Numerical modeling of acoustic visco-thermal losses: simplified implementations and their limitations

Several numerical adaptations have been proposed to account for viscous and thermal losses of acoustic waves. This is a physical effect that is mostly relevant in a region very close to boundaries, the so-called boundary layers, in the micrometer range. It is therefore relevant when modeling small
devices such as acoustic transducers and acoustic metamaterials. An often used modeling technique collapses the viscous and thermal losses into a boundary layer impedance (BLI), which is used in a calculation where the regular wave equation with no losses is discretized. However, this method has two shortcomings: i) the boundary layers may not overlap, and ii) it assumes flat surfaces. The BLI can be used either with the Finite Element Method (FEM) or the Boundary Element Method (BEM). BEM and FEM implementations with visco-thermal losses having no such restrictions also exist, at the cost of a heavier computational burden. This contribution discusses the shortcomings and advantages of the simulations using BLI as compared with full implementations and points to possible ways to overcome them. The BEM is employed to illustrate the analysis.