A computationally efficient finite element model with perfectly matched layers applied to scattering from axially symmetric objects

A frequency-domain finite-element (FE) technique for computing the radiation and scattering from axially symmetric fluid-loaded structures subject to a nonsymmetric forcing field is presented. The Bérenger perfectly matched layer (PML), applied directly at the fluid-structure interface, makes it possible to emulate the Sommerfeld radiation condition using FE meshes of minimal size. For those cases where the acoustic field is computed over a band of frequencies, the meshing process is simplified by the use of a wavelength-dependent rescaling of the PML coordinates. Quantitative geometry discretization guidelines are obtained from a priori estimates of small-scale structural wavelengths, which dominate the acoustic field at low to mid frequencies. One particularly useful feature of the PML is that it can be applied across the interface between different fluids. This makes it possible to use the present tool to solve problems where the radiating or scattering objects are located inside a layered fluid medium. The proposed technique is verified by comparison with analytical solutions and with validated numerical models. The solutions presented show close agreement for a set of test problems ranging from scattering to underwater propagation.