*3.4. Moving Mesh*

The adaptive lens working mechanism relies on the transfer of piezoelectric forces to the flexible membrane through the fluid forces. In COMSOL Multiphysics-R , the coupling of the piezoelectric effect and the fluid-structure interaction is not possible through a direct Multiphysics feature. Hence, the moving mesh physics module is used to couple the piezoelectric forces with the fluid forces and apply the resultant on the flexible membrane. The explicit coupling of piezoelectric and laminar flow physics is performed in a way such that the solid domain velocities Equations (8) and (9) generated by the deformation of the piezoelectric actuator are applied as the mesh velocities on the walls of the fluid chamber as shown in Figure 4c. The geometric domains with the free deformation mesh and with the fixed mesh are as shown in Figure 4a,b, respectively.

$$V\_I = solid \cdot u\_\text{\\_tR} \tag{8}$$

$$V\_z = \text{solid} \cdot \text{u\\_tZ} \tag{9}$$

Equations (8) and (9) equate the solid velocities *u*\_*tR* and *u*\_*tZ*, which are produced by the piezoelectric actuator in radial axis (R) and deformation axis (Z), to the corresponding mesh velocities *Vr* and *Vz*. The mesh velocities applied to the fluid chamber wall are implicitly considered to be the external forces in the Navier–Stokes Equation (5) of the fluid-structure interaction physics module Equation (4). In this way, the moving mesh module explicitly couples the piezoelectric actuator force to the fluid force.

**Figure 4.** The domains specified in the Moving Mesh module to be (**a**) free mesh and (**b**) fixed mesh. (**c**) The solid domain velocity applied on the walls of the fluid chamber.
