Mesh-free distributed point source method for modeling viscous fluid motion between disks vibrating at ultrasonic frequency

The distributed point source method (DPSM) is extended to model wave propagation in viscous fluids. Appropriate estimation on attenuation and boundary layer formation due to fluid viscosity is necessary for the ultrasonic devices used for acoustic streaming or ultrasonic levitation. The equations for DPSM modeling in viscous fluids are derived in this paper by decomposing the linearized viscous fluid equations into two components - dilatational and rotational components. By considering complex P- and S-wave numbers, the acoustic fields in viscous fluids can be calculated following similar calculation steps that are used for wave propagation modeling in solids. From the calculations reported the precision of DPSM is found comparable to that of the finite element method (FEM) for a fundamental ultrasonic field problem. The particle velocity parallel to the two bounding surfaces of the viscous fluid layer between two rigid plates (one in motion and one stationary) is calculated. The finite element results agree well with the DPSM results that were generated faster than the transient FEM results.