Mesh-free distributed point source method for modeling guided wave propagation in a viscous fluid layer trapped between two solid plates

Abstract

Distributed Point Source Method (DPSM) is extended to model wave propagation in viscous fluids. Appropriate estimation on attenuation and boundary layer due to fluid viscosity is necessary for the ultrasonic devices that utilize acoustic streaming or ultrasonic levitation. Since the boundary layer is often much thinner than the wavelength, numerical simulations based on the finite element method suffer from large computational cost because very fine mesh is needed to trace the layer. DPSM can efficiently model this problem. The computational cost for modeling the viscous fluid with DPSM is reduced close to the cost of non-viscous fluid analysis. In this paper, equations for DPSM modeling in viscous fluids are derived by decomposing the linearized viscous fluid equations into two components - dilatational and rotational. By considering complex P-wave and S-wave numbers, the sound fields in viscous fluids can be calculated using the same calculation routines used for waves in solids. To verify the calculation precision, a comparison between approximated theory and DPSM generated results for a fundamental ultrasonic field problem is performed. The particle velocity profile parallel to the surface in a viscous fluid between two vibrating plates is calculated. Theoretical results agree well with the DPSM generated results.