for example, the full set of flow equations. However, these equations are more computationally expensive due to their non-linearity. Here, we present a formulation for efficiently modeling visco-acoustic propagation problems on moving domains combined with fluid-solid-acoustic interaction. Therefore, we apply the Arbitrary-Lagrangian-Eulerian (ALE) framework to the fully linearized flow equations for a Newtonian fluid. Neglecting the non-linearity means that no sub-iterations during the solving process are necessary compared to the full set of flow equations. For the mesh deformation, we utilize a quasi-static mechanical field which is iteratively coupled to the flow equations in a strong sense. Furthermore, we use non-conforming interfaces to couple the acoustic and flow fields directly. The formulation presented is verified through convergence studies, proving second-order convergence using Taylor-Hood elements. Finally, the formulation is applied to model a Micro-Electro-Mechanical-System (MEMS) loudspeaker unit cell useable for ultrasound-based pumping principles like Advanced Digital Sound Reconstruction (ADSR). In summary, this formulation can efficiently model acoustic propagation problems of moving objects at the micro-scale.